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Talk:Congruence (geometry)

A handy mnemonic
An easy way to remember that SSA (Side-Side-Angle) does not prove congruence for triangles is to simply reverse the order of the letters. --Jediknil

all of it is so wrong Unsigned comment added by 86.1.74.239 at 17:34 on January 21st, 2013

I mean Angle-Side-Side (No I will not say the acronym) is technically a legitimate name for SSA — Preceding unsigned comment added by Elitematterman (talk • contribs) 13:53, 17 April 2019 (UTC)

Equality
"In less formal language, two sets are congruent if they have the same shape and size, but are in different positions (for instance one may be rotated, flipped, or simply moved)."

Should we specify two different sets? Every set is congruent to itself.--Syd Henderson 01:16, 22 September 2006 (UTC)

The dilation edit is a recent edit, a week or so ago. I removed the bad link and if a dilation page is created, we can put in a valid link. JackOL31 (talk) 22:20, 7 December 2009 (UTC)

 * Yes, that seems a sound policy. Do you think we need an article on dilation, or is it adequately covered elsewhere?    D b f i r s   23:10, 9 December 2009 (UTC)

 * I just found out there is a good link to dilation on the similarity page. I see no reason to have one here. Not really applicable to congruence in my opinion. JackOL31 (talk) 05:33, 10 December 2009 (UTC)

 * Ah, so we do have an article! I'm happy to leave congruence as it is without a link.  Clearly congruence is a special case of similarity by the definition given for dilation.    D b f i r s   08:38, 10 December 2009 (UTC)

Determining congruence
Dbfirs, I see you undid and edit for AAS. I presume your position is that AAS stands on its own and needs no further explanation. However, I don't see how the addl explanation negatively affects the article. In the US, AAS is typically taught by first noting the two corresponding angle congruencies (Given), the third angle must be congruent (No-Choice Thm), followed by the congruent corresponding sides (Given), thereby showing the triangles are congruent (ASA). Perhaps presented as additional information rather than justification is a good compromise. JackOL31 (talk) 02:39, 13 November 2009 (UTC)

 * Yes, ASA is not taught in the UK (except as a special case of AAS). We could add a comment to that effect if you wish.    D b f i r s   10:56, 13 November 2009 (UTC)

 * Please bear in mind that what is or is not taught in the UK shouldn't necessarily come into play. Whether the information is accurate (or at least perceived accurate) and whether it is relevant to the article is the concern. Yes, I believe adding the ASA connection would be appropriate. You've seen the Anon editor's words and my words, what did you have in mind? JackOL31 (talk) 22:08, 14 November 2009 (UTC)

 * I'll go ahead and make the change after the holidays. JackOL31 (talk) 00:40, 18 November 2009 (UTC)

 * My proposed addition to the AAS postulate. Additionally, if two pairs of angles of two triangles are equal in measurement, then the remaining pair of angles are also equal in measurement (all angle measurements in a triangle sum to 180). With all three pairs of angles equal in measurement, ASA now applies. JackOL31 (talk) 18:05, 21 November 2009 (UTC)

 * Would it not also be logical to say that ASA is a special case of AAS? I consider that it reduces the clarity of AAS to add a "proof" in terms of a special case.    D b f i r s   18:56, 23 November 2009 (UTC)

By convention, the acronym AAS means that the side is never an included side. Likewise, SSA means the angle is never an included angle. This is supported by the descriptions given in the section. We make this distiction to highlight the difference between the two cases of AAS (6 combinations) and ASA (3 combinations). Without loss of generality, the same for SSA (6 combinations) and SAS (3 combinations). Therefore, I would say it is not logical to say that ASA is a special case of AAS. Note: this is my last post until after the Thanksgiving holidays. JackOL31 (talk) 02:31, 24 November 2009 (UTC)

 * Ah! I see. In the UK "AA(corr)S" includes both AAS and ASA.  I assume that they are separate in the USA because ASA is taught as a separate theorem.  Do you teach AAS in the USA?  I hope you are having a happy Thanksgiving (something else that we don't have in the UK).    D b f i r s   09:31, 26 November 2009 (UTC)

 * Hmmm, I have always seen the acronyms portrayed as indicating relative positioning. That is, one starts at the first triangle component and moves in a consistent direction to the next adjacent component. Therefore, AAS (and its mirror SAA) results in the first and last components being opposite. Accordingly, the same holds true for SSA and its mirror (assume "and its mirror" from now on). Given the different treatments for SSA and SAS in the article, I would make the same distinction for AAS and ASA. I can't speak for all US school districts and/or math teachers, but I believe the general approach is to introduce the SSS, SAS and ASA postulates. Then reintroduce the idea that having two angles for a triangle means we have the third angle. Therefore, given two triangles with two pairs of corresponding congruent angles, the remaining pair of corresponding angles are also congruent (No-Choice Theorem). Now, if we are given that a pair of corresponding sides are also congruent, we can apply the ASA postulate and state that AAS also determines congruency. Subsequently, I guess one could now note that two pairs of congruent angles and any pair of corresponding congruent sides (which I will abbreviate as A-A-S) indicates congruency between two triangles. In other words, I would hold (IMHO) that the A-A-S grouping is more of an artificial grouping rather than a postulate in and of itself. I don't see AAS as a special case of A-A-S since both AAS and ASA are "special cases" and require independent checking. They just happen to render the same congruency results allowing for the artificial grouping. For S-S-A, we know this not to be the case since SSA and SAS do not render the same congruency results. To answer your question directly, I have never seen A-A-S stated as some type of postulate (eh, before now). Anyway, that's my take on it. Re: Thanksgiving Day holidays - I did have a good time, thank you. I visited my son at the university he is attending - 3,470 km away. JackOL31 (talk) 00:47, 2 December 2009 (UTC)

 * I can see the logic and rigour of the US approach. AA(corr)S was taught just as a sufficient condition for congruence in the UK, without considering order, and without dividing it into a theorem/postulate and a corollary.  Perhaps we should keep the US approach with just a note on the UK sufficient condition, since most students who are looking for the formal approach will be from the USA.  There is no university in the UK that could be even half that distance from any residence! At least your travel costs are much lower than they are here!    D b f i r s   13:55, 4 December 2009 (UTC)

I've seen "Two Angles and One Side" forming only one triangle as a prelude to the Law of Sines, but never in reference to triangle congruency. I do agree that since ASA and AAS cover all the bases (for two angles and one side), it is reasonable to mention the sufficiency condition. I think we want to avoid any confusion between AA(corr)S and AAS. Personally, I wouldn't abbreviate it but rather spell it out the long way - two angles and one side. What do you think of this parenthetical at the end of the AAS paragraph with a link to the Similarity page - (AAS condition ==> AA similarity ==> AAA similarity ==> ASA congruency.)? I'm not thrilled with it, but I can't seem to come up with anything better. JackOL31 (talk) 16:08, 5 December 2009 (UTC)

 * It was taught as AA (corr)S two angles and a corresponding side) in the UK (in fact I'd never seen ASA and AAS until I read Wikipedia), but I'll do a bit of research to see how widespread and current this mnemonic is now. Since Euclidean geometry is not a major part of the modern curriculum in the UK, it seems sensible to retain the American mnemonics in the Wikipedia articles.  Perhaps we could add just a note at the end, rather than confuse the list of mnemonics known in the USA.  I'm happy with your parenthetical, though I wonder if AAS should be relegated to a note, or is AAS taught as a separate condition in the USA?    D b f i r s   17:11, 5 December 2009 (UTC)

 * Now I don't feel so bad about trapeziums and rhomboids. I can say that my kids learned AAS as a separate topic, however they used the same textbook. I recall learning it as SAA, but not the details of where in relation to the other topics. Based the original editor's input that started this discussion, that person appears to have learned AAS after ASA. I think it's fine to leave it there. JackOL31 (talk) 19:14, 5 December 2009 (UTC)

SSA
Should we include a diagram showing how SSA doesn't work? Just a suggestion. Altopian asa sas sss are congruence theorem but ass aaa saa aas are not

Just so you know, and it's already in the article saa and aas do show congruence at least in Euclidean geometry. In this case, the third angles in each triangle must be congruent because each of them must be equal to 180 degrees less the two congruent angles. The two triangles are then congruent by angle-side-angle. 19:29, 30 April 2009 (UTC) —Preceding unsigned comment added by 84.102.218.220 (talk)

"SSA recent addition" - I changed the labelling to that used in the Triangle and Trigonometry articles. To wit A, B, and C are angles and a, b, and c are the sides opposite those angles, respectively. Also, the 4th condition should be A ≤ B for b < 90 degrees. The fifth condition should read A < B where angle b is obtuse or right. The 6th condition does not make sense and I am not sure what is being said. Note: I believe this content is not appropriate for this section but decided not to delete it without discussion. I tried to maintain, as best I could, the same spirit that the original information presented but with the necessary corrections. I will state my concerns regarding this content in a future post. JackOL31 (talk) 03:05, 2 December 2009 (UTC)

 * I have some concerns regarding the Side-Side-Angle section. First, the opening sentence should end with, "... does not prove two triangles are congruent." Why? The terminology SSA and its cousins always imply corresponding components. Additionally, once the ambiguous case has been shown, then SSA can never prove congruency. Bear in mind that we know nothing other than Angle A is congruent to Angle A', Side b is congruent to Side b', and Side a is congruent to Side a'. SSA can make no other claims since the lengths of the congruent sides nor the measure of the congruent angles are known. Regarding the 6 newly added SSA points, they do not really pertain to triangle congruency, but whether a given set of two sides and one non-included angle results in 0, 1, or 2 triangles. It is better suited for the Trig page under "Law of sines". If we want to mention an aside where SSA is used in conjunction with known measurements, we should only refer to the 4 cases where triangles are possibles since we are using SSA to compare actual triangles. The six numbered statements also repeat some of what is said in the paragraphs. My recommendation, remove the six "lines" and organize the 4 short paragraphs to cover the conditions for congruency based on additional information (5 short paragraphs when you add back in the HL postulate). JackOL31 (talk) 04:13, 2 December 2009 (UTC)

Oops - forgot to login for the "SSA implies corresponding sides & angles, stmt not necessary" edit. We always assume corresponding parts, therefore to say SSA means that we haven't swapped the sides around between the two triangles. JackOL31 (talk) 03:27, 2 December 2009 (UTC)

 * I have composed a rough draft for the replacement of the SSA content. Open for comments:

 * The SSA condition (Side-Side-Angle) which specifies two sides and a non-included angle (also known as ASS, or Angle-Side-Side) does not prove congruence. In order to show congruence, additional information such as the measure of the corresponding angle and in some cases the lengths of the two corresponding sides are required. There are four possible cases:

 * If two triangles satisfy the SSA condition and the corresponding angles are either obtuse or right, then the two triangles are congruent. In this situation, the length of the side opposite the angle will be greater than the length of the adjacent side. Where the angle is a right angle, also known as the Hypotenuse-Leg (HL) condition or the Right-angle-Hypotenuse-Side (RHL) condition, the third side can be calculated using the Pythagorean Theorem thus allowing the SSS postulate to be applied.

 * If two triangles satisfy the SSA condition and the corresponding angles are acute and length of the side opposite the angle is greater than or equal to the length of the adjacent side, then the two triangles are congruent.

 * If two triangles satisfy the SSA condition and the corresponding angles are acute and length of the side opposite the angle is equal to the length of the adjacent side multiplied by the sine of the angle, then the two triangles are congruent.

 * If two triangles satisfy the SSA condition and the corresponding angles are acute and length of the side opposite the angle is greater than the length of the adjacent side multiplied by the sine of the angle (but less than the length of the adjacent side), then the two triangles cannot be shown to be congruent. This is the ambiguous case and two different triangles can be formed from the given information.

 * UPDATED JackOL31 (talk) 16:22, 5 December 2009 (UTC)

 * Yes, definitely an improvement! (I've tried myself, and given up on my attempt to make it simple, but I think your draft makes it as clear as the situation permits.)  If no-one else objects, I suggest you go ahead and make the change.  In your last sentence, it would be sufficient to know that both triangles are acute (or obtuse-angled), so only this fact about the measure would be required, but this is a very minor point.    D b f i r s   12:42, 4 December 2009 (UTC)

 * Perhaps more detail (diagrams of the six cases and an explanation of "b sin A") in the trig article with a link to said article is what is needed. Sadly, I'm not nearly clever enough to draw those graphics. You were correct in your last point - I was suffering from tunnel vision, so I edited that sentence out in my draft. However, I believe the larger issue is that any additional information takes us out of the realm of SSA, be it a pair of corresponding measures, corresponding congruencies (side), or the triangle angle-classifications. Therefore, nothing more should be said. Yes, no, maybe? JackOL31 (talk) 16:45, 5 December 2009 (UTC)

 * I'd support just a link to a more detailed explanation (though ambiguous case isn't quite what we want), or perhaps just put your text in a footnote. I'm not skilled in creating computer graphics either, though I've done that sort of thing on an interactive whiteboard.  Would it be adequate to draw just an example of two non-congruent triangles satisfying the SSA condition?    D b f i r s   17:43, 5 December 2009 (UTC)

I think that link is great. Yes, it is not a 100% fit, but close enough. I would say the 4 paragraphs including the "ambiguous case" link should do it. If I really had my druthers, I'd just cite the ambiguous case and be done. However, I think that would upset some. JackOL31 (talk) 19:20, 5 December 2009 (UTC)

Politically charged statement
I don't think that the word "infamous" belongs in the phrase "the infamous SMSG system". Having both learned my geometry from SMSG and taught geometry, I wish that book would come back. The textbooks currently available attempt to be rigorous but are sorely lacking. In fact, the last time I taught geometry, I tracked down a copy and taught from photcopies.

Congruent angles?
I have altered two occurrences of congruent to equal. In cautious standard usage, angles are never congruent, nor are sides. They are equal, and their being equal is a necessary condition for a pair of figures to be congruent. See major British and American dictionaries: SOED, and Webster's Third International ("2 geometry : superposable so as to be coincident throughout"). See Congruence (geometry).

I see that there is an external link mentioning "congruent" angles; I have left that as it is, but its usage should not affect the accuracy of Wikipedia's own text.

–  Noetica ♬♩ Talk 20:46, 10 December 2007 (UTC)

 * Yes, Euclidean geometry must call angles equal (following Euclid) because their representations in diagrams are often demonstrably not congruent. Similarly, it is clearer to describe line segments as equal in length, reserving congruent to describe shapes in two or more dimensions where the word has special meaning.   D b f i r s   11:28, 13 February 2009 (UTC)

 * Since the version with "equal" has been accepted without objection for more than 12 months, and (Greek:"isos", "equal") is the usage of Euclid, I am reverting the recent change back to congruent by anon editor 71.202.147.182 who, to be fair, has a rational argument based on an interpretation of "equal" to mean identical in position as well as size. To avoid misunderstanding, I shall use "equal in length" for sides so that there is no ambiguity for those who have been taught this meaning of "equal".    D b f i r s   07:33, 14 February 2009 (UTC)
 * Of course, in some rigorous modern usage the term congruent is indeed applied to line segments and angles, and all sorts of things. If these are to count as "figures" (not yet adequately defined anywhere at Wikipedia), then congruence can apply to them. Essential definitional questions concerning angles need to be addressed before we speak of "congruent angles" in our articles. It is no simple matter! Arguments raged even in ancient times about the ontology of angles, and we can't simply assume that there is a single modern orthodoxy on the matter.
 * We can have such discussion here, if we want to; or perhaps at Talk:Angle, where there is already something about figures.
 * – ⊥ ¡ɐɔıʇǝo N oetica! T– 21:01, 16 February 2009 (UTC)

The term congruent angles is already in use for a large population without meaning a congruent figure. I don't see any reason to not keep up with what is in use. I'm not suggesting universal agreement on what is an angle and a congruent angle, but simply stating both definitions. Therefore, citing the definition from the Cambridge University Press website (thesaurus.maths.org) we have: an angle is a measure of turn. This supports the following definition from Schaum's Outlines: Geometry, 3rd Ed., copyright 2000 (originally copyrighted 1963) which states, "Congruent angles are angles that have the same number of degrees. In other words, if m<A = m<B, then <A is congruent to <B." [Note: m<A means measure of angle A] Of course, this definition can also be found in numerous texts and on numerous websites. I would like to include this definition of congruent angles on this page and I am seeking input. JackOL31 (talk) 21:11, 3 November 2009 (UTC)
 * The CUP definition also supports "equal angles are angles that have the same number of degrees", so may we go back to just using "equal", like Euclid did, and as is the standard language in the UK?   D b f i r s   23:37, 4 November 2009 (UTC)
 * Citing the article, Teaching Geometry according to Euclid, authored by Robin Hartshorne, professor of mathematics at the University of California at Berkeley, he writes: "In Euclid’s Elements there is an undefined concept of equality (what we call congruence) for line segments, which could be tested by placing one segment on the other to see whether they coincide exactly. In this way the equality or inequality of line segments is perceived directly from the geometry without the assistance of real numbers to measure their lengths. Similarly, angles form a kind of magnitude that can be compared directly as to equality or inequality without any numerical measure of size."

 * From a Dr. Math webpage: "Euclid used the word "equal" of two figures that had the same AREA. (He had no word for "congruent"!) We no longer use "equal" as he did, but we do reserve it generally for equal numbers (such as areas or lengths), and use the "new" word "congruent" to specifically say that the figures themselves are "the same" in a carefully defined sense."

 * It seems to me that transporting Euclid's "equal" from yesterday's world to today's world necessitates its proper translation to the term "congruent". Also, I believe you stated that you would use "equal in measure" for numeric quantites since all would understand that terminology. In addition, wouldn't both the UK and US (and others) understand the geometrical meaning of "congruent" for non-numeric quantities. Mixing in Euclid's nonstandard (pre-congruent) use of "equal" confuses the articles and generates all the contoversy on these discussion pages. JackOL31 (talk) 05:26, 5 November 2009 (UTC)

 * On the contrary, I believe that it would be wrong to introduce the non-standard "congruent", unnecessarily for sides, and very confusingly for angles, when, as your Dr Math webpage says, we still use "equal" for lengths. I agree fully with the necessity of defining "congruent" for shapes in two or more dimensions where the concept is necessary to distinguish from Euclid's equality of areas etc.  I agree 100% with Robin Hartshorne that "equality" doesn't need a numerical value, just as equality of transfinite numbers doesn't need a count.  He seems happy to use "equal" in the sense that Euclid used it, which I would claim is the normal everyday sense.  The CUP definition of angle makes this usage perfectly acceptable and rigorous.    D b f i r s   11:44, 5 November 2009 (UTC)

 * I believe you have possibly misread it. I'm fairly certain the meaning was more like this [I added bracketed info]: "In Euclid’s Elements there is an undefined concept of equality (what we call congruence) for line segments, which could be tested by placing one segment on the other to see whether they coincide exactly. In this way the equality or inequality [again, what we now call congruence or noncongruence] of line segments is perceived directly from the geometry without the assistance of real numbers to measure their lengths. Similarly, angles form a kind of magnitude that can be compared directly as to equality or inequality [once more, what we now call congruence or noncongruence] without any numerical measure of size." Dr. Hartshorne, well respected in this field, is quite clearly saying that "Euclid's equal" is synomymous with what we now call "congruence".

 * Dr. Math was also quite clear: "Euclid used the word "equal" ... (He had no word for "congruent"!) We no longer use 'equal' as he did...use the "new" word 'congruent'... ."

 * I don't agree with your assessment of "...non-standard "congruent", unnecessarily for sides, and very confusingly for angles...". If one goes to the CPCTC wiki page you'll see that CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent. The article then lists the 6 congruencies, 3 for the triangle's sides and 3 for the triangle's angles. I can say that every US kid learns about CPCTC. The concept of congruency applies equally to line segments, angles, triangles, etc.

 * Equal for lengths is correct. If two line segments are congruent, then their lengths (measures) are equal.

 * Again, what Dr. Hartshorne was explaining is how Euclid called figures that coincided as equal without using numerical measures, but we now call them congruent.

 * If you read it over again, I believe you'll see that the phrase, "In this way...", in the second sentence refers back to the first sentence and Euclid's equality is still what we call congruence. The third sentence is just another example using angles instead of line segments. In that light, we cannot use the word equal as Euclid did because it is now known as congruence and would be confused with the current usage of equal. JackOL31 (talk) 03:25, 6 November 2009 (UTC)

 * I think you are reading much more into the text than was originally there. UK students would find your US usage very confusing, and I don't see why it is necessary to dispense with the universally understood word equal. We seem to be "divided by a common language". I have no objection to the CPCTC page since it is unlikely to be read by anyone who has not been taught what it means.    D b f i r s   09:43, 6 November 2009 (UTC)

 * No, I believe I'm reading it correctly. Dr. Hartshorne is explaining how Euclid used the concept of equality and he indicated that it is, in the modern world, referred to as congruence. I guess I don't see how UK students will be confused by equal in measure. However, regarding the use of "equal", you will find instances of inconsistency in the US. For example, "...sides are equal" or "...angles are equal" when they should read "...sides are equal in length" or "...angles are equal in measure". Yes, it is technically not correct but the intended meaning is as I just mentioned. I don't believe the meaning in those cases is "Euclid's equal", which I would consider to be "congruent". My intent is to consistently approach it in this manner and I understand that you may have a different approach. JackOL31 (talk) 17:04, 7 November 2009 (UTC)

 * As mentioned earlier, I would like to include another popular definition for "congruent angles". (See the Interactive animations demonstrating Congruent angles at the bottom of the article) Note: I will replace the bolding with the appropriate section heading coding when finalized. Since there appears to be disagreement regarding the "accurate definition" for congruent angles and concern for Wikipedia's text on the matter, I'll post my proposed changes. Any comments?

 * Alternate definition for Congruent Angles

 * Congruent angles are angles having the same measure. The length of the sides of an angle are not considered since the term "angle" refers to the angular magnitude and not to the angular figure. To illustrate this concept, corresponding angles for similar polygons are congruent while corresponding sides are not.

JackOL31 (talk) 19:02, 7 November 2009 (UTC)

 * I'll work on this new section in a couple of weeks after the holidays. I'm thinking of possibly adding examples of how certain definitions or postulates elsewhere in Wiki would look written using the way many interpret angles in polygons. For example: ASA If two angles and the included side of one triangle are congruent to the corresponding parts of another, then the triangles are congruent. However, not those exact words since they are from Schaum's Outline of Geometry, 3rd Ed 1999 (First Ed 1963). JackOL31 (talk) 01:04, 18 November 2009 (UTC)

 * I would regard this as "an alternative meaning of the word congruent" (as is the usage in modular arithmetic). I don't think "congruent" meaning "of equal measure" is the same as the usage in Congruence (geometry) unless you restrict the meaning of "angle" to the set of points between infinite intersecting rays.    D b f i r s   12:50, 4 December 2009 (UTC)

 * I wouldn't say it is an alternative usage of the word congruent as in congruent numbers (modulus) and congruent transformation (congruent matrices). It is within the usage of Congruence (geometry) using the definition for an angle given by the Cambridge University Press (thesaurus.maths.org) - an angle is a measure of turn. I don't agree that this article should maintain the notion that Congruence (geometry) only applies to figures.

 * Math on Call: A Mathematics Handbook (1998) - When two angles have the same angle measure, we say they are congruent. Figures that have the same size and shape are congruent. Sides are congruent if they have the same length. Angles are congruent if they have the same number of degrees.

 * Geometry for Enjoyment and Challenge (1991) - Definition: Congruent angles are angles that have the same measure. Definition: Polygons are congruent if and only if all pairs of corresponding parts are congruent.

 * Schaum's Geometry (2000 Third Ed, {since 1968}) - Congruent angles are angles that have the same number of degrees. In other words, if m∠A = m∠B, then ∠A ≅ ∠B. Congruent figures are figures that have the same size and the same shape; they are exact duplicates of each other.

 * www.mathopenref.com - Two line segments are congruent if they have the same length. Two circles are congruent if they have the same size. Congruent polygons have an equal number of sides, and all the corresponding sides and angles are congruent. Angles are congruent if they have the same angle measure in degrees. To be congruent the only requirement is that the angle measure be the same, the length of the two arms making up the angle is irrelevant.

 * mathwords.com - Congruent angles have the exact same measure. For any set of congruent geometric figures, corresponding sides, angles, faces, etc. are congruent.

 * math.com - Two angles that have the same measure are called congruent angles. Two polygons are congruent if they are the same size and shape - that is, if their corresponding angles and sides are equal.

 * mathsisfun.com - Congruent Angles have the same angle in degrees. That's all. They don't have to point in the same direction. They don't have to be on similar sized lines. If one shape can become another using turns, flips and/or slides, then the two shapes are called Congruent. After any of those transformations (turn, flip or slide), the shape still has the same size, area, angles and line lengths.

 * Plus many, many more... JackOL31 (talk) 15:29, 5 December 2009 (UTC)

 * Your examples clearly show that many modern American texts use the word "congruent" where all British texts use the word "equal". I still cannot accept that this usage is identical to the meaning given in Congruence (geometry) except in the specific case where angle is defined by reference to two infinite intersecting rays.  The CUP definition of angle clearly supports the use of "equal".    D b f i r s   18:07, 5 December 2009 (UTC)

 * Yes, it is not identical to the definition of congruence for figures given on the Congruence (geometry) page, but it is an alternative definition for congruence of an angle for the Congruence (geometry) page. The definition currently presented on this page is not the definition of congruence for all of geometry, which can be clearly seen by my previous post (it is actually an advanced mathematical definition not used at the elementary or high school level). I would state on prima facie evidence (my previously cited geometry references), that this is an alternative definition of conguence used in geometry and, ... well, you know where this is heading. Also, if you accept the CUP definition for angles which does not take into consideration the length of the sides when determining angle equality, then there is a nonnumeric counterpart that does not take into consideration the length of the sides when determining angle congruence. JackOL31 (talk) 22:03, 6 December 2009 (UTC)

 * Since is is not an example of Conguence (geometry), I would say that it doesn't belong on this page, but perhaps it deserves a page of its own since it is clearly widespread in the USA.   D b f i r s   07:50, 7 December 2009 (UTC)

Actually, I would think it is an example of Congruence (geometry). "Congruent angles" is most assuredly a topic is geometry and it is also a topic of Congruency within geometry. It need not match the given definition because the given definition does not represent all definitions for geometrical congruency. Alternate definitions wouldn't typically trigger a separate page, especially when the topic is the same. I only intend a small section describing the alt defn and indicating how many would replace the phrase "equal in measure" given for angles with the word "congruent". Having it on a different page would defeat the purpose of trying to make this page less US unfriendly. Also, it needs to be on the same page since it is widespread around the world. I don't believe it is prudent to have math concepts divided onto different pages due to cultural differences. JackOL31 (talk) 22:12, 7 December 2009 (UTC)

 * It certainly does not match Wikipedia's definition of Congruence (geometry), and I would have thought that most mathematicians (other than educators in the USA) would not recognise this usage. It would be useful to have some input from other parts of the world to see whether my guess is correct.  My aim is not to make the page US unfriendly, but just to make it more friendly to the rest of the world.    D b f i r s   23:03, 9 December 2009 (UTC)

 * Well, I thought I had explained this in my previous two posts, but perhaps not clearly enough. Yes, the alternative definition or usage is not the same as what is given at the beginning of this article. No one is disputing the correctness of that definition. I believe you are confusing the topic with the definition. For example, imagine the title of the article as "Isosceles Triangles". One topic, two definitions. This is an article on congruence in geometry, period. Does the alternate definition for 'congruent angles" replace what is already given? No. It is in addition to and admittedly less rigorous than the first definition. However, when we talk about angles, 99 44/100% of the time we are referring to the amount of turn with no interest in the length of an angle's two sides. One needs to go no further than the ASA, SAA and SSA diagrams or the usage of "equal in measure" for angles to observe this. Following the "measure of turn" definition for angles, when two angles are superpositioned and line up with the same amount of opening, they are congruent. This is a usage in which the term "congruent angles" is employed. As such, If there are alternate definitions for [you name it] in circulation, then those definitions should all be present on the [you name it] page. If there are alternate definitions for [you name it], those definitions need to be present. I believe I have adequately shown there is an alternate definition in circulation, therefore it needs be present on the Congruence (geometry) page. JackOL31 (talk) 05:12, 10 December 2009 (UTC)

 * I still think that you are confusing Hilbert's congruence of sets of points between infinite intersecting rays with an imprecise use of "congruence" to mean "equal in measure", but if this is what is taught in US schools, then I suppose that we ought to record the fact, just as we ought to record the fact that most people outside the USA (and many within) would just say "equal".   D b f i r s   08:50, 10 December 2009 (UTC)

 * Think as you may, but I am not confusing anything with anything else. Bear in mind that the use of "equal in measure" is an imprecise usage. "Equal in measure" implies that we have numerical values for the angle measures, those values have been compared against each other and have been found to be equal. This is obviously not the case and I would never suggest that implication when it is wholly unnecessary. Of course, shortening it to "equal" just compounds the situation. Simply because you tout your impreciseness over mine doesn't make yours better. I would venture to say the alternate usage for "congruent angles" is used world-wide, including the UK. CPCTC (Corresponding Parts of Congruent Triangles are Congruent) clearly indicates that the corresponding parts are congruent and those itemized parts are the three separate sides and the three separate angles (where only the amount of rotation is of interest). Regarding your last claim, what one says in a casual conversation with a common understanding is different from what one writes in an informative article. Also, I have no issue with you recording your fact, as long as it meets the criteria for verifiability. JackOL31 (talk) 19:17, 12 December 2009 (UTC)

 * It is not necessary to measure two angles to show that they are equal in measure (or just equal in the UK, or congruent in the US), one needs only to show that the arms partially coincide when they are superimposed. You are assuming that American school texts are used throughout the English-speaking world.  This is certainly not so in the UK. CPCTC is almost unknown here.    D b f i r s   23:38, 12 December 2009 (UTC)

 * From where I sit, it is necessary. The superpositioning shows congruence, measures not required. Measures involve numbers and arithmetic with those numbers (degrees or radians). I don't assume US texts are used throughout the English-speaking world. At least, no more than you assume that "equal in measure" or just "equal" is used throughout the English-speaking world. JackOL31 (talk) 00:47, 13 December 2009 (UTC)

 * From where I sit, superpositioning often shows lack of congruence unless one defines angle as the set of points bordered by two infinite rays. We just use the words differently.  I think your US text books use "equal in measure" don't they?  And, yes, I was surprised to learn that equal does not mean the same in the USA.   D b f i r s   01:03, 13 December 2009 (UTC)

Equality refers to arithmetical or algebraic quantitative magnitude. Measurement of the numerical magnitude of angles or lines can result in equalities. Geometric shapes, however, cannot be equal. Geometric shapes can have similarities or congruences, which are qualitative forms. No geometrical forms or figures can be equal. They can only be similar. In Topology, which developed from geometry, there are no equations. There are only similarities in the form of Homeomorphisms. As in geometry, the qualitative analysis of forms and shapes is accomplished by determining congruences or sameness, not equality, which is a quantitative measurement. Lestrade (talk) 03:31, 13 December 2009 (UTC)Lestrade

 * I agree that geometric shapes should not be described as "equal" (except in the sense of "equal in area"), and that the words "similar" and "congruent" are appropriate for geometric shapes where an isometry exists (with and without a dilation). The problem with angles is that congruence only makes sense when an angle is defined as a set of points bounded by infinite rays.  Angles of the same measure, considered as figures, are often only partially superpositionable.  If angle is defined as a measure of turn, then equality is clearly possible.  The Wikipedia article on angle allows all three definitions.    D b f i r s   16:38, 13 December 2009 (UTC)

Quantitative measurement of angles and sides can have equalities, not congruences, because they measure magnitude. Qualitative geometrical and topological shapes cannot have equalities. They can have congruences, similarities, or homeomorphisms. There are no equations in geometry or topology. Newton's quasi–geometrical Principia did not contain a single equation.Lestrade (talk) 16:44, 13 December 2009 (UTC)Lestrade

 * Yes, fair comment. Our article on angle claims that Euclid regarded an angle as a relationship.    D b f i r s   16:59, 13 December 2009 (UTC)

 * The contribution I have is what I have said before. Elementary and HS textbooks show the definition of congruent angles as equal in measure and the reference to angles is simply the amount of rotation. First, that description is needed on the angle page. Then, the alternate definition of congruent angles can be added here. I don't envision anything but a short section. Unless you are disputing all the references I've cited, I don't see the issue. This is an encyclopedia, not a graduate textbook on the theory of geometry. Am I missing something here? JackOL31 (talk) 20:24, 13 December 2009 (UTC)

 * No, you have clearly shown that some US textbooks use the word "congruent" when they mean "equal in measure", so you are right to record this fact on the page. There seems to be a long-standing dispute amongst mathematicians and philosophers about exactly what an angle is, and at least some of the alternative views are given on the angle page.  However much I, personally, disagree with your usage, if it is common in text books on your side of the pond, then a record of the fact belongs here.   D b f i r s   18:19, 14 December 2009 (UTC)

R.H.S?
From my Mathematics textbook, R.H.S. (Right angle, hypoteneuse, side) can also determine congruent triangle. Am I right?--Sap00acm (talk) 09:20, 26 November 2008 (UTC)

 * That's correct. This is described in the third paragraph of the "Angle-Side-Side" section. -- Jitse Niesen (talk) 10:28, 26 November 2008 (UTC)

I have taught Geometry for 13 years in Louisiana. Multiple textbooks including Dr. Ron Larson reference this as HL(Hypotenuse-Leg) NOT RHS — Preceding unsigned comment added by 208.67.117.129 (talk) 19:24, 17 October 2014 (UTC)

Essence
I deleted the statement that the study of invariant properties is the essence of geometry. Geometry can be studied without being concerned with unchanging properties. Therefore, the study of invariant properties is not the essence of geometry.Lestrade (talk) 18:34, 15 April 2009 (UTC)Lestrade

Distance is invariant

 * Note that congruences alter some properties, such as location and orientation, but leave others unchanged, like distance and angles.

Distance is variant. Presumably it means length. Unless I am mistaken. —Preceding unsigned comment added by George Makepeace (talk • contribs) 13:08, 5 November 2010 (UTC)

Inconsistency in the definition
The article begins by stating that two objects are congruent if either object can be repositioned so as to coincide precisely with the other object. Then it adds that this is equivalent to an an isometry, i.e., a combination of translations, rotations and reflections. This is not the same thing, you cannot reposition in space a right hand glove in order to coincide with a left hand one, a reflection is needed. Csoliverez, February 10, 2012, 21:02 UTC. — Preceding unsigned comment added by Csoliverez (talk • contribs) 21:03, 10 February 2012 (UTC)

 * It's not inconsistent. In geometry, repositioning two objects so that they coincide means repositioning by means of a rigid transformation (isometry), which includes reflections.--fwchapman (talk) 02:31, 8 October 2013 (UTC)

AAA (Angle-Angle-Angle) in spherical and hyperbolic geometry
I have issues with the following sentence: "However, in spherical geometry and hyperbolic geometry (where the sum of the angles of a triangle varies with size) AAA is sufficient for congruence on a given curvature of surface." I'm no expert, but I see 2 problems. First, AAA would prove similarity, but not congruence. Second, I think the sum of the angles of a triangle varies, not with size, but in some other way. I'm not sure what it is. But here's an easy example. On a spherical model of Earth, draw 2 triangles. Each triangle has a vertex at a pole, say 30 degrees; also each has 2 right angles. Sides: 2 sides of each triangle are on longitudes, 1 is on a latitude. Whatever the latitude is, AAA applies; the triangles are similar, the sum of angles is the same (210 degrees), but the sizes (areas, side lengths) vary. Thus, the quoted sentence isn't correct as it stands. Would someone who knows spherical and hyperbolic geometry please fix this part of the article? Oaklandguy (talk) 06:19, 17 May 2012 (UTC)

 * The statement that AAA proves congruence in spherical geometry is correct. In spherical geometry, all similar triangles on spheres of the same radius are actually congruent. Your counterexample doesn't work because the lines in spherical geometry are great circles (circles whose centers coincide with the center of the sphere). That means the only latitude that can be the side of a triangle is the equator. The two sides from a pole to the equator both have length one quarter of the circumference of the sphere. The triangles in your example are congruent by SAS, which is valid in spherical geometry.--fwchapman (talk) 02:26, 8 October 2013 (UTC)

Spherical triangles
I have moved this material here from Spherical trigonometry without attempting to integrate it correctly. Further edits may help. Peter Mercator (talk) 13:53, 28 July 2013 (UTC)

Congruent triangles on a sphere
I think the given example of a family of spherical triangles with side lengths of π, π/2, and π/2 actually results in degenerate triangles. The two sides through the point p on the equator actually lie on the same great circle. Thus, each triangle in the family actually has only two non-collinear sides, which is a degenerate triangle. We need three non-collinear sides to create a non-degenerate triangle. Is this correct? If so, can anyone suggest how to remedy this? --fwchapman (talk) 20:48, 7 October 2013 (UTC)

Actually, it's worse than I thought. According to http://www.math.uga.edu/~clint/2008/geomF08/spherical.htm, SSS congruence is true in spherical geometry, which means the given example is not a counterexample at all.--fwchapman (talk) 21:25, 7 October 2013 (UTC)

Moreover, a two-sided polygon in spherical geometry is called a lune. It is not a triangle.--fwchapman (talk) 21:30, 7 October 2013 (UTC)

Here is another source that claims the SSS congruence criterion is valid in spherical geometry: http://math.iit.edu/~mccomic/420/notes/Bolin_spherical.pdf. Apparently SSS, SAS, and ASA are all valid in spherical geometry, but AAS is not.

'''We need to remove the SSS "counterexample" from this section (it's wrong) and add that SSS and SAS are valid congruence criteria, along with ASA (already mentioned). We should also state that AAS fails as a congruence criterion in spherical geometry.'''--fwchapman (talk) 02:15, 8 October 2013 (UTC)

 * Thanks. Done. Duoduoduo (talk) 15:34, 11 November 2013 (UTC)

Some comments, suggestions, images
Hiya! While I think the section on congruence of triangles in the plane is extremely important, I think perhaps we might first focus on congruence of figures in the plane in general.

I think we should add that an isometry is a combination of rigid motions. The actual article on isometry jumps right into metric spaces.

... by an isometry, i.e., a combination of rigid motions, namely translations, rotations and reflections.

BTW: I don't see the need for plurals in this last, but it doesn't matter.

I think we should add (here is a reference ], although probably the given definition of congruence suffices):
 * two line segments are congruent if they are the same length.
 * two angles are congruent if they are have the same measure (regardless of direction).
 * two circles are congruent if they have the same diameter.
 * two plane figures are congruent if their corresponding sides are congruent, their corresponding interior angles are congruent, their corresponding diagonals are congruent, their perimeters are equal and their areas are equal.

BTW: I wasn't exactly sure how to word this last statement, but being mathematically absolutely correct down to the last detail defeats the purpose ...

I think we should add (something like):
 * two distinct plane figures are congruent if we can cut them out of paper and then match them up completely. Turning the paper over is permitted.

I think we should add a section: Checking congruence of plane figures
 * First, match and label the corresponding vertices of the two figures.
 * Second, draw a vector from one of the vertices of the one of the figures to the corresponding vertex of the other figure. Translate the first figure by this vector so that these two vertices match.
 * Third, rotate the translated figure about the matched vertex until one pair of corresponding sides matches.
 * Fourth, reflect the rotated figure about this matched side until the figures match.

If at anytime the step cannot be completed, the figures are not congruent.

I might add the images at right. Please feel free to improve the text below them. I have a no-callout gif uploaded for multi-language translation of the animated gif; the 2nd image is a png - anybody can feel free to make an svg (I balked at the grid). The colors seem to be good for standard colorblindness.

Thanks for reading. I would appreciate any comments to these suggestions.

Lfahlberg (talk) 14:56, 16 October 2013 (UTC)

 * Since no one has commented, I plan to make these changes.

Lfahlberg (talk) 09:13, 25 October 2013 (UTC)

 * My only reservation would be the concept of congruent angles. Angles of equal measure are congruent in a Hilbertian sense as long as we delimit the angles using infinite rays, but representations of angles of equal measure need not be congruent in the normal sense that you explain so clearly.  This doesn't matter in the USA where everyone is taught Hilbertian angles, but could cause confusion in the UK where angles of equal measure are normally just called "equal", not congruent.    D b f i r s   21:26, 25 October 2013 (UTC)

 * Hiya all. We discussed "congruent angles" with Dbfirs and agreed on the format in the changed article. BTW: I changes the svg at the top to be 4 triangles as I was concerned that a reader might get the false impression that the 4th figure was not congruent just because it was not a triangle. I desperately want to credit MADe (the original author of the old svg: https://en.wikipedia.org/wiki/File:Congruentie.svg) on this svg, but every time I tried to upload my svg to wiki commons with the credit it would not accept it so I finally gave up. If anyone knows how to add the credit to my image file, please do (or tell me how). Thanks. Lfahlberg (talk) 18:41, 27 October 2013 (UTC)

Semi-protected edit request on 20 June 2014
In the section "Determining congruence of polygons", the sentence beginning " Third, ..." contains the phrase " corresponding sides". Please link this to corresponding sides.

208.50.124.65 (talk) 18:30, 20 June 2014 (UTC)
 * Yes check.svg Done with thanks, Nici  Vampire  Heart  19:08, 20 June 2014 (UTC)

Semi-protected edit request on 17 October 2014
Multiple high school Geometry textbooks (Dr. Ron Larson's textbook)used in the USA refer to RHS as HLItalic text (Hypotenuse-Leg). consider including this as this could avoid confusing high school students seeking homework help via Wikipedia.

Sincerely, High School Teacher (13 years)

208.67.117.129 (talk) 19:29, 17 October 2014 (UTC)
 * Yes check.svg Done Stickee (talk) 06:23, 19 October 2014 (UTC)

External links modified
Hello fellow Wikipedians,

I have just added archive links to 1 one external link on Congruence (geometry). Please take a moment to review my edit. If necessary, add after the link to keep me from modifying it. Alternatively, you can add to keep me off the page altogether. I made the following changes:
 * Added archive https://web.archive.org/20131111162553/http://146.163.152.131/teaching/projects/creech_final.pdf to http://146.163.152.131/teaching/projects/creech_final.pdf

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Cheers. —cyberbot II  Talk to my owner :Online 02:26, 28 August 2015 (UTC)

Semi-protected edit request on 7 December 2016
97.93.99.144 (talk) 23:18, 7 December 2016 (UTC)Hi
 * Red information icon with gradient background.svg Not done: No request made. -- Dane  talk  04:30, 8 December 2016 (UTC)

Im no expert but...
"In the School Mathematics Study Group system SAS is taken as one (#15) of 22 postulates." in Determining Congruence Seems out of place considering its placed in ASA instead of SAS. I can make the change myself but I want someone to either confirm or put my suspicions to rest NikkeKatski [Elite] (talk) 16:16, 17 April 2019 (UTC)
 * I can see why you think this is out of place, but the solution to that problem is not as simple as moving it to a different heading. The entire discussion of which of these are treated as theorems and which as postulates needs to be pulled out from the ASA section and handled after all the acronyms have been defined. I will try to do this soon. --Bill Cherowitzo (talk) 18:25, 18 April 2019 (UTC)
 * Thank you c: --NikkeKatski [Elite] (talk) 17:41, 19 April 2019 (UTC)

title: Talk:Congruence (geometry)


text:
Talk:List of University of Maryland, College Park alumni

On Blair: imo, he needs to be somewhere. His wiki page lists him as a "disgraced reporter" so I've continued the trend. On Clark: Moved him from the notable others page with Howard's help.--Rbeas 16:24, 21 August 2005 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
QRB

QRB may refer to:
 * Qualitätssicherungssystem Recycling Baustoffe
 * The Quarterly Review of Biology
 * Queenstown Road railway station has National Rail code QRB
 * QRB is Q code for "What is your distance?"
 * Qué Rica Bieja

title: QRB


text:
Jagannath Temple (disambiguation)

The Jagannath Temple is a temple dedicated to the Hindu god Jagannath in Puri, Odisha, India.

Jagannath Temple may also refer to:

India

 * Jagannath Temple, Ahmedabad, Gujarat
 * Jagannath Temple, Alwar, Rajasthan
 * Jagannath Temple, Bangalore, Karnataka
 * Jagannath Temple, Baripada, Mayurbhanj, Odisha
 * Jagannath Temple, Chennai, Tamil Nadu
 * Jagannath Temple, Dibrugarh, Assam
 * Jagannath Temple, Kanyakumari, Tamil Nadu
 * Jagannath Temple, Delhi
 * Jagannath Temple, Dharakote, Odisha
 * Jagannath Temple, Digha, West Bengal
 * Jagannath Temple, Gunupur, Odisha
 * Jagannath Temple, Hyderabad
 * Jagannath Temple, Koraput, Odisha
 * Jagannath Temple, Mohanpur, West Bengal
 * Jagannath Temple, Nayagarh, Odisha
 * Jagannath Temple, Puri, Odisha
 * Jagannath Temple, Ranchi, Jharkhand
 * Jagannath Temple, Rayagada, Odisha
 * Jagannath Temple, Thalassery, Kerala
 * Chhatia Bata, Jajpur, Odisha
 * Jagannath Temple, Surada, Odisha

Elsewhere

 * Shri Jagannath Puri Temple, Inanda, KwaZulu-Natal, South Africa
 * Comilla Jagannath Temple, Comilla, Bangladesh
 * Jagannath Temple, Pabna, Bangladesh
 * Jagannath Temple, Sialkot, Pakistan

title: Jagannath Temple (disambiguation)


text:
Talk:Borden, Kent

Untitled
Very sweeping statements here! In particular: Peter Shearan 16:20, 21 August 2005 (UTC)
 * surely "village" is better than "community"?
 * the impression in the village itself (ie the original village) is that it is very compact: OK there are outlying settlements such as Hearts Delight, but that applies to most villages
 * Sittingbourne, to which it is almost joined, hardly gets a mention
 * have all the orchards been "scrubbed" (shouldn't that be "grubbed up" anyway?): in many parts of Kent they have been replaced with easier to manage lower trees; and the land must be used for something, surely?
 * and is it really true that "most people commute"?

Lady Robergia
Could this information from Terry Mason be applied to add some citations to the source of the town's name? Evan Borden 12:46, 5 October 2011 (UTC)
 * Lady Roberga de Bourdon http://tmason1.com/pafn180.htm#2876
 * Simon de Bourdon http://tmason1.com/pafn180.htm#2875

 * In a word, "NO".
 * The reference to "Lady Robergia" is from Cook, 1905,

https://archive.org/details/robergiastoryofo01cook

 * which is a work of early 20th century fiction. Cook's introduction makes it clear that the story he tells was something he made up for the benefit of his grandchildren.  His appendices include some useful factual information, but nothing of genealogical significance.  One shouldn't have to read the introduction to realize this is a work of fiction.  The main line of the story involves the appearance of the Ghostly Apparition of Lady Robergia, in the local church at midnight, who reveals the location of a hidden manuscript telling her story.  That alone should tell you that this is a work of fiction.  As to the genealogy, there's as much value with what's in Cooke 1905 as there is in the genealogy of Lord Graystroke provided by Edgar Rice Burroughs in his Tarzan series. Both lineages seem credulous, but are in fact works of fiction.

 * A healthy portion of Cook's work provides solid information based on original parish records, and from wills filed with the Commissary Court of Canterbury. This "good stuff" is from the end of his book, in an appendix. The main part of the book is a fiction---literally.  It was never intended to be taken as historically, or genealogically true, but only as an entertainment. See the Preface, p. x, where he makes it clear that the lineage is "only" traced to c 1370, and one Henry Borden, well after the death of Robergia the heroine of his story, and roughly 200 years after the Norman Conquest. Almost everything preceding her was made up for purposes of the story he was telling.  This, by the way, is not a criticism of Cook.  His purpose was to entertain.  His collection of genealogical records in the appendix seems good, and where I've attempted to verify them, I can find the same wills in other sources well predating his work.  There are some discrepancies between his abstracts, and those I find in other sources, but by and large these sources are consistent with each other.  None of them (at least those that I've looked at) carry the line back further than Henry b c1370.  We can find persons by this name at earlier dates, living in either Cranbrook or Headcorn, and even in Borden.  Weld also references other Bordens (using the de Bourdon variant spelling of the name), dating to the mid 1200's (I've not been able to verify them so far.)  But even she does not trace their line down to Henry---just points out that they existed.

 * Irrespective of the above, the idea that the Bordens were in origin companions of William the Conqueror who fought at Hastings, is probably not well founded. This idea was introduced by Weld 1899, who traced the modern descendancy of Richard Borden of Headcorn in Kent,forward to the late 1800's.  She makes a complicated argument for the family originating in Bourdonay, France, and settling in Borden parish after the Conquest.  She points to the use of "bourdons" (pilgrims staff) as heraldic emblems in the Coat of Arms of Bourdonnay, and in the COA's of some lines of Bordens---Here she assumes that this must mean that the Borden family originated in Bourdonnay.  Perhaps so, though she provided no real proof of this, just a simple conjecture based on the common use of the bourdon in heraldic emblems. More critically, she overlooked the fact that Bourdonnay is in the Moselle District of France, and quite some distance from Normandy. Cook 1905 seems to have noticed this discrepancy, and attempted to rectify it by placing the family origin in Bayeux which does lie in Normandy.  What ever was gained by this change in location of the homeland of the Bordens is largely lost because a) there is no evidence that they came from Bayeux, and b) whatever was gained by Weld in pointing to the use of the bourdon in the arms of Bourdonnay, is lost when the origin is transferred to Bayeux, whose shield lacks those bourdon's.

TwelveGreat (talk) 23:12, 19 December 2017 (UTC)

Name Meaning
According to the current text the source of the parish name...
 * is more likely to stem from Sir Francis de Bourdon...who descended from the de Bourdons of Bayeux, in Normandy, France. Francis de Bourdon became Lord of the existing castle and surrounding lands previously Lorded over by the Saxon Ethelwolf of Kent, who perished at Hastings, by William the Conqueror as a gift to his vassal after the great Norman victory in 1066 and at which time became known as Bourdon

This is based on Cook 1905's work "Robergia:A story of Old England", cited in the sources. While Cook provides extracts of various wills for the Borden family, those wills date to the 14th century and later and are confined to an appendix at the back of the main work. He presents no supporting evidence for Francis de Bourdon, his wife Robergia, etc. As far as I can tell, while many use this work to show that the Borden family came to England from Bayeux, Normandy, during the Norman Conquest no evidence is presented by Cook to support this, nor has anyone else that I can tell.

The main text of Cook 1905 simply a work of fiction. I do not believe he ever intended for it to be anything other than this. It is worth pointing out that neither the Domesday Book of 1088, nor its ecclesiastical equivalent, the Domesday Monachorum, mention the parish of Borden, or anyone using that surname or variations thereof. If the Borden family did in fact descend from one of William the Conquerors supporters, you'd expect to see something about either them, or their supposed place of residence in one or another of the two Domesday records.

As to the actual source of the Parish name, the terminal ending of the name "-den" suggests that the name arose from the use of the area as a foraging ground for pigs, known either as dens, hursts or lays, depending on local dialectical preferences. That usage is well documented, and there are literally hundreds of place names in Kent ending in "-den", and an equal number ending in "-hursts. KentArchaeology.com has a nice map showing the distribution these names.  They are heaving concentrated in the Kentian Weald, but there are others throughout Kent, including some in the the parish of Borden.  Whatever the meaning of "Bor", the ending in "-den", seems near conclusive evidence that the name of the parish represents the presence of a denn in that area at an early date.  There are a few records for the presence people bearing the surname "de Bordon" there in the 13th century (Weld, 1899). This has probably been the spring board from which people have taken to the idea that the Borden family had a Norman connection.  More likely the name simply reflects usage of french during the Norman period in England, and its significance is only that the persons bearing the name "de Borden" (or variants there of) came from the parish of Borden. TwelveGreat (talk) 13:38, 29 November 2017 (UTC)

Iron Foundry
The text currently reads

→Borden also had a bell foundry and small ironmongers.

Were the ironmongers simply short, or were there a small number of them, or does "small ironmongers" mean something else---ie did they only make small iron objects?. I'd correct this but I don't know what the intent of the statement.TwelveGreat (talk) 22:15, 19 December 2017 (UTC)

title: Talk:Borden, Kent


text:
User:Shropshire Lad

Shropshire Lad is a writer living in the UK's most beautiful county. He's interested in history and heritage, the environment and outdoor world, and in politics and current affairs.

He is a prolific user of Wikipedia, and an occasional contributor. Grateful thanks go to those dedicated souls who tidy up my contributions.

title: User:Shropshire Lad


text:
Grimalkin

A grimalkin, also known as a greymalkin, is an archaic term for a cat. The term stems from "grey" (the colour) plus "malkin", an archaic term with several meanings (a low class woman, a weakling, a mop, or a name) derived from a hypocoristic form of the female name Maud. Scottish legend makes reference to the grimalkin as a faery cat that dwells in the highlands.

During the early modern period, the name grimalkin –and cats in general –became associated with the devil and witchcraft. Women tried as witches in the 16th, 17th and 18th centuries were often accused of having a familiar, frequently a grimalkin.

Uses in fiction
Beware the Cat was published in 1570 by William Baldwin. The novel is a story of talking cats, and part of it relates the story of the Grimalkin's death. According to the editors of a modern edition, the story, and thus the name, originates with Baldwin in terms of being the earliest example known in print. It is also spelled Grimmalkin or Grimolochin.

A cat named Grimalkin in William Shakespeare's 1606 play Macbeth helped the Three Witches look into Macbeth's future.

A grimalkin appears in chapter 18 of The House of the Seven Gables by Nathaniel Hawthorne. The narrator questions if it's a cat looking at a mouse or the devil looking for a soul, in this case that of Judge Pyncheon.

A grimalkin is also mentioned in Emily Brontë's Wuthering Heights, who briefly sits on a bench next to Mr. Lockwood before being removed hastily by Joseph.

The Anna Seward poem An Old Cat's Dying Solilioquy, published in The Gentleman's Magazine in 1792, contains the line "Before thou lay’st an aged grimalkin low".

A cat named Grimalkin appears in Shirley Jackson's short story "The Man in the Woods". It is soon ousted in a brief catfight by the new, unnamed black cat who has just arrived in the heels of the young protagonist Christopher. The new cat assumes the name of Grimalkin.

A grimalkin is mentioned in the Episode "The Joke's on Catwoman" (Episode 17 of Season 3) of the 1960's Batman TV Series.

Grimalkin is a character in The Dresden Files by Jim Butcher. A malk, cat-like faerie acting as a servant to Mab. She uses him as an interpreter, with Grimalkin speaking to other people in her stead while she remains silent. He first appears in Summer Knight.

Grimalkin is the most powerful witch assassin in the popular children's series, Spook's, by Joseph Delaney. She is depicted as a cruel torturer who uses a large pair of scissors to take the thumb bones of her enemies. Her main role is as a close ally and mentor of the main character, Thomas Ward.

A faery cat named Grimalkin appears in Julie Kagawa's book series The Iron Fey Series. He has similarities to the Cheshire cat from Alice in Wonderland

The Grimalkin are an anthropomorphic feline race in the Ni No Kuni franchise.

In Wicked (Maguire novel), the main character Elphaba has a pet cat named Grimalkin while staying in the Emerald City.

A cat named Grimalkin is a companion to Sham and Agba in Marguerite Henry's Newbery Medal children's novel King of the Wind.

A cat named Grimalkin is mentioned as a deceased former companion to Elaine in Anna Biller's 2016 film The Love Witch.

A cat identified as a "Grey Malkin" (as of an exotic cat breed) is the eponymous subject of the serial story The Riddle of the Gray Malkin, starting with Part 1 in Issue #1899 (August, 2021) of the Australian published edition of The Phantom comic series.

A cat familiar named “Grimalkin” is the watch cat of Dr. Julian Karswell in the 1957 film Curse of the Demon directed by Jacques Tourneur. It normally looked like a small housecat, but had the ability to transform into a large jaguar to attack intruders.

Grimalkin is the name of a mysterious black cat in the game Cat Cafe Manager.

In Bruva Alfabusa's "Hunter: The Parenting" webseries based on the World of Darkness setting, 'Grimaline' is the name of a side-character, which is a name derived from Grimalkin.

In Roger Zelazny's story A Night in the Lonesome October, a cat called Graymalk is the companion or familiar of a Witch known as Crazy Jill.

title: Grimalkin


text:
Susan Straight

Susan Straight (born October 19, 1960) is an American writer. She was a National Book Award finalist for the novel Highwire Moon in 2001.

Biography
Susan Straight attended John W. North High School in Riverside, California and took classes at Riverside Community College while in high school. She went on to earn a scholarship to the University of Southern California and, in 1984, earned her M.F.A. from the University of Massachusetts Amherst's MFA Program for Poets & Writers. She co-founded the Master of Fine Arts in Creative Writing & Writing for the Performing Arts program at University of California, Riverside, where she is currently a Distinguished Professor of Creative Writing and the director of the graduate program.

Straight has published eight novels, a novel for young readers and a children's book. She has also written essays and articles for numerous national publications, including The New York Times, Los Angeles Times, The Nation and Harper's Magazine, and is a frequent contributor to NPR and Salon. Her story "Mines", first published in Zoetrope: All-Story, was included in The Best American Short Stories 2003.

Personal life
Straight lives in Riverside, California. She has three daughters.

For younger readers

 * Bear E. Bear (1995)
 * The Friskative Dog (2007)

Nonfiction

 * In the Country of Women (2019)

Essays, reporting and other contributions

 * Race: An Anthology in the First Person (essay, "Letter to My Daughters") (1997)
 * Mothers Who Think: Tales of Real-Life Parenthood (essay, "One Drip at a Time") (1999)
 * When Race Becomes Real: Black and White Writers Confront Their Personal Histories (essay, "Country Music") (2002)
 * Life As We Know It: A Collection of Personal Essays from Salon.com (essay, "Love Me, Love My Guns") (2003)
 * Dog Is My Co-Pilot: Great Writers on the World's Oldest Friendship (essay, "Brave and Noble Is the Preschool Dog") (2003)
 * Some of My Best Friends: Writers on Interracial Friendships (essay, "Cartilage") (2004)
 * Little Women (afterword) (2004)
 * Because I Said So: 33 Mothers Write About Children, Sex, Men, Aging, Faith, Race, and Themselves  (essay, "The Belly Unbuttoned") (2005)
 * I Married My Mother-in-law And Other Tales of In-laws We Can't Live With - And Can't Live Without (essay, "A Family You Can't Divorce") (2006)
 * Inlandia: A Literary Journey Through California's Inland Empire (introduction) (2006)
 * Bad Girls: 26 Writers Misbehave (essay, "Reckless") (July 2007)
 * The Show I'll Never Forget: 50 Writers Relive Their Most Memorable Concertgoing Experience (essay, "The Funk Festival at Los Angeles Coliseum, Los Angeles, May 26, 1979") (2007)

title: Susan Straight


text:
CGIS

CGIS may refer to:

 * Canada Geographic Information System, a system designed to assist in regulatory procedures of land-use management and resource monitoring
 * Coast Guard Investigative Service, a division of the United States Coast Guard that investigates crimes where the Coast Guard has an interest

title: CGIS


text:
File:William Gamble USA.JPG

1860s photo

title: File:William Gamble USA.JPG


text:
Buttahatchee River

The Buttahatchee River is a tributary of the Tombigbee River, about 125 mi long, in northwestern Alabama and northeastern Mississippi in the United States. Via the Tombigbee River, it is part of the watershed of the Mobile River, which flows to the Gulf of Mexico.

Course
The Buttahatchee River rises in northwestern Winston County, Alabama, near the town of Delmar, and flows generally westward through Marion County, where it collects a short tributary, the West Branch Buttahatchee River. At Hamilton, the river turns to the southwest and flows through Lamar County, Alabama and Monroe County, Mississippi; its lower reach is used to define part of the boundary between Monroe and Lowndes counties. The Buttahatchee joins the Tombigbee near Columbus Air Force Base, 12 mi (19 km) north-northwest of Columbus.

Name
The name "Buttahatchee" is Choctaw for "sumac river", from bati, "sumac", and hahcha, "river".

The Board on Geographic Names settled on "Buttahatchee River" as the river's official name and spelling in 1947. According to the Geographic Names Information System, the Buttahatchee River has also been known as:

title: Buttahatchee River


text:
User:Liberlogos/Debates/Archives

This personal subpage is in the process of a clean-up.

 * Talk:Basque Country
 * Special:Contributions/A._Lafontaine
 * User talk:Thomas Aquinas
 * Talk:Québécois
 * Image:Acadia Flag.png
 * Talk:American
 * Talk:Quebec
 * Talk:René Lévesque
 * Talk:Pierre Falardeau
 * Talk:List of Quebec television series
 * Talk:National Question (Quebec)
 * Talk:Quebec general election, 2003
 * Talk:Denys Arcand
 * Talk:Le Mouton noir
 * Talk:Christian Democratic Union of Germany
 * Talk:List of Quebec comedians
 * User talk:Earl Andrew
 * User talk:Ground Zero
 * Talk:United Kingdom general election, 2005
 * Talk:Jack McConnell
 * Talk:Scottish National Party
 * Talk:Bloc Québécois
 * Talk:Bloc Québécois
 * Image talk:Canadapoliticalchart.png
 * User talk:Liberlogos -

title: User:Liberlogos/Debates/Archives


text:
1792 in art

Events from the year 1792 in art.

Events

 * Ozias Humphry is appointed Portrait Painter in Crayons (i.e., pastels) to King George III of Great Britain.
 * François-André Vincent becomes a professor at the Académie royale de peinture et de sculpture in Paris.
 * Nationalmuseum in Stockholm, Sweden, founded as the Kungliga Museet ("Royal Museum").

Works

 * Richard Cosway – Portrait miniature of George, Prince of Wales
 * Jacques-Louis David – Portrait of Madame Marie-Louise Trudaine
 * Samuel Jennings – Liberty Displaying the Arts and Sciences
 * Alexander Kucharsky – Louis-Charles, Prince Royal of France
 * George Stubbs
 * A Couple of Foxhounds
 * Rhinoceros
 * John Trumbull
 * Alexander Hamilton
 * General George Washington at Trenton
 * Utamaro – Famous Beauties of Edo, Ten Learned Studies of Women and Ten Types of Women's Physiognomies (print series begun)

Births

 * February 19 – Lucie Ingemann, née Mandix, Danish religious painter (died 1868)
 * February 24 – István Ferenczy, Hungarian sculptor (died 1856)
 * June 16 – John Linnell, English landscape painter (died 1882)
 * June 26 – Christian Albrecht Jensen, Danish painter (died 1870)
 * August 9
 * Alvan Fisher, United States landscape and genre painter (died 1863)
 * Charles-François Lebœuf, French sculptor (died 1865)
 * August 12 – Hans Harder, Danish painter and drawing master (died 1873)
 * August 30 – Alexis Joseph Depaulis, French sculptor and medallist (died 1867)
 * September 1 – Chester Harding, American portrait painter (died 1866)
 * October 31 – Jean-Baptiste Roman, French sculptor (died 1835)
 * December 17 – George Hayter, English portrait painter (died 1871)
 * December 20 – Nicolas Toussaint Charlet, French designer and painter, especially of military subjects (died 1845)
 * date unknown
 * Arnoldus Bloemers, Dutch painter of flowers, fruit, and animals (died 1844)
 * Peter Andreas Brandt, Norwegian painter and illustrator (died 1862)
 * Carl Georg Enslen, Austrian painter (died 1866)
 * Ferdinand Wolfgang Flachenecker, German painter (died 1847)
 * James Arthur O'Connor, Irish landscape painter (died 1841)
 * James Pollard, British painter and aquatint engraver especially of coach, fox hunting and equine scenes (died 1867)
 * Ulla Stenberg, Swedish damask maker (died 1858)
 * William Guy Wall, American painter of Irish birth (died 1864)
 * Thomas Wyon, English engraver of medals (died 1817)
 * 1792/1793: George Mills, British sculptor, engraver and medallist (died 1824)

Deaths

 * February 1 – Nicolas-Guy Brenet, French historical painter (born 1728)
 * February 21 – Jacob Schnebbelie, English illustrator and engraver (born 1760)
 * February 23 – Sir Joshua Reynolds, English painter, specializing in portraits (born 1723)
 * March 3 – Robert Adam, Scottish-born architect and interior designer (born 1728)
 * May 7 – Aert Schouman, Dutch painter, glass engraver and art dealer (born 1710)
 * December 4 – Antonio Ponz, Spanish painter (born 1725)
 * December 12 – William Hoare, English painter, noted for his pastels (born 1707)
 * December 17 – Gottlieb Welté, German etcher and landscape painter (born 1745/1749)
 * date unknown
 * Francesco Appiani, Italian painter of the late-Baroque period, active mainly in Rome and Perugia (born 1704)
 * Manuel de la Cruz, Spanish painter (born 1750)
 * Anna Maria Mengs, German portrait painter in pastel and miniature (born 1751)
 * Pietro Scalvini, Italian painter (born 1718)
 * Katsukawa Shunshō, Japanese painter and printmaker in the ukiyo-e style (born 1726)

title: 1792 in art


text:
Sugilite

Sugilite  is a relatively rare pink to purple cyclosilicate mineral with the complex chemical formula KNa2(Fe, Mn, Al)2Li3Si12O30. Sugilite crystallizes in the hexagonal system with prismatic crystals. The crystals are rarely found and the form is usually massive. It has a Mohs hardness of 5.5–6.5 and a specific gravity of 2.75–2.80. It is mostly translucent. Sugilite was first described in 1944 by the Japanese petrologist Ken-ichi Sugi (1901–1948) for an occurrence on Iwagi Islet, Japan, where it is found in an aegirine syenite intrusive stock. It is found in a similar environment at Mont Saint-Hilaire, Quebec, Canada. In the Wessels mine in Northern Cape Province of South Africa, sugilite is mined from a strata-bound manganese deposit. It is also reported from Liguria and Tuscany, Italy; New South Wales, Australia and Madhya Pradesh, India.

Sugilite is commonly pronounced with a soft "g", as in "ginger". However, as with most minerals, its pronunciation is intended to be the same as the person it is named after; in this case, the Japanese name Sugi has a hard "g", as in "geese".

The mineral is also referred to as lavulite, luvulite, and royal azel by gem and mineral collectors.

In Japan, sugilite is found as yellowish-white to colourless, and is not good for jewellery.

title: Sugilite


text: User:SoM/Comicswikiportal

title: User:SoM/Comicswikiportal


text:
Talk:Sugilite

Sugilite/Temp created pending resolution of copyvio. Feel free to edit the temp page. Vsmith 16:29, 21 August 2005 (UTC)

title: Talk:Sugilite


text: User:SoM/Comicswikiportal/box-header

title: User:SoM/Comicswikiportal/box-header


text: User:SoM/Comicswikiportal/box-footer

title: User:SoM/Comicswikiportal/box-footer


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GURPS Alternate Earths

GURPS Alternate Earths is a GURPS role-playing game supplement by Kenneth Hite, Craig Neumeier, and Michael S. Schiffer, which was published by Steve Jackson Games in 1996. It presents six versions of Earth with alternate histories to the real world, and background material for creating adventures for each of these worlds.

Contents
GURPS Alternate Earths presents six versions of Earth possessing alternate histories to that of our own world, as well as a number of less-detailed alternate settings scattered throughout the book in sidebars. Attention is given to the ways in which agents of the Infinity Patrol presented in GURPS Time Travel and their rivals from the mysterious parallel known as Centrum attempt to influence the course of history in each parallel. There is a sequel volume, GURPS Alternate Earths II, and the concept of the conflict between the Infinity Patrol and Centrum across the many parallel Earths was made central to the Fourth Edition of GURPS as the default setting in the Basic Set and in the supplement GURPS Infinite Worlds.

Dixie
Dixie posits an alternate history where the Southern filibuster William Walker, as President of Nicaragua, chose to protect Cornelius Vanderbilt's Accessory Transit Company rather than turn on his tycoon supporter. Without Vanderbilt's opposition to his regime in this timeline, Walker was able to conquer Cuba and make his Nicaragua the most powerful nation in Latin America. During the American Civil War, Walker's ships ran the Union blockade and ensured that Southern troops were well-supplied, leading to their victory over Northern forces and the independence of the Confederate States of America. In turn, the United States allied themselves with Germany and took most of Canada from the Confederacy's British supporters while the Confederates absorbed Mexico and most of Central America.

The "current year" in Dixie is 1985, with the world dominated by the U.S.A., the C.S.A., the moribund German Empire, the nascent Russian Republic, and the rapidly modernizing United Republic of India. Technology is somewhat more advanced than at the same date in our world, with personal hovercraft and supersonic transports commonplace, and the presence of nuclear-armed orbital weapons platforms and the juxtaposition of the progressive "Yankees" and the stratified "Southron" society adds to the tension caused by the "Long Drum Roll" (the U.S.A-C.S.A. analogue to the Cold War).

Reich-5
Reich-5 (so named because it was the fifth parallel world discovered by the Infinity Patrol in which Nazi Germany had won World War II) takes as its point of divergence from real history the successful assassination of president-elect Franklin D. Roosevelt by Giuseppe Zangara in 1933. While vice president-elect John Nance Garner attempted to implement Roosevelt's New Deal, he was unable to unify the country. U.S. politics seesawed back and forth between radical left- and right-wing administrations under Henry Wallace and Charles Lindbergh, with the country as a whole mired in isolationism and a continuing Great Depression, while Germany and Japan fought and won World War II, conquering the Allies without American involvement. In 1944, following Japanese attacks against American targets across the Pacific, including Pearl Harbor and the West Coast, Vice President William Dudley Pelley seized control of the nation after the assassination of Republican president Charles Lindbergh; the German invasion of Canada in the following year gave Pelley an excuse to arrogate to himself dictatorial powers. His theft of the 1948 election from Robert Taft (running on a combined Republican/Democratic ticket) prompted a Second American Civil War that was ended by a Nazi invasion of the United States and their development and use of the atomic bomb in 1950 against American cities.

The "current year" in Reich-5 is 1995. Greater Germany dominates Europe, Africa, and India, while the U.S.A. is little more than a puppet state of Nazi Germany, with a resistance movement only just recovering from a brutal defeat in the Uprising of '76. The Japanese Empire controls China, Southeastern Asia, Australia, New Zealand, Oceania, the Eastern Soviet Union, and the entire Pacific Rim.

Roma Aeterna
Roma Aeterna diverged from real history when Nero Claudius Drusus survived his German campaigns and founded a different Julio-Claudian dynasty than in our history. Their patronage of the Heronian Academy led to a more rapid development of industry, which produces in the Roma Aeterna setting a very different world in which the Third Roman Empire based in Hesperia (roughly corresponding to Mexico and Texas) rules much of North and South America, Northern Africa, Europe, the Middle East, and India. The only other significant political entities in the world are Serica (China) and its North American kingdom Fu-Sang (centered on San Francisco), Taehan (a growing empire based on the Korean Peninsula), and the isolationist South American kingdom of Huaraca. The "current year" in Roma Aeterna is 1878.

Shikaku-Mon
Shikaku-Mon ("four-cornered world" in the local version of Japanese, because of the four super-power nations that dominate it) is a setting proceeding from a point of divergence in the early 16th century - the survival of Juan of Aragon, son of Ferdinand II of Aragon and Isabella I of Castile, to ascend the throne of Spain as John III. Without the Spanish throne to inherit from John's sister Joanna of Castile, Holy Roman Emperor Charles V was unable to fight France, the Ottoman Empire, and the Protestants of Europe as he did in our history. Combined with the redirection of Sebastian of Portugal's attentions from Inquisition and Crusade to missionary activity in Asia, especially Japan, the changes to world history are innumerable.

The "current year" in Shikaku-Mon is 2015 (the same as "Homeline" Earth, setting for the "Infinity Patrol" reality, thus making it of particular interest to the IP). The Westernized and Christian Japanese Empire controls 40% of the globe but 65% of its inhabitants, most of whom are ethnically non-Japanese subjects held to be inferior peoples. The totalitarian "synarchist" Swedish Empire is similar to the Soviet Union; it controls much of the upper half of North America and exiles dissenters against the state to labor camps in the far north. The Empire of Brazil is a relatively progressive nation which dominates South America. The Kingdom of France is a scientifically and technologically advanced nation with a permanent settlement on the Moon. Shikaku-Mon can be said to partake of its own brand of cyberpunk themes.

Ezcalli
Ezcalli is dominated by the Tenochca (Aztec) Empire. In this world, Carthaginian explorers landed in South America in 580 B.C., two millennia before contact between the Old World and the New in our history. The early exchange of biota resulted in the decimation of the American peoples by Eurasian diseases, but the low technological disparity between the two continents at the time meant the newcomers could not take full advantage of this before new populations with resistance to the diseases developed. More importantly, the introduction of American animals and crops (especially the potato) gave peasant farmers a greater ability to feed themselves and prevented potentates from controlling their subjects through grain imports. This caused the nascent Roman Empire to fly apart in the 1st century CE, and the successor states were still squabbling a millennium later when the hordes of the Mongol Empire arrived.

Europe and Asia are now covered with a half-dozen Mongol khanates (the greatest of which is the Khanate of Ch'in) and dozens of semi-independent petty kingdoms that are easy targets for steam-powered Tenochca slave raids. The Tenochca have coaling stations around the world and their continental lands now stretch from the Ohio River to the northern Andes. North of the Tenochca Empire's American territories are the iron mines and weapons factories of the Hotinosavannah League (the Iroquois) to the east and the Tlingit Confederacy to the west. Africa is home to Zoroastrian Egypt, the rapidly arming southern state of KwaZulu and the Songhay Empire, inheritors of Christianity and Roman civilisation. The "current year" in Ezcalli is 1840.

Gernsback
Gernsback is a parallel that seems drawn straight from a 1930s science fiction adventure story (it is named for the editor Hugo Gernsback, founder of Amazing Stories in which many such tales appeared). Its point of divergence is the marriage of Nikola Tesla to Anne Morgan, daughter of banker and financier J. P. Morgan. In our history the pair were friends, but Tesla died penniless; in Gernsback, their marriage stabilized Tesla, whose inventions went on to revolutionize the world, especially his perfection of a technique for broadcasting electrical power wirelessly. Tesla's brother-in-law J. P. Morgan, Jr. and his companies became instrumental in helping the world's economies recover from the ensuing stock market crash. German and American influence was crucial to the success of the League of Nations in Gernsback; when atomic power was developed in the late 1930s, its World Science Council was placed in charge of nuclear research.

Joseph Stalin's Soviet Union saw the potential of atomic energy as a weapon, but the League of Nations sought to forestall the misuse of knowledge in this manner by invading in 1951. The "current year" in Gernsback is 1965; the League of Nations dominates a world which is economically dominated by the World Science Council and socially frozen (especially in matters of race and gender) in the 1930s. The appeal of Gernsback as a setting is less in its alternative history than in its alternative science and retro-futuristic style; its technological development followed a completely different path in the 20th century than did our world (flying cars are ubiquitous, but the transistor has yet to be developed).

Publication history

GURPS Alternate Earths was published by Steve Jackson Games in 1996, and written by Kenneth Hite, Craig Neumeier and Michael S. Schiffer.

A sequel was published as GURPS Alternate Earths II in 1999.

Reception
Rick Swan reviewed GURPS Alternate Earths for Dragon magazine #236 (December 1996). He called the book an "off-the-wall, one-of-a-kind" game supplement which turned out to be one of "the best in many a moon". He stated that "Alternate Earths presents six parallel worlds with haywire history, such as the Confederate States of America (where the Omaha Black Sox play the Mexico City Aztecs in the World Series) and Reich-5 (where you-know-who won World War II)." Swan also noted that the book is "adaptable", saying that the material "translates to other game systems with a minimum of tweaking", and also that the book is funny: "Alternate Earths features rock star Jerry Lee Swaggart and time traveling Nazis".

Other reviews

 * Valkyrie #13.
 * Alarums & Excursions #261.

 * Shadis #30 (1996)
 * Arcane #12 (November 1996)
 * Casus Belli #98

title: GURPS Alternate Earths


text:
User:Potzomchick/sandbox2

A dental extraction is the surgical removal of a tooth from the mouth. Simple extractions may be done by a dentist, and are performed on teeth that are visible in the mouth, under local anaesthetic. Typically the dentist grasps the tooth with forceps, rocking it back and forth until it is loosened from the alveolar bone. Sometimes a luxator, an instrument which fits between the tooth and gum, is used to help loosten the tooth. Surgical extractions are performed by an oral surgeon and involve the removal of teeth that cannot be easily accessed, either because it has broken under the gum line or because it has not come in yet. In a surgical extraction the surgeon makes an incision in the gum to reach the tooth and may also require the removal of overlying bone tissue. After the tooth is removed, a clot will usually form in the socket. Occasionally this clot can become disloged, resulting in a condition called dry socket. This will lengthen the healing process and cause additional pain and discomfort.

A tooth may be removed for a variety of reasons. It may be badly damaged or decayed, could be impacted, could be causing overcrowding or preventing a tooth from erupting.

Historically, dental extractions have been used to treat a variety of illnesses. Before the discovery of antibiotics chronic tooth infections were often linked to a variety of health problems, and therefore removal of a diseased tooth was a common treatment for various medical conditions. Instruments used for dental extractions date back several centuries. In the 14th century, Guy de Chauliac invented the dental pelican (resembling a pelican's beak) which was used through the late 18th century. The pelican was replaced by the dental key which, in turn, was replaced by modern forceps in the 20th century. Potzomchick 16:09, 25 August 2005 (UTC)

title: User:Potzomchick/sandbox2


text: User talk:69.157.112.113

title: User talk:69.157.112.113


text: User talk:Sleepnomore/Archive 0002

title: User talk:Sleepnomore/Archive 0002


text:
User:R6144

 * "I hate changes," cried Pat, almost in tears.

This is a quote from my favorite novel, Pat of Silver Bush, by L. M. Montgomery (see here). Well, though changes aren't exactly my favorite thing, if I hated them that much, how could I like this Wiki'ish place? :)

Please leave something in my user talk page if you can. Even a "Been here" is welcome, but constructive criticism is even better.

Introduction
I'm a graduate student on communications from Shanghai, PRC. Born in 1984. Aside from my research work, I'm interested in computer software (especially free software and digital freedom), juvenile literature (such as those by L. M. Montgomery), and all kinds of science in general, for example physiology, physics and economics. I'm fluent in Chinese and English, and I'm also learning a bit of Latin, but it is still below la-1 level.

Long-term plans

 * interference (communications)
 * multiuser detection (or maybe multi-user detection)
 * radio resource management
 * I made such a stub Mange01 09:50, 10 November 2006 (UTC)
 * LMM books
 * Have a look at my factual Everything2 nodes and copy the useful bits here.

Useful places

 * footnote4

Interesting places

 * Sandbox/Game_of_Go

Interesting users

 * User:Natalinasmpf
 * User:Valhallia

Notice further changes

 * Links to the Hazardous Chemical Database broken (see General complaints)
 * nitrogen dioxide (vapor pressure)
 * water (molecule) (conductivity change due to impurity)

title: User:R6144


text:
Category:Regional WikiProjects

This category comprises the WikiProjects related to specific geographic regions.

title: Category:Regional WikiProjects


text:
Arthur Shields

Arthur Shields (15 February 1896 – 27 April 1970) was an Irish actor on television, stage and film.

Early years
Born into an Irish Protestant family in Portobello, Dublin, Shields started acting in the Abbey Theatre when he was 17 years old. He was the younger brother of Oscar-winning actor Barry Fitzgerald. They were the sons of Adolphus Shields, who "was well-known in Dublin as a labour organiser" although the 1901 census listed his occupation as "press reader", and Fanny Sophia Shields (née Ungerland), who was German.

Irish nationalist activity
Along with six others of the Abbey Players, Shields fought in the Easter Rising of 1916. He was interned for six months in the Frongoch internment camp in Frongoch, Wales. His obituary in The Times of San Mateo, California, reported, "... upon his release he was decorated by the Republic of Eire."

Stage
Shields returned to the Abbey Theatre and had a varied career there from 1914 to 1939 as actor, assistant director, director and stage manager. He appeared in many productions ("more than 300 roles in 350 plays) while he was there, three of the productions he appeared in were by Irish playwright Teresa Deevy 'The Reapers'  'Temporal Powers' and 'Katie Roche'. Three times he brought the Abbey Company to the United States.

Film and television
In 1936, John Ford brought him to the United States to act in a film version of The Plough and the Stars, and in 1939 Shields decided to live permanently in California, where the mild climate would help his tuberculosis. Some of his memorable roles were in Ford films. Shields portrayed the Reverend Playfair in Ford's The Quiet Man, opposite John Wayne, Maureen O'Hara and his brother, Barry Fitzgerald. He played Dr. Laughlin in She Wore a Yellow Ribbon with Wayne and Joanne Dru, and appeared yet again with Wayne and Barry Fitzgerald in Ford's Long Voyage Home. His other films include: Little Nellie Kelly, The Keys of the Kingdom, The Fabulous Dorseys, Gallant Journey, The Shocking Miss Pilgrim, Drums Along the Mohawk, Apache Drums, Lady Godiva, National Velvet and The River. He also made television appearances including a 1958 role on Perry Mason as Dr. George Barnes in "The Case of the Screaming Woman" as well as a 1960 episode of Maverick starring Roger Moore titled "The Bold Fenian Men."

Personal life
Shields married Bazie Magee in 1920, and their son Adam was born in 1927. In 1943, the couple were divorced and Shields married Aideen O'Connor. Their daughter Christine was born in 1946. Aideen died in 1950. Shields' third marriage to Laurie Bailey in 1955 lasted until his death.

Shields died of complications related to emphysema on 27 April 1970, in Santa Barbara, California. He was survived by his wife, a daughter, a son and four grandchildren. His body was cremated, with the ashes taken to his native city of Dublin and buried with military honours in Deans Grange Cemetery.

Filmography

 * Knocknagow (1918) – Phil Lahy
 * The Sign of the Cross (1932) – Chaplain Costello (1944 Re-Release Prologue) (uncredited)
 * The Plough and the Stars (1936) – Irish Leader
 * Drums Along the Mohawk (1939) – Reverend Rosenkrantz
 * The Long Voyage Home (1940) – Donkeyman
 * Little Nellie Kelly (1940) – Timothy Fogarty
 * Lady Scarface (1941) – Matt Willis
 * The Gay Falcon (1941) – Inspector Mike Waldeck
 * How Green Was My Valley (1941) – Mr. Parry, deacon
 * Confirm or Deny (1941) – Jeff, Blind Typist
 * Broadway (1942) – Pete Dailey
 * This Above All (1942) – Chaplain
 * Pacific Rendezvous (1942) – Prof. Harvey Lessmore
 * The Loves of Edgar Allan Poe (1942) – Griswald – Broadway Journal (uncredited)
 * Dr. Renault's Secret (1942) – Inspector Duval (uncredited)
 * Nightmare (1942) – Sergeant
 * Gentleman Jim (1942) – Father Burke
 * Dr. Gillespie's New Assistant (1942) – Mr. Kipp (uncredited)
 * The Black Swan (1942) – The Bishop (uncredited)
 * Random Harvest (1942) – Liverpool Chemist (uncredited)
 * Above Suspicion (1943) – Walmer Hotel Porter (uncredited)
 * The Man from Down Under (1943) – Father Polycarp
 * Lassie Come Home (1943) – Andrew
 * Madame Curie (1943) – Businessman (uncredited)
 * The White Cliffs of Dover (1944) – Benson (uncredited)
 * Youth Runs Wild (1944) – Mr. Dunlop
 * National Velvet (1944) – Mr. Hallam
 * The Keys of the Kingdom (1944) – Father Fitzgerald – Dean at Holywell
 * Roughly Speaking (1945) – Minister (uncredited)
 * The Picture of Dorian Gray (1945) – Street Preacher (uncredited)
 * The Corn Is Green (1945) – Glyn Thomas
 * The Valley of Decision (1945) – Callahan
 * Too Young to Know (1945) – Mr. Enright
 * Three Strangers (1946) – Prosecutor
 * Gallant Journey (1946) – Father Kenton
 * The Verdict (1946) – Rev. Holbrook
 * Never Say Goodbye (1946) – McCarthy (uncredited)
 * The Shocking Miss Pilgrim (1947) – Michael
 * Easy Come, Easy Go (1947) – Timothy Mike Donovan
 * The Fabulous Dorseys (1947) – Mr. Dorsey
 * Seven Keys to Baldpate (1947) – Prof. Bolton
 * Fighting Father Dunne (1948) – Mr. Michael O'Donnell
 * My Own True Love (1948) – Iverson
 * Tap Roots (1948) – Reverend Kirkland
 * The Fighting O'Flynn (1949) – Dooley
 * She Wore a Yellow Ribbon (1949) – Dr. O'Laughlin
 * Red Light (1949) – Father Redmond
 * Challenge to Lassie (1949) – Dr. Lee
 * Tarzan and the Slave Girl (1950) – Dr. E.E. Campbell
 * A Wonderful Life (1951) – Pastor
 * Blue Blood (1951) – Tim Donovan
 * Apache Drums (1951) – Rev. Griffin
 * Sealed Cargo (1951) – Kevin Dolan
 * The River (1951) – Mr. John
 * The People Against O'Hara (1951) – Mr. O'Hara
 * The Barefoot Mailman (1951) – Ben Titus
 * Jack and the Beanstalk (1952) – Patrick the Harp (voice)
 * The Quiet Man (1952) – Reverend Mr. Cyril Playfair
 * Scandal at Scourie (1953) – Father Reilly
 * South Sea Woman (1953) – 'Jimmy-legs' Donovan
 * Main Street to Broadway (1953) – Actor in Fantasy Sequence
 * World for Ransom (1954) – Sean O'Connor
 * Pride of the Blue Grass (1954) – Wilson
 * River of No Return (1954) – Minister at Tent City (uncredited)
 * Lady Godiva of Coventry (1955) – Innkeeper
 * The King and Four Queens (1956) – Padre
 * The Daughter of Dr. Jekyll (1957) – Dr. Lomas
 * Enchanted Island (1958) – James 'Jimmy' Dooley
 * Night of the Quarter Moon (1959) – Captain Tom O'Sullivan
 * For the Love of Mike (1960) – Father Walsh
 * The Pigeon That Took Rome (1962) – Monsignor O'Toole (final film role)

Television

 * Your Show Time – 26 episodes – The Bookshop Man (1949)
 * The Hardy Boys: The Mystery of the Applegate Treasure – 8 episodes –  Boles (1956)
 * Perry Mason – episode – The Case of the Screaming Woman – Dr. George Barnes (1958)
 * Captain David Grief – episode – The Return of Blackbeard – Angus Macmor (1959)
 * Bat Masterson – episode – The Conspiracy: Parts 1 & 2 – Dana Ruggles (1959)
 * Maverick – episode – The Bold Fenian Men – Terence Fogarty (1960)
 * Wagon Train – episode – The Amos Gibbon Story – Judge Tremayne (1960)
 * Rawhide – episode – Incident of the Dust Flower – Sam Cartwright (1960)
 * Bonanza – episode – The Stranger – Dennis (1960)
 * Death Valley Days – episode – Loophole – Jebal McSween (1961)

Playography

 * The Reapers (1930)
 * Temporal Powers (1932)
 * Katie Roche (1936)

title: Arthur Shields