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Talk:Curve

Untitled
Older discussion at Talk:Curve/archive1

Addition to 'See also'
I added French curve to the 'See also' section. Perhaps trivial and obsolete, but certainly curve-related. —Preceding unsigned comment added by Moris JM (talk • contribs) 17:49, 7 February 2010 (UTC)

Explanation of rewrite
I rewrote the article to focus on the curve definition used in differential geometry. I think it is much more accessible now and with the importance of differential geometry for physics most people will come looking for this definition. I moved the topological definition of curve to the end of the article.

The last edit by 145.254.193.73 was also me, forgot to log in :)

MathMartin 14:29, 5 May 2004 (UTC)

I am still working on the article. My main goal is to make the article more accesible and useful by focussing on the differential geometric aspects of curves and the common definitions like regular, jordan curve etc.

I removed the following from the article because it talks to much about manifolds and too little about curves. Furthermore some of the text is now duplicated in the definition section.

 * If X is a differentiable manifold, then we can define the notion of differentiable curve. If X is a Ck manifold (i.e. a manifold whose charts are k times continuously differentiable), then a Ck differentiable curve in X is a curve c : I --> X which is Ck (i.e. k times continuously differentiable).  If X is a smooth manifold (i.e k = ∞, charts are infinitely differentiable), and c is a smooth map, then c is called a smooth curve.  If X is an analytic manifold (i.e. k = ω, charts are expressible as power series), and c is an analytic map, then c is called an analytic curve''.

''

 * There are other things people might be looking for. I expanded the section on algebraic curves, which is certainly one of them. Gene Ward Smith 18:32, 25 April 2006 (UTC)

What do we gain by using manifolds instead of Rn ?

MathMartin 15:44, 5 May 2004 (UTC)~

If we had the jet bundle article there would be a quick comeback on that.

One thing to bear in mind, is that in the longer term articles do aim to be comprehensive. That is not the same thing as having an expository strategy, and following it.

BTW, this page is getting long, and some archiving is called for, especially if it is going to be actively edited.

Charles Matthews 16:00, 5 May 2004 (UTC)

 * If we had the jet bundle article there would be a quick comeback on that.

Did not get this. What do you mean ?

 * One thing to bear in mind, is that in the longer term articles do aim to be comprehensive. That is not the same thing as having an expository strategy, and following it.

What do you mean by this ? Should I revert the definitions to the more abstract stuff ? What is a longer term article ? I do not think a have removed stuff from the page. I just reordered it (topological curve and algebraic curve at the end) and focussed on the differential geometric stuff. At least thats my intention.

MathMartin 16:22, 5 May 2004 (UTC)~

Well, jet bundle is a Requested Article which will get done one day. Jets are equivalence classes of curves in manifolds (cf your removal from the page); and are a basic concept.

So, all I'm saying is that future developments should be borne in mind, here. This is always going to be a major page. There is more than one way up the mountain, and I'm not objecting to your path.

Charles Matthews 16:45, 5 May 2004 (UTC)

last changes "focussing on differential geometry"
I can not stand these last changes, there is Diff geom subsection, if you feel something should be added do it there or make new page, call it curves in euclidean space or so. Tosha 02:13, 7 May 2004 (UTC)

Please, can we have a proper discussion of issues here, on this page?

Charles Matthews 06:53, 7 May 2004 (UTC)

My main point, aside from what I said before is: I do not think it is good to use the most abstract definition (like defining length on metric spaces instead of euclidean spaces). I think the page should have mostly one level of abstraction (at the moment the beginning of the page talks about topological spaces, then we use metric spaces, then we use differentiable manifolds). The page should use one setting (e.g. euclidean space) to define interesting curve definitions. If necessary on can always say "this definition can be abstracted to topological spaces ..".

If you do not agree Tosha, I will probably start my own page on euclidean curves, but then we will duplicate much material. And I would probably link to your curves page whenever I wanted to point out the more abstract definitions.

So it makes more sense for me to put the curve stuff in one central page. But I cannot "stand" the page as it is right now. The differential geometric subsection is not enough for me. I think most people come looking for the differential geometric definitions and not the more abstract definitions, so those should be central to the page.

MathMartin 08:57, 7 May 2004 (UTC)

There can be different ideas on exposition. If this is a disagreement about the order of topics, mainly: could MathMartin and Tosha just give their ideal orders, and discuss that. If it's about level of treatment in the differential geometry, in the end probably there will be multiple discussions; but it is better if they all start 'in the same place'.

Charles Matthews 09:32, 7 May 2004 (UTC)

I do not think this is about order of topics, but more about focus of article (differential geometric curves vs. more abstract curves)

Ok here is my order of topics:
 * Introduction:already in the article, albeit a bit short
 * Definition: This should list the most important and accessible definitions relating to curves. The definitions people mainly come looking for on this page. Should be very brief.
 * Notes: Explain the definitions a bit, give some background why the definitions are useful
 * Examples: See definitions in action
 * History: Curves are quite old, so we should have some historical information (curves as conic sections, usage in physics)
 * other topics deserving their own section: Length, Equivalence classes, arc length ...
 * more abstract curve definitions: Curves on topological spaces, metric spaces, algebraic curves ..

MathMartin 10:07, 7 May 2004 (UTC)

I understand your point, but this is an article about curve, if you want you can make one say curve in Eucledan space, make a remark in the beggining of curve that this article is a bit advanced and send less advenced readers to the new one. I think it would be a good idea and copying material from page to page is not a problem.

In my opinion the article was much more interesting before your changes.

On history, there was nearly no information in the history subsection, exapt that straight line was not curve before but now it is. I could not imagine a person who would get anything out of it so I removed it. I think the history subsection should be included only if the history is interesting, not just born grow.

Tosha 15:02, 7 May 2004 (UTC)

I do not understand in what sense the previous article was more interesting ? I did not see any clear focus in the article. If you already know about curves you probably can find some interesting information in the old article but it was definitely lacking a coherent presentation and was not accessible.

I admit my history section was a bit thin. What I was trying to point out is how the concept of a curve changed from a static one (conic section) to a dynamic one (curve of a point mass).

Charles Matthews does not think it is a good idea to have two articles on curves. But I do not think we can reach any conclusion other than doing two articles on curves. If I have time I will create a new curve article using the name "Curves (in Euclidean Space)" or something. Perhaps someone neutral can later merge the pages.

MathMartin 15:48, 7 May 2004 (UTC)

Well, OK, assuming these are understood positions, now. I could try to find a compromise edit. I don't myself have such strong feelings - is the Frenet stuff, which used to be in all the textbooks, important? Or is it quite boring, as Frank Adams once told me? I think it could be argued either way.

The point about curves in Euclidean space not being completely separate: better to have a summary in this article, and See main article ... there. This should ensure better consistency, and also gives a chance for two expositions, at different paces.

Charles Matthews 16:07, 7 May 2004 (UTC)

the new editition "focussing on differential geometry" looses style, it becomes borring topic in calculus. I do not object (and never did) someone will need such presentation but this one should also survive.

I just want to note that it is unlikely that anybody will open this page to find out what curve is, and most likely that someone will look for specific information about curve here, that is the reason it should contain general definitions (not just "do it your self"). I do not see why not to make separate article on smooth curves, I think the subject is very different, all these regular-free curves could be covered and it is too much for one article.

One more thing, we should not look hard for compromize, it will simply make the article worse

To make it short: Let's split. Tosha 23:48, 7 May 2004 (UTC)

I agree with Tosha. Martin, I think you're bringing too much of a bias to what is considered important. You just automatically assume that (of course??) anyone who comes here must be interested in differential geometry. This is not necessarily true. It is true that differential geometry is a hot topic and important in physics, but it is hardly the only manifestation of the "curve concept", and to assume that the needs and desires of readers who come here are matched in line with your own is a bit "diffeo-centric" (pardon the term). There are many topologists who study curves outside the setting of Reimannian metrics, e.g. purely for their topological properties or metric space properties. There are others who are fascinated with nowhere-differentiable curves, Peano curves, and other "pathological" examples. There are fractal curves, which are more and more important. People in number theory and algebraic geometry will most likely think of elliptic curves and varieties when they first hear the term "curve", and since there is a definite geometric interpretation and flavour to these objects, they also qualify as "curves". This article should give a general overview of the curve concept (which can have intuitive explanation and history, but will need to be somewhat abstract by nature), a summary of different types of "curves" in different areas of math, and then each of these can probably be fleshed out in a separate article. This happens often with really general topics. It's also a fine line between being too abstract and not general enough, usually this is worked out by giving some motivation and examples from concrete cases before general definition. Also, as more subtopic pages become available, links within other articles can be made to point to the SUBTOPIC so as not to lose a casual reader in an abstract definition (this is done with limit, where the author has a choice of several different pages to "direct" the reader to.) Revolver (YES...I know I said I was on leave to write my paper, but I've popped in very occasionally anonymously...guess I must be "wikipediholic"...)

I think we can have a perfectly satisfactory, balanced curve page, mentioning at least all the major usages; and providing links to more detailed expositions. In fact, it is hard to see how anything else should work, in the long run.

Charles Matthews 09:46, 8 May 2004 (UTC)

I have now looked at the two mathematical encyclopedias I have. This article compares quite well; and the differential geometry/algebraic curve material is put in separate articles. Charles Matthews 13:19, 8 May 2004 (UTC)

Ok you convinced me. I probably have a bias towards differential geometry. I wont change the structure of the article and will try to put my stuff in the differential geometry section. If this section becomes big enought I will put it on a seperate page.

MathMartin 19:52, 10 May 2004 (UTC)

I've actually collected up a number of short articles that were already here, and made differential geometry of curves. It's a start; I'm aware that it requires edits to sort out.

Charles Matthews 20:47, 10 May 2004 (UTC)

I am a bit perplexed. My and Tosha did nothing but arguing about the curve page and meanwhile you have rewritten the page and created a new differential geometry curves page. This seems like a very good strategy to create/rewrite pages. I will just argue a bit and you do all the work :)

MathMartin 21:00, 10 May 2004 (UTC)

It's actually a revolutionary new management strategy. I'm thinking of called it 'where angels fear to tread', or something. Or perhaps it's a very old strategy, called 'getting your hands dirty'.

Charles Matthews 21:30, 10 May 2004 (UTC)

universal curve
The redirect for uc seems too specific. Perhaps an abstract here would be a good idea? -MagnaMopus 18:57, 18 January 2006 (UTC)

Mechanical curve
I've created Mechanical curve as redirect to this page, but if there's someplace better for it to redirect please edit it. From the page at Archimedes: "the first Greek mathematician to introduce mechanical curves (those traced by a moving point) as legitimate objects of study". Is that like Spirograph or something? Thanks! Ewlyahoocom 20:20, 11 May 2006 (UTC)
 * Yes, a spirograph is one example, but a simpler one might be an astroid, an involute, or really any continuous function if the moving point is taken to be an abstract and not necessarily a concrete object whose movement is being measured by the curved function. LokiClock (talk) 20:11, 25 June 2009 (UTC)

Curved lines in applied geometry
Mechanics, engineering and applied geometry are somehow related although, here, isn't it that the surface lines are only called curved lines for example, I dont understand why the addition of "curved" to a line is needed here even for nonstraight plane objects since it is obviously a line, anyway. --Mathstrght (talk) 09:10, 4 November 2022 (UTC)

I would like to put my two cents in
I say that a straight line is a curve with an undefined radius.--Luke Elms 20:25, 22 November 2006 (UTC)

 * This sounds true to me, but I would use the term radius of curvature. We have $$\rho = \frac{1}{\kappa}$$ where $$\rho$$ is radius of curvature and $$\kappa$$ is the curvature. Since $$\kappa = 0$$ for a straight line, $$\rho$$ is undefined. FionaLovesCats (talk) 23:54, 21 April 2022 (UTC)

Same curve or not?
Consider the following two plane curves:
 * $$\gamma_1 : [0, 2] \rightarrow \mathbb{R}^2, ~\gamma_1(t) = (t, t^2),$$
 * $$\gamma_2 : [0, 1] \rightarrow \mathbb{R}^2, ~\gamma_2(t) = (2t, 4t^2).$$

Clearly, viewed as functions, these two are different. Are they also different when viewed as curves? Or are they different representations of the same curve? The present text equates the curve and the function, and thus appears to make them different. Most people (and, I suspect, most mathematicians) would consider them the same curve, just like 0.5 and 1/2 are different representations of the same number.

Is anyone aware of a (reliable, published) source that pays attention to this issue? If so, what do they have to say about it? --Lambiam Talk 20:33, 27 December 2006 (UTC)

 * This topic is discussed at the end of section Curve#Differential_geometry. 88.73.158.80 14:24, 3 May 2007 (UTC)

Comparative geometry of curved lines
Is something that is very easily applied with projections of curved lines into straight plane or planes. --Mathstrght (talk) 09:08, 4 November 2022 (UTC)

Unwarranted extra disambig
really, really, really wants curve(s) to be about Curves International, as was made clear in a prior discussion. As consensus made clear, it ain't gonna happen. Nor is there any good reason for an extra disambig notice above the usual one here; the disambig page already includes the necessary info. Reverting. --KSmrqT 02:23, 1 August 2007 (UTC)
 * KSmrq, I think you really, really, really are closed minded and full of POV. Yes there was a discussion on the Curves talk page as I originally created the Curves page and had it redirect to Curves International. However, the math guru's decided they wanted it to go to Curve, the math concept and so I agreed with consensus and left it alone, though I feel it was a bit biased with editors of math articles voting. Fast forward to now, since I discovered that it is perfectly fine within the wikipedia community to utilize otheruses4 (see firefly, Paraffin, Apollo, Brass, Jerome, Syntax, Spice) as a few of the many examples which utilize this. The community allows the tag and it is not hindering nor vandalizing the community. However, what I see here is a monopoly of math experts not wanting to follow suit with a perfectly excepted format of wikipedia.

 * Curves International is only the largest fitness franchise in the world, larger than Bally's and Gold's gyms combined...so it's not just some gym. Since you, apparently, have read the discussion on the Curves talk page you will see I'm doing this as a compromise, if you will, rather than seeking another rfc. Most people when they search for Curves, are not looking for the math concept, but in fact are looking for the women's fitness center. This entry is in no way defacing the article, and edit wars (hopefully) could be avoided, so I think this is a good compromise.

 * As I asked another editor, and I now ask you, why you oppose this entry? Curves is the fastest growing fitness company in the world with 10,000 locations. Last year, for the first time since the U.S. Government started keeping tract, the rise in women's obesity went unchanged. It did not increase, nor did it decrease. However, the significance, as mentioned, it did not increase. But in the male category, there was still an increase. The only major contribution that could possible have made the difference in the female population, though the research is not yet complete, is the rise of female attendance in physical fitness. Curves has about 4+ million members and all the copycats combined are around one million, and have many many former members who had results. Curves is such a phenomena and is known to be such that Avon has partnered with them and has placed them in every Avon Magazine for the past year; and there is now a new partnering campaign with General Mills where they are making and selling Curves cereal, and Curves bars (snack). If you look a the search engines, there are more items for the fitness club than any other and there are more searches for Curves than there are for the math concept or any other. I fail to see why you all remain close minded and will not allow this minor compromise, which has been done by many other articles. I think your comment shows your ignorance as Curves has set major records in the Guinness book of world records, in Business Atlas, in the New York Times, etc. To tell the world that you are the fast growing franchise in the history of franchises is not just some gym. The company has gained the attention of the world business market, all the competition, the President of America's fitness council, the industry, and the medical world because of the milestones, the waves, contributions, and the changes it has brought/made in the fitness and medical world through exercise. I'm not trying to sell the company, but I am trying to show you how ignorant your comment was and how significant this company is and continue to be in the world. In the female population, Curves is a common household name and most likely everyone on here has a mom, sister, girlfriend, wife, niece, or aunt in the program or considering it. Now, I challenge you to defend why you refuse to allow a perfectly acceptable practice, otheruses4, within the wikipedia community and defend your close mindedness. Kind regards. --User: (talk) 13:51, 1 August 2007 (UTC)
 * There is discussion too at User talk:Maniwar. Oleg Alexandrov (talk) 15:13, 1 August 2007 (UTC)
 * Let's try to keep the conversation here and not be all over the place. A central place will be good, in my opinion. --User: (talk) 15:47, 1 August 2007 (UTC)

Curve (civil engineering)
What about curves in civil engineering??? Peter Horn 02:43, 19 July 2008 (UTC)

The most general definition of curve
The most general definition of curve is that of a 1-dimensional Topological manifold. Why this definition is not given at all in the page?--pokipsy76 (talk) 10:21, 8 March 2009 (UTC)

 * Because that is not a definition of curve. JumpDiscont (talk) 05:27, 11 January 2011 (UTC)

 * NO, it is a perfectly correct definition and it is given in the page as "A curve is a topological space which is locally homeomorphic to a line". In fact, the term "1-dimensional Topological manifold" has been substituted by its definition to remains at the lowest possible mathematical level. Nevertheless, when Pokipsy76 did ask his question, this sentence was not yet in the page.
 * Note also that, usually, edits in talk pages are done at the end, and that there is a discussion on the definition of a curve at the end, which is more recent than Pokipsy76's question.
 * D.Lazard (talk) 10:35, 11 January 2011 (UTC)

Jordan curve vs Jordan arc
The text treats “Jordan curve” and “Jordan arc” as synonyms. I believe this is wrong; a Jordan curve is a homeomorphic image of a circle, as stated, but a Jordan arc, as far as I know, is a homeomorphic image of a closed interval. In other words, a Jordan curve is closed, a Jordan arc is not. Isn't that how the terms are used in the literature? Hanche (talk) 02:26, 10 November 2009 (UTC)

Incorrect details in Differential geometry section
The text starting "Another way to think about a curve..." and ending "by Frank Ayers, Jr." is incorrect. First let me note that I have Ayers book (I'm presuming it's his Schaum's book on DE's). On page 41 he gives the correct formulae for the equations of the tangent line and it's x and y intercepts for a general curve F(x, y) = 0. The equation given in the text for the tangent is incorrect and should have parentheses around the X-x part, i.e. it should read Y-y = (dy/dx)(X-x). The equation given for the y intercept is correct. The equation for the x intercept is incorrect and should be X = x-ydx/dy. The statement "...but this case we will use it to find the X and Y intercepts which are when x and y equal to 0" should read "...but this case we will use it to find the x and y intercepts which are when X and Y respectively are equal to 0". These are minor mistakes and easily fixed. A bigger problem is that the whole concept is wrong. It is not true to say that the sum of the x and y intercepts has to be equal to 2 for a curve. This is easily seen by considering the curve y=3 whose tangent line is itself and which has no x intercept and y-intercept 3. Another problem is that the two equations being combined are only simultaneously true when the tangent line passes through the origin in which case they again do not add up to 2. Recommend that the entire text be removed. Psmythirl (talk) 19:27, 6 January 2010 (UTC)
 * I don't understand this part or how it relates to the rest of the Differential geometry section. I think it uses X in a different sense to the rest of the section, but it doesn't make that explicit or define its terms. It seems to have more to do with the "Graph of a function" sense. But if it's mistaken as well as confusing, I agree it should go. (In fact, seeing as no one has offered a defence of it since your comment in January, I've decided to remove it for now.) Dependent Variable (talk) 11:12, 30 August 2010 (UTC)

Demoting to Start class
There a few issues with this article that lead me to the opinion that it still requires much work and is not of B class quality. First, there is an almost complete lack of references given for the material. The St Andrews and 2dcurves.com are good resources and make good external links, but they are mainly catalogs of individual curves, not a resource for the definition of a general curve or its properties. That leaves a single note and a single reference to support one section out of the entire article. Second, several of the sections are much to long considering the material is covered in another article. I brief introduction to the idea should be given only and details should merged with the other article. Finally, the article attempts to give a single definition of a curve when really there are several definitions depending on the context; a curve in topology is very different from a curve in algebraic geometry. I will try to address some of these issues myself, but the article should not be marked B class in its present state.--RDBury (talk) 19:17, 26 January 2010 (UTC)
 * It seems I have missed something vital here. What does B class mean? Where do I look for more info? Hanche (talk) 02:34, 5 February 2010 (UTC)
 * See the math rating banner at the top of the page, it has links to more information.--RDBury (talk) 07:14, 24 February 2010 (UTC)

Definition of a curve
I reverted the edits by Paolo.dLfor the following reasons:
 * The new version looks like a definition, while it is only an informal description. This is misleading.
 * The term of series is improper, set would be proper.
 * The new version omits the important fact that a line has no thickness.

Nevertheless there is an issue with these two pages curve and line. I'll try to solve them in a better way by editing them.

 * The old version, that you reverted, does not give a definition, but just refers to the definition of line (which is a special kind of curve), which in turn refers to the definition of curve. It's a circular definition. So, you are right that my definition is informal, but that's better than a fake definition. Besides the definition, there was additional text in my edit that you deleted without explanation. So, I am going to restore my edit, using the word "sequence" instead of "series", and explaining that the curve has no thickness, and you'll change whatever you don't like when you'll find a more formal and non-circular definition. Paolo.dL (talk) 10:06, 13 December 2010 (UTC)

 * The reference to the concept of Curvature or "straightness" (null curvature) is crucial to obtain a clear definition, and that was the part you deleted without explanation.
 * I see that topologists start from the definition of line. OK, then I'll change the informal definition of line to avoid circularity. Informal definitions are often needed in introductions. Notice, however, that the concept of "direction" is based on the concept of straight line, so the informal definition is not perfect.
 * Paolo.dL (talk) 13:45, 12 December 2010 (UTC)

 * Quite a tricky thing to define well without resorting to advanced mathematics. Neither def really seems to be good. The American Heritage® Science Dictionary has a fairly nice def:  "A line or surface that bends in a smooth, continuous way without sharp angles." I also think mentioning its 1 dimensional might help.--Salix (talk): 11:41, 13 December 2010 (UTC)

I feel uncomfortable with the "curved line" definition. I don't think it is an appropriate definition. Lines and curves are different geometrical entities. if the line is the extension of the shortest path between any two distinct points in the plane, then the curve encompasses all other paths. This "curved line" definition is a huge misconception, I believe.--74.192.202.208 (talk) 08:18, 2 December 2011 (UTC)
 * In older terminology, up to about World War I, the word "line" was used to mean what we would call a curve in today's language. The phrases "straight line" and "right line" were used for what we would call a "line", while "curved line" was a "line" that wasn't straight. See 1911 Encyclopædia Britannica/Line for an example of the old terminology in use. Such shifts in language are actually very common and it makes reading mathematics from more than a hundred hears ago a bit of a challenge.--RDBury (talk) 15:35, 2 December 2011 (UTC)

path-image, alternate definitions, dubious
The section "Conventions and terminology", after defining a path to be a continuous map from R into a manifold, says that the word "curve" is used in diff.geom. & vect.calc. for a path, but that it is used in topologoy for the image of a path. This contradicts the definition given in the immediately preceding section, "Topology". What gives?

Also, the lead defines a "curve" as a space which is locally homeomorphic to a line, i.e., a one dimensional manifold. Is this wrong? I mean, it works for a simple curve that doesn't ever cross over itself, but in general the image of a curve may include (infinitely many) points that are not locally homeomorphic to a line. Is there a definition without this problem (without referencing paths, as they brings in the issue of multiple paths having identical images). Also, is a single point supposed to qualify as a topological curve (since it is the image of the path whose map function happens to be just a trivial constant)?

I think the different approaches and terminology should be given more priority in the article (ie. explained earlier and making the distinctions more clearly). Cesiumfrog (talk) 01:01, 3 May 2011 (UTC)

Space curves
The section "Algebraic curve" says
 * Algebraic curves can also be space curves, or curves in even higher dimension, obtained as the intersection (common solution set) of more than one polynomial equation in more than two variables.

Would it be correct to make this more specific by saying the following?:
 * Algebraic curves can also be space curves, or curves in even higher dimension n, obtained as the intersection (common solution set) of n–1 polynomial equations in n variables.

Loraof (talk) 15:12, 15 October 2015 (UTC)
 * This is not correct. However, I agree that we need to be specific. I'll edit the page for fixing this. D.Lazard (talk) 11:42, 16 October 2015 (UTC)

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Sections on differentiable curves
Because of several non-equivalent definitions of a curve, this article must be structured as a broad-concept article. I have done the job, except for the sections on differentiable curves.

IMO, should redirect to Differential geometry of curves (this latter title is confusing, as I do not understand why this article is not named "Differentiable curve" and what is the difference between "Differentiable geometry of curves" and "Study of differentiable curves"). The part of Curve devoted to differentiable curves should be reduced to a summary of Differential geometry of curves, whose size should be of the same order as that of the two other sections. If some content would be lost by this reduction, it should be added to Differential geometry of curves.

Also, the two articles must be made coherent: presently, a eight-shaped curve is a differentiable curve in one of the articles, and not in the other.

I could probably do these modifications, but it would be much better if they would be done by an expert. D.Lazard (talk) 16:36, 1 May 2019 (UTC)

Differentiatial geometry and calculations for curved lines
Also it is segments that maybe used in differential geometry calculus and these are actually used. --Mathstrght (talk) 09:06, 4 November 2022 (UTC)

What is a curve?
In articles about curves, one cn find several contradictory definitions of a (topological or differentiable) curve, that are contradictory. For example
 * Roughly speaking a is a curve that is defined as being locally the image of an injective differentiable function $\gamma \colon I \rightarrow X$ from an interval $I$ of the real numbers into a differentiable manifold $X$, often $\mathbb{R}^n.$ More precisely, a differentiable curve is a subset $C$ of $X$ where every point of $C$ has a neighborhood $U$ such that $C\cap U$ is diffeomorphic to an interval of the real numbers. In other words, a differentiable curve is a differentiable manifold of dimension one. (in Curve.) This implicitly asserts that an injective differentiable function is a diffeomorphism on its image. For example, the cusp $$\gamma(t)=(t^2, t^3)$$ is a curve for the first sentence, not for the second one.)
 * a vector-valued function $\gamma: I \to \mathbb{R}^{n}$ of class $ C^{r} $ (i.e., the component-functions of $ \gamma $ are $ r $-times continuously differentiable) is called a parametric $ C^{r} $-curve or a $ C^{r} $-parametrization. Note that $ \gamma[I] \subseteq \mathbb{R}^{n} $ is called the of the parametric curve. (In Differential geometry of curves). This means that a parabola is not a curve, but the image of a curve, and that $$\gamma(t)=(t, t^2)$$ and $$\gamma(t)=((t+1), (t+1)^2)$$ are different curves. Also, an eight-shaped curve is a differentiable curve for this definition, but not for either definition given in curve.

In summary, we have three different definitions of a differentiable curve: one that includes cusps and eight-shaped curves, one which exclude eight-shaped curves but not cusps, and one that excludes both cusps and eight-shaped curves. Moreover, often in contradiction with the common usage, this is the parametrization that is called a curve, not its image. It seems that it is a WP:OR tentative for formalizing the common usage of using "the curve $$\gamma$$" as an abbreviation for "the curve defined by $$\gamma$$".

Suggestion. I suggest to use the following definitions in all related articles:
 * A topological curve is the image of an interval by a continuous function $$\gamma.$$ If the function is differentiable, then this is a differentiable curve.
 * In the preceding definition, $$\gamma$$ is a parametrization of the curve.
 * The phrase "the curve $$\gamma$$" is a commonly used abbreviation for "the curve defined by $$\gamma$$".
 * A parametric curve is the pair formed by a curve and a defining parametrization. ("Parametrized curve" would be more proper, but is less common.)
 * A regular curve is a curve that can be parametrized by a function that is a diffeomorphism of an interval or a circle onto its image. Regular curves are (connected) differentiable manifolds of dimension one.

As implementing this suggestion may need to edit several article, some comments would be useful before editing these articles. So, I'll add notifications at WT:WPM, Talk:Differential geometry of curves and Talk:Plane curve. D.Lazard (talk) 13:59, 9 May 2019 (UTC)

 * I'm a bit squeamish about some of this. For one, I've never heard "topological curve" used as such.  A continuous function from the interval to a space is generally just called a path (or an arc if it's injective).  Presumably you're doing this by analogy with topological manifold, but does this actually get used?  Even if so, I can't imagine it's all that common.  Also, for injectivity (smooth or not), if that's really needed, it's often fine and easier to just state separately.  It really depends on context, but using manifold language may be overkill in certain places.  Might have more to say later, but that was the main thing that struck me right away.  –Deacon Vorbis (carbon • videos) 15:48, 9 May 2019 (UTC)

 * [0, 1]2 as a subset of R2 is both the image of a Peano curve and of a Hilbert curve. I would not call these the same. What about defining a curve as an equivalence class of parametrizations, where two parametrizations γ and γ' are equivalent if there exists an order-preserving isomorphism φ between their domains such that γ = γ'∘φ? --Lambiam 20:57, 17 May 2019 (UTC)
 * The parametrization γ defined by γ(t) = (t2, 0) if t < 0, (0, t2) otherwise, is a differentiable function, but I wouldn't call the corresponding curve differentiable at the origin. --Lambiam 21:05, 17 May 2019 (UTC)
 * I have clarified that "topological curve" is a term that is introduced here for practical purpose. D.Lazard (talk) 13:45, 21 May 2019 (UTC)
 * I'm afraid it is still not always clear when "curve" refers to the image (a subset of some space), and when it refers to a function whose domain is an interval and whose range is such an image. Note that Differentiable curve redirects to Differential geometry of curves, although the latter article does not actually present a definition of the notion "differentiable curve"; the term does not even occur. Similarly, Parametric curve redirects to Parametric equation, but that article also does not actually present a definition of the notion "parametric curve" – although the term is used, but somewhat ambiguously. Furthermore, some curves are defined as a locus, which may or may not be specified in the form of an equation, but does not generally determine a parametric curve (take e.g. the definition of an ellipse as the set of points having a given sum of the distances to two given points). Above, where you wrote, "If the function is differentiable, then this is a differentiable curve", I interpreted "the function" to refer to the function mentioned in the preceding sentence, and "this" to the entity called there a "topological curve", no other plausible antecedent being in sight. --Lambiam 14:22, 21 May 2019 (UTC)
 * Thinking more about it, I (now) feel that the best course of action is to present a historical account, starting with how the Ancient Greek geometers approached this (a locus defined in words), then the approach through parametric equations arising with the invention of analytic geometry, and finally as the image of a function on an interval. A comparison – without suggesting that any of these is intrinsically better than any other – will reveal that these definitions of "curve" are not interchangeable (e.g., a hyperbola can be defined as a locus, but only one branch at a time as the image of a function on an interval; conversely, (the image of) a bounded space-filling curve is never the solution set of an algebraic equation – one has to cheat and use a non-algebraic equation like $$\mathrm{max}(|x|,|y|,1) = 1$$). To conclude, there could be a section about different notions of equality for curves. --Lambiam 14:56, 21 May 2019 (UTC)
 * There is already an historical section, and I understand your suggestion of a "historical account" as a suggestion for rewriting this section (the first one) for focusing on the evolution of the concept of curve. I would agree with this. It is in this spirit that I have added to the lead the remark that Euclid's definition is not really different from the modern one as the image of a continuous function.
 * About the various definitions: I have recently rewritten the lead and added the section "topological curve" for clarifying that there are various definitions of a curve, which are strongly related but not equivalent. I have tried to include all common definitions of a curve as a guide for the reader for understanding to which specific article he should go. This can certainly be improved, and I may have forgotten some important kinds of curves, but I think that this is the right starting point, and the remaining problems can be solved by a specific discussion, except for differentiable curves.
 * For differentiable curves, the problem is deeper: we have, in Wikipedia, at least three non-equivalent definitions. A reader who want to know whether a specific curve is differentiable cannot find the answer in Wikipedia. I have given the example of eight-shaped curves and cusps. You have found another example. So, we desperately need an accurate definition of a differentiable curve. Without that, we cannot have a correct version of the corresponding section of Curve, and of the detailed article Differentiable curve. D.Lazard (talk) 01:36, 22 May 2019 (UTC)
 * I have not looked into this, but it is possible – in fact, not unlikely – that the literature also contains materially different definitions for the concept of "differentiable curve". For a simple curve, I think the only sane definition is that there is a (unique) tangent for every interior point of the curve. In particular, for a curve defined as the set of points ($x$, $y$) that satisfy an equation of the form $y$ = $f$($x$), i.e. the graph of a function, this should boil down to the differentiability of function $f$ provide that we allow the derivative to assume values ±∞. For a general topological curve, sanity similarly requires that we retrieve the definition for a simple curve when applied to a curve that happens to be simple. Parametrizations are an entirely different species; does the literature actually use the terminology of "differentiable curve" for these? --Lambiam 20:57, 22 May 2019 (UTC)

A few complaints
Hello curve enthusiasts! Here's what I think should change here.

In the section Curve#Differentiable_arc it is stated that "Arcs of lines are called segments or rays, depending whether they are bounded or not". I think that the whole line should also be considered an arc to itself. I propose that it instead say "Arcs of lines are segments, rays, or lines depending how they are bounded". This issue comes down to whether we require a strict subset relation or not in the definition of arc, and I think we should be explicit about that either way.

In the section Curve#Length_of_a_curve a formula is written

\operatorname{Length}(\gamma) ~ \stackrel{\text{def}}{=} ~ \sup \! \left( \left\{ \sum_{i = 1}^{n} d(\gamma(t_{i}),\gamma(t_{i - 1})) ~ \Bigg| ~ n \in \mathbb{N} ~ \text{and} ~ a = t_{0} < t_{1} < \ldots < t_{n} = b \right\} \right). $$ I think we should lose the parentheses because it's common to see $$\sup A$$ where $$A$$ is some set, and we don't lose any information by doing this. I would prefer

\operatorname{Length}(\gamma) ~ \stackrel{\text{def}}{=} ~ \sup \! \left\{ \sum_{i = 1}^{n} d(\gamma(t_{i}),\gamma(t_{i - 1})) ~ \Bigg| ~ n \in \mathbb{N} ~ \text{and} ~ a = t_{0} < t_{1} < \ldots < t_{n} = b \right\}. $$

Within that same section is the formula

{\operatorname{Speed}_{\gamma}}(t) ~ \stackrel{\text{def}}{=} ~ \limsup_{[a,b] \ni s \to t} \frac{d(\gamma(s),\gamma(t))}{|s - t|}. $$ I think that $$[a,b] \ni s \to t$$ is unnecessarily confusing. I would use the  LaTeX command like in this article to stack $$s \to t$$ and $$s \in [a,b]$$ but that doesn't seem to be supported by Wikipedia. At least I get errors when I try :(. I would even just consider

{\operatorname{Speed}_{\gamma}}(t) ~ \stackrel{\text{def}}{=} ~ \limsup_{s \to t} \frac{d(\gamma(s),\gamma(t))}{|s - t|}. $$ as the domain of $$\gamma$$ has already been specified. FionaLovesCats (talk) 01:03, 22 April 2022 (UTC)
 * These seem good suggestions. Be WP:BOLD and edit the article yourself. D.Lazard (talk) 10:01, 22 April 2022 (UTC)

Straight lines, functions, bend spaces with curves
I think curved line is very rear to use but curve simply never in mathematics, this is some jargon that is not acceptable. --Mathstrght (talk) 09:04, 4 November 2022 (UTC)

"Curved line" listed at Redirects for discussion
An editor has identified a potential problem with the redirect Curved line and has thus listed it for discussion. This discussion will occur at Redirects for discussion/Log/2022 November 16 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. Steel1943 (talk) 17:29, 16 November 2022 (UTC)

Direction
Shouldn't the definiton of curve mention the notion of direction ? A continuous unidimensional line which gradually varies direction. JMGN (talk) 16:24, 12 April 2024 (UTC)

 * If the direction changes, one has a curved line; that is a curve. So this definition is circular. Moreover if the direction is defined, this means that one has a differentiable curve, and there are many curves that are not differentiable. Moreover, if the direction varies gradually, one has a continuously differentiable curve.
 * In short, the concept of the direction of a curve cannot be defined without having first defined a curve, and, in any case, your definition is much too restrictive. D.Lazard (talk) 16:44, 12 April 2024 (UTC)

title: Talk:Curve


text:
1956 in literature

This article contains information about the literary events and publications of 1956.

Events

 * c. January – The first book in Ed McBain's long-running 87th Precinct police procedural series, Cop Hater, is published in the United States under Evan Hunter's new pseudonym.
 * February 2 – Eugene O'Neill's semi-autobiographical Long Day's Journey into Night (completed in 1942) receives a posthumous world première at the Royal Dramatic Theatre, Stockholm, in Swedish (Lång dags färd mot natt), directed by Bengt Ekerot and starring Lars Hanson. Its Broadway debut at the Helen Hayes Theatre on November 7 follows an American première at the Shubert Theatre (New Haven).
 * February 25 – The English poet Ted Hughes and American poet Sylvia Plath meet in Cambridge, England.
 * March 11 – The U.S. release of Sir Laurence Olivier's film version of Shakespeare's Richard III plays simultaneously on NBC network television and as afternoon matinée screenings in movie theaters. Its TV audience is put at 25–40 million – almost certainly the largest to date for a Shakespeare production.
 * March 19 – The widowed English author Aldous Huxley marries the Italian-American film-maker and author Laura Archera at a drive-in wedding chapel in Yuma, Arizona.
 * April 23 – The British author C. S. Lewis and American poet Joy Gresham have a civil marriage at Oxford register office.
 * May 8 – The first performance of John Osborne's play Look Back in Anger is given by the newly formed English Stage Company at the Royal Court Theatre in London. Alan Bates has his first major role as Cliff. The press release describes Osborne as one of the angry young men of the time, a phrase used on July 26 in a Daily Express headline.
 * June 16 – Ted Hughes and Sylvia Plath marry at St George the Martyr, Holborn in the London Borough of Camden.
 * June 21 – Playwright Arthur Miller appears before the House Un-American Activities Committee in Washington, D.C.
 * June 26 and August 23 – Books published by the discredited psychoanalyst Wilhelm Reich are burned in the United States under a court injunction.
 * June – Nineteen-year-old Hunter S. Thompson is arrested as an accessory to robbery.
 * June 29 – Arthur Miller marries Marilyn Monroe in White Plains, New York.
 * July – After pleas by Israeli diplomats, the Romanian communist regime releases A. L. Zissu, formally sentenced to life imprisonment in 1954. Zissu emigrates to Israel, where he dies on September 6.
 * July 4 – The National Library of Scotland's first purpose-built premises open in Edinburgh.
 * July 8 – The drama series Armchair Theatre, produced by ABC Weekend TV for the ITV network in the United Kingdom, begins a twelve-year run.
 * August 14 – Iris Murdoch marries John Bayley at Oxford register office.
 * September 14 – Harold Pinter marries Vivien Merchant in a civil ceremony at Bournemouth, after they meet while touring in repertory theatre.
 * October – The Ladder becomes the first nationally distributed lesbian magazine in the United States.
 * November 1 – Allen Ginsberg's Howl and Other Poems, a signal work of the Beat Generation, is published by City Lights Bookstore in San Francisco.
 * December
 * J. G. Ballard's first professional publications, the science fiction short stories "Escapement" and "Prima Belladonna", appear in this month's issues of New Worlds and Science Fantasy respectively.
 * Martin Gardner begins his Mathematical Games column in Scientific American.
 * December 3 – The author Romain Gary wins the Prix Goncourt for Les Racines du ciel. He would later become the only person to win the prize twice, publishing La Vie devant soi under the pseudonym Émile Ajar in 1975.
 * unknown dates
 * Finished in 1952, Egyptian author Naguib Mahfouz's Cairo Trilogy (Palace Walk, Palace of Desire, Sugar Street), is first published.
 * Sixteen-year-old Michael Moorcock becomes editor of Tarzan Adventures.
 * Jorge Luis Borges becomes a professor of English and American literature at the University of Buenos Aires.

Fiction

 * Nelson Algren – A Walk on the Wild Side
 * Eric Ambler – The Night-Comers
 * Kingsley Amis – That Uncertain Feeling
 * Poul Anderson – Planet of No Return
 * Charlotte Armstrong – A Dram of Poison
 * Isaac Asimov – The Naked Sun
 * James Baldwin – Giovanni's Room
 * Sybille Bedford – A Legacy
 * Saul Bellow – Seize the Day
 * Pierre Berton – The Mysterious North
 * Alfred Bester – The Stars My Destination (as Tiger! Tiger!)
 * W. E. Bowman – The Ascent of Rum Doodle
 * Pearl S. Buck – Imperial Woman
 * Anthony Burgess – Time for a Tiger
 * Albert Camus – The Fall (La Chute)
 * John Dickson Carr
 * Patrick Butler for the Defense
 * Fear is the Same (as Carter Dickson)
 * Henry Cecil – Friends at Court
 * Agatha Christie – Dead Man's Folly
 * Arthur C. Clarke – The City and the Stars
 * A. J. Cronin
 * A Thing of Beauty
 * Crusader's Tomb
 * Antonio di Benedetto – Zama
 * Cecil Day-Lewis – A Tangled Web
 * Nh. Dini – Dua Dunia (Two Worlds, stories)
 * Philip K. Dick
 * The Man Who Japed
 * The Minority Report
 * Gordon R. Dickson
 * Alien From Arcturus
 * Mankind on the Run
 * Alfred Döblin – Tales of a Long Night (Hamlet oder Die lange Nacht nimmt ein Ende)
 * Friedrich Dürrenmatt – A Dangerous Game (Die Panne – The Breakdown – or Traps)
 * Ian Fleming – Diamonds Are Forever
 * Naomi Frankel – Shaul ve-Yohannah (שאול ויוהאנה, "Saul and Joanna", publication begins)
 * Sarah Gainham – Time Right Deadly
 * Romain Gary – Les Racines du ciel
 * William Golding – Pincher Martin
 * Winston Graham – The Sleeping Partner
 * Walter Greenwood – Down by the Sea
 * Edward Grierson – The Second Man
 * Henri René Guieu – Les Monstres du Néant
 * Mark Harris – Bang the Drum Slowly
 * Frank Herbert – The Dragon in the Sea (first book publication)
 * Georgette Heyer – Sprig Muslin
 * Kathryn Hulme – The Nun's Story
 * James Kennaway – Tunes of Glory
 * Feri Lainšček – Petelinji zajtrk
 * Meyer Levin – Compulsion
 * C. S. Lewis – Till We Have Faces: A Myth Retold
 * E. C. R. Lorac – Murder in Vienna
 * Rose Macaulay – The Towers of Trebizond
 * Ross Macdonald – The Barbarous Coast
 * Compton Mackenzie – Thin Ice
 * Ed McBain – Cop Hater
 * Naguib Mahfouz – Palace Walk (بين القصرين, Bein el-Qasrein, first of the Cairo Trilogy)
 * Ngaio Marsh – Off with His Head
 * Grace Metalious – Peyton Place
 * Yukio Mishima (三島 由紀夫) – The Temple of the Golden Pavilion (金閣寺)
 * Gladys Mitchell – Twelve Horses and the Hangman's Noose
 * Nicholas Monsarrat – The Tribe that Lost its Head
 * Farley Mowat – Lost in the Barrens
 * Agnar Mykle – The Song of the Red Ruby (Sangen om den røde rubin)
 * Patrick O'Brian – The Golden Ocean
 * Edwin O'Connor – The Last Hurrah
 * Pier Paolo Pasolini – Ragazzi di vita
 * Mervyn Peake – Boy in Darkness
 * Mary Renault – The Last of the Wine
 * Kenneth Roberts – Boon Island
 * João Guimarães Rosa – The Devil to Pay in the Backlands (Grande Sertão: Veredas)
 * Françoise Sagan – A Certain Smile (Un certain Sourire)
 * Samuel Selvon – The Lonely Londoners
 * Irwin Shaw – Lucy Crown
 * Georges Simenon – The Little Man from Archangel (Le Petit Homme d'Arkhangelsk)
 * Khushwant Singh – Train to Pakistan
 * Rex Stout
 * Might as Well Be Dead
 * Three Witnesses
 * Julian Symons – The Paper Chase
 * A. E. van Vogt – The Wizard of Linn
 * Heimito von Doderer – Die Dämonen. Nach der Chronik des Sektionsrates Geyrenhoff (The Demons)
 * Angus Wilson – Anglo-Saxon Attitudes
 * P. G. Wodehouse – French Leave
 * Kateb Yacine – Nedjma
 * Frank Yerby – Captain Rebel
 * Eiji Yoshikawa (吉川 英治) – The Heike Story: A Modern Translation of the Classic Tale of Love and War (Shin Heike monogatari, a retelling of The Tale of the Heike)
 * Francis Brett Young – Wistanslow

Children and young people

 * Rev. W. Awdry – Percy the Small Engine (eleventh in The Railway Series of 42 books by him and his son Christopher Awdry)
 * Polly Cameron – The Cat Who Thought He Was a Tiger
 * R. F. Delderfield – The Adventures of Ben Gunn
 * Fred Gipson – Old Yeller
 * Rumer Godden – The Fairy Doll
 * C. S. Lewis – The Last Battle
 * Alf Prøysen – Little Old Mrs Pepperpot (first in a long series of Mrs Pepperpot – Teskjekjerringa – books)
 * Maurice Sendak – Kenny's Window
 * Ian Serraillier – The Silver Sword
 * Dodie Smith – The Hundred and One Dalmatians
 * Virginia Sorensen – Miracles on Maple Hill
 * Eve Titus – Anatole (first in the Anatole and Basil series of 14 books)

Drama

 * Jean Anouilh – Pauvre Bitos, ou Le dîner de têtes (Poor Bitos)
 * Ferdinand Bruckner – The Fight with the Angel (Der Kampf mit dem Engel)
 * José Manuel Castañón – Moletú-Volevá
 * Friedrich Dürrenmatt – The Visit (Der Besuch der alten Dame)
 * Max Frisch – Philipp Hotz's Fury (Die Grosse Wut des Philipp Hotz)
 * Anna Langfus – Les Lepreux (The Lepers, first performed)
 * Hugh Leonard – The Birthday Party
 * Saunders Lewis – Siwan
 * Bruce Mason – The Pohutukawa Tree
 * Ronald Millar – The Bride and the Bachelor
 * Arthur Miller – A View from the Bridge (revised version)
 * Yukio Mishima – Rokumeikan
 * Heiner Müller and Inge Müller – Der Lohndrücker (The Scab, written)
 * Eugene O'Neill – Long Day's Journey into Night
 * John Osborne – Look Back in Anger
 * Arnold Wesker – Chicken Soup with Barley (written)

Poetry

 * Allen Ginsberg – Howl
 * Anne Morrow Lindbergh – The Unicorn and Other Poems
 * Harry Martinson – Aniara
 * Yevgeny Yevtushenko – Stantsiia Zima (Станция Зима, Zima Station, translated as Winter Station)

Non-fiction

 * Peter Frederick Anson – The Call of the Cloister: Religious Communities and Kindred Bodies in the Anglican Communion
 * John G. Bennett – Dramatic Universe
 * Peter M. Blau – Bureaucracy in Modern Society
 * Gerald Durrell – My Family and Other Animals
 * Margery Fish – We Made a Garden
 * Georges Friedmann – Le travail en miettes (The Anatomy of Work)
 * Carl Gustav Jung – Mysterium Coniunctionis
 * A. J. Liebling – The Sweet Science
 * Norman Mailer – The White Negro
 * Karl Mannheim – Essays on the Sociology of Culture
 * C. Wright Mills – The Power Elite
 * Alva Myrdal and Viola Klein – Women's Two Roles: Home and Work
 * Octavio Paz – El arco y la lira
 * Lobsang Rampa – The Third Eye
 * Irving Stone – Men to Match My Mountains (Account of the opening of the American Old West, 1840–1900)
 * John Strachey – Contemporary Capitalism

Births

 * January 2 – Storm Constantine, British science fiction and fantasy author
 * January 4 – Sarojini Sahoo, Indian journalist, author, and poet
 * January 8 – Jack Womack, American novelist
 * January 10 – Antonio Muñoz Molina, Spanish novelist
 * January 21 – Ian McMillan, English poet
 * January 14 – Ronan Bennett, Northern Irish novelist
 * February 20 – François Bréda, Romanian essayist, poet, literary critic, literary historian, translator and theatrologist (died 2018)
 * February 26 – Michel Houellebecq, French novelist
 * March 3 – Frank Giroud, French comics writer (died 2018)
 * March 7 – Andrea Levy, English novelist (died 2019)
 * March 12 – Ruth Ozeki, American novelist and filmmaker
 * March 20
 * Minken Fosheim, Norwegian actress and author (died 2018)
 * Win Lyovarin, Thai novelist and short story writer
 * March 23 – Steven Saylor, American historical novelist
 * April 7 – Christopher Darden, African-American attorney, author, actor and lecturer
 * April 12 – Yasuo Tanaka, Japanese novelist and politician
 * April 29 – Alexander Jablokov, American writer and novelist
 * May 4 – David Guterson, American journalist and novelist
 * May 9 – Cindy Lovell, American educator and writer
 * May 18 – John Godber, English dramatist
 * May 20
 * Boris Akunin, Russian novelist and essayist
 * Ingvar Ambjørnsen, Norwegian author
 * June 9 – Patricia Cornwell, American crime novelist
 * June 25 – Anthony Bourdain, American chef, writer and television personality (died 2018)
 * June 26 – Davide Ferrario, Italian film director, screenwriter and author
 * June 29 – Richard Summerbell, Canadian mycologist, author and songwriter
 * July 2 – Cynthia Kadohata, Japanese-American children's writer
 * July 4 – Éric Neuhoff, French novelist
 * July 11 – Amitav Ghosh, Bengali Indian novelist
 * September 6 – Mai Yamani, Saudi Arabian independent scholar, author and anthropologist
 * October 9 – Robert Reed, American science fiction author
 * October 13 – Chris Carter, American screenwriter
 * October 16 - Meg Rosoff, American-British children's and young-adult writer
 * October 18 – Lucy Ellmann, Anglo-American novelist
 * October 21 – Carrie Fisher, American actress and novelist (died 2016)
 * November 11 – Tim Pears, English novelist
 * November 20 – Elena Gremina, Russian dramatist (died 2018)
 * November 26 – John McCarthy, English journalist and hostage
 * December 22 – Percival Everett, American writer and novelist
 * unknown dates
 * James Aboud, Trinidad poet and judge
 * James Belich, New Zealand historian
 * Amy Gerstler, American poet

Deaths

 * January 13 – Wickham Steed, English journalist, editor and historian (born 1871)
 * January 14 – Sheila Kaye-Smith, English novelist (born 1887)
 * January 29 – H. L. Mencken, American journalist and English language scholar (born 1880)
 * January 31 – A. A. Milne, English children's author, novelist and dramatist (born 1882)
 * March 30 – Edmund Clerihew Bentley, English novelist and inventor of the clerihew (born 1875)
 * April 22 – Otto Roth, Hungarian Romanian politician, journalist, and literary promoter (born 1884 )
 * May 15 – Arthur Talmage Abernethy, American theologian and poet (born 1872)
 * May 20 – Max Beerbohm, English humorist (born 1872)
 * May 22 – Ion Călugăru, Romanian novelist, short story writer and journalist (born 1902)
 * June 7 – Julien Benda, French philosopher and novelist (born 1867)
 * June 22 – Walter de la Mare, English poet (born 1873)
 * June 24 – Nicos Nicolaides, Greek writer (born 1884)
 * July 7 – Gottfried Benn, German poet and essayist (born 1886)
 * July 8 – Giovanni Papini, Italian essayist, poet and novelist (born 1881)
 * August 14 – Bertolt Brecht, German dramatist (born 1898)
 * September 6
 * Michael Ventris, English linguistic scholar (born 1922)
 * A. L. Zissu, Romanian novelist and Zionist leader (born 1888)
 * September 12 – Hans Carossa, German novelist and poet (born 1878)
 * October 30 – Pío Baroja, Spanish novelist (born 1872)
 * December 6 - Bhimrao Ramji Ambedkar, the principal architect of the Constitution of India (born 1891)
 * December 13 – Arthur Grimble, Hong Kong-born English travel writer (born 1888)
 * December 25 – Robert Walser, Swiss novelist and poet writing in German (born 1878)

Awards

 * Carnegie Medal for children's literature: C. S. Lewis, The Last Battle
 * Deutscher Jugendbuchpreis (first award): Roger Duvoisin and Louise Fatio, Happy Lion (Der glückliche Löwe); Astrid Lindgren, Mio, My Son; and Kurt Lütgen, Kein Winter für Wölfe ("Two Against the Arctic: Story of a Restless Life between Greenland and Alaska")
 * Duff Cooper Prize: Alan Moorehead, Gallipoli
 * James Tait Black Memorial Prize for fiction: Rose Macaulay, The Towers of Trebizond
 * James Tait Black Memorial Prize for biography: St John Greer Ervine, George Bernard Shaw
 * Madan Puraskar (first award): Satya Mohan Joshi, Hamro Lok Sanskriti; Chittaranjan Nepali, Janaral Bhimsen Thapa Ra Tatkalin Nepal; and Bala Ram Joshi, Adhikbibhav Sthirbidhoot Utpadhak
 * Newbery Medal for children's literature: Jean Lee Latham, Carry On, Mr. Bowditch
 * Nobel Prize for literature: Juan Ramón Jiménez
 * Premio Nadal: José Luis Martín Descalzo, La frontera de Dios
 * Prix Goncourt: Romain Gary for The Roots of Heaven
 * Pulitzer Prize for Drama: Albert Hackett and Frances Goodrich, Diary of Anne Frank
 * Pulitzer Prize for Fiction: MacKinlay Kantor, Andersonville
 * Pulitzer Prize for Poetry: Elizabeth Bishop, Poems – North & South
 * Queen's Gold Medal for Poetry: Edmund Blunden

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

title: 1956 in literature


text:
1957 in literature

This article contains information about the literary events and publications of 1957.

Events

 * January 10 – T. S. Eliot marries his secretary Valerie Fletcher, 30 years his junior, in a private church ceremony in London. His first wife, Vivienne Haigh-Wood, died in 1947.
 * January 15 – The film Throne of Blood, a reworking of Macbeth by Akira Kurosawa (黒澤明), is released in Japan.
 * March – The Cat in the Hat, written and illustrated by Theodor Geisel as 'Dr. Seuss' as a more entertaining alternative to traditional literacy primers for children, is first published in a trade edition in the United States, initially selling an average of 12,000 copies a month, a figure which rises rapidly.
 * March 13 – A 1950 Japanese translation of D. H. Lawrence's Lady Chatterley's Lover by Sei Itō (伊藤整) is found on appeal to be obscene.
 * March 15 – Élet és Irodalom (Life and Literature) is first published in Hungary as a literary magazine.
 * March 21 – C. S. Lewis marries Joy Gresham in a Christian ceremony at her bedside in the Churchill Hospital, Oxford, England.
 * March 25 – Copies of Allen Ginsberg's Howl and Other Poems (first published 1 November 1956) printed in England are seized by United States Customs Service officials in San Francisco on grounds of obscenity. On October 3, in People v. Ferlinghetti, a subsequent prosecution of publisher Lawrence Ferlinghetti in the city, the work is ruled not to be obscene.
 * April – John Updike moves to Ipswich, Massachusetts, the model for the fictional New England town of Tarbox in his 1968 novel Couples.
 * June 2 – Joe Orton submits The Last Days of Sodom, a novel jointly written with Kenneth Halliwell, to a publisher; it is rejected within three days and they give up working in partnership.
 * July 1 – The opening performance is held at the Stratford Shakespearean Festival's Festival Theatre in Stratford, Ontario, with its thrust stage designed by Tanya Moiseiwitsch.
 * July 19 – The largely autobiographical novel The Ordeal of Gilbert Pinfold by Evelyn Waugh is published.
 * August 7 – Italo Calvino's letter of resignation from the Italian Communist Party appears in l'Unità.
 * October – The first American Beat Generation (poets Allen Ginsberg and Peter Orlovsky) stay at the "Beat Hotel" (Hotel Rachou) in Paris.
 * November 22 – Boris Pasternak's novel Doctor Zhivago is first published, in Italian translation, by Giangiacomo Feltrinelli in Milan, having been rejected for publication in the Soviet Union.
 * unknown dates
 * Justine, the first novel in Lawrence Durrell's The Alexandria Quartet, is published. The last will be published in 1960.
 * Dorothy Parker begins writing book reviews for Esquire.
 * E. E. Cummings gains a special citation from the National Book Award Committee in the United States for his Poems, 1923–1954.
 * Malcolm Muggeridge is replaced by Bernard Hollowood as editor of the British Punch magazine.
 * The Harry Ransom Center for research in the humanities is founded in the University of Texas at Austin by Harry Ransom.
 * John Sandoe opens a bookshop in Chelsea, London.
 * Noh is inscribed as an Intangible Cultural Property (Japan).
 * Three neo-Grotesque sans-serif typefaces are released: Folio (designed by Konrad Bauer and Walter Baum), Neue Haas Grotesk (Max Miedinger) and Univers (Adrian Frutiger), will influence the International Typographic Style of graphic design.

Fiction

 * Caridad Bravo Adams – Corazón salvaje
 * James Agee – A Death in the Family
 * Lars Ahlin – Natt i marknadstältet (Night in the Market Tent)
 * Isaac Asimov
 * Earth Is Room Enough
 * The Naked Sun
 * John Bingham – Murder Off the Record
 * Ray Bradbury – Dandelion Wine
 * John Braine – Room at the Top
 * Fredric Brown – Rogue in Space
 * Pearl S. Buck – Letter from Peking
 * Michel Butor – La Modification
 * John Dickson Carr – Fire, Burn!
 * Louis-Ferdinand Céline – Castle to Castle (D'un château l'autre)
 * John Cheever – The Wapshot Chronicle
 * Agatha Christie – 4.50 from Paddington
 * Mark Clifton and Frank Riley – They'd Rather Be Right
 * Ivy Compton-Burnett – A Father and His Fate
 * Thomas B. Costain – Below the Salt
 * James Gould Cozzens – By Love Possessed
 * L. Sprague de Camp – Solomon's Stone
 * Freeman Wills Crofts – Anything to Declare?
 * Cecil Day-Lewis – End of Chapter
 * Daphne du Maurier – The Scapegoat
 * Lawrence Durrell – Justine
 * Shusaku Endo (遠藤 周作) – The Sea and Poison (海と毒薬)
 * Ian Fleming
 * The Diamond Smugglers
 * From Russia, with Love
 * Janet Frame – Owls Do Cry
 * Sarah Gainham
 * The Cold Dark Night
 * The Mythmaker
 * Jean Giono – The Straw Man (Le Bonheur fou)
 * José Giovanni – The Break (Le Trou)
 * Martyn Goff – The Plaster Fabric
 * Richard Gordon – Doctor in Love
 * Winston Graham – Greek Fire
 * L.P. Hartley – The Hireling
 * Bill Hopkins – The Divine and the Decay
 * Aldous Huxley – Collected Short Stories
 * James Jones – Some Came Running
 * Anna Kavan – Eagle's Nest
 * Jack Kerouac – On the Road
 * Frances Parkinson Keyes – Blue Camellia
 * Christopher Landon – Ice Cold in Alex
 * Halldór Laxness – The Fish Can Sing (Brekkukotsannáll)
 * Chin Yang Lee – The Flower Drum Song
 * Meyer Levin – Compulsion
 * H. P. Lovecraft and August Derleth – The Survivor and Others
 * Compton Mackenzie – Rockets Galore
 * Józef Mackiewicz – Kontra
 * Alistair MacLean
 * The Guns of Navarone
 * South by Java Head
 * Naguib Mahfouz – Sugar Street
 * Bernard Malamud – The Assistant
 * Richard Mason – The World of Suzie Wong
 * James A. Michener – Rascals in Paradise
 * Gladys Mitchell – The Twenty-Third Man
 * Nancy Mitford – Voltaire in Love
 * C. L. Moore – Doomsday Morning
 * Elsa Morante – L'isola di Arturo
 * Sławomir Mrożek – Słoń (The Elephant, short stories)
 * Iris Murdoch – The Sandcastle
 * Vladimir Nabokov – Pnin
 * Björn Nyberg and L. Sprague de Camp – The Return of Conan
 * Marcel Pagnol – Le Château de ma mère
 * Boris Pasternak – Doctor Zhivago
 * Anthony Powell – At Lady Molly's
 * Maurice Procter – The Midnight Plumber
 * Qu Bo (曲波) – Tracks in the Snowy Forest (林海雪原)
 * Ayn Rand – Atlas Shrugged
 * Robert Randall (pseudonym of Robert Silverberg and Randall Garrett) – The Shrouded Planet
 * Alain Robbe-Grillet – La Jalousie
 * Nevil Shute – On the Beach
 * Robert Paul Smith – Where Did You Go? Out. What Did You Do? Nothing
 * Muriel Spark – The Comforters
 * Howard Spring – Time and the Hour
 * John Steinbeck – The Short Reign of Pippin IV
 * Rex Stout
 * Three for the Chair
 * If Death Ever Slept
 * Julian Symons – The Colour of Murder
 * Elizabeth Taylor – Angel
 * Kay Thompson – Eloise in Paris
 * Roger Vailland – La Loi
 * Jack Vance – Big Planet
 * Arved Viirlaid – Seitse kohtupäeva (Seven Days of Trial)
 * Henry Wade – The Litmore Snatch
 * Evelyn Waugh – The Ordeal of Gilbert Pinfold
 * Patrick White – Voss
 * Angus Wilson – A Bit Off the Map
 * John Wyndham – The Midwich Cuckoos
 * Ivan Yefremov – Andromeda Nebula
 * Frank Yerby – Fairoaks

Children and young people

 * Mabel Esther Allan – Ballet for Drina
 * Gillian Avery – The Warden's Niece
 * Rev. W. Awdry – The Eight Famous Engines (twelfth in The Railway Series of 42 books by him and his son Christopher Awdry)
 * Narain Dixit – Khar Khar Mahadev (serialized)
 * Aileen Fisher – A Lantern in the Window
 * Edward Gorey – The Doubtful Guest
 * Éva Janikovszky – Csip-csup (Piffling)
 * Tove Jansson – Moominland Midwinter (Trollvinter)
 * Harold Keith – Rifles for Watie
 * Elinor Lyon – Daughters of Aradale
 * William Mayne – A Grass Rope
 * Otfried Preußler – Die kleine Hexe (The Little Witch)
 * Dr. Seuss
 * The Cat in the Hat
 * How the Grinch Stole Christmas!
 * Pat Smythe – Jacqueline Rides for a Fall (first of the Three Jays series of seven books)
 * Elizabeth George Speare – Calico Captive
 * Tomi Ungerer – The Mellops Go Flying
 * Dare Wright – The Lonely Doll

Drama

 * Samuel Beckett – Endgame and Act Without Words I (first performed); All That Fall and From an Abandoned Work (first broadcast of both)
 * Emilio Carballido – El censo
 * William Douglas Home – The Iron Duchess
 * Christopher Fry – The Dark is Light Enough
 * Jean Genet – The Balcony (Le Balcon)
 * Günter Grass – Flood (Hochwasser)
 * Graham Greene – The Potting Shed
 * William Inge – The Dark at the Top of the Stairs
 * Errol John – Moon on a Rainbow Shawl
 * Bernard Kops – The Hamlet of Stepney Green
 * John Osborne
 * The Entertainer
 * Epitaph for George Dillon
 * Harold Pinter – The Dumb Waiter (written)
 * N. F. Simpson – A Resounding Tinkle
 * Wole Soyinka – The Invention
 * Boris Vian – Les Bâtisseurs d'Empire (The Empire Builders)
 * Tennessee Williams
 * Baby Doll
 * Orpheus Descending

Poetry

 * Robert E. Howard – Always Comes Evening
 * Ted Hughes – The Hawk in the Rain
 * Pier Paolo Pasolini – Le ceneri di Gramsci
 * Octavio Paz – Piedra de Sol
 * Jibanananda Das – Rupasi Bangla
 * Robert Penn Warren – Promises: Poems, 1954–1956. Won National Book Award for Poetry  – Won 1958 Pulitzer Prize for Poetry

Non-fiction

 * Abdelmajid Benjelloun – Fī l-Ṭufūla
 * B. R. Ambedkar (died 1956) – The Buddha and His Dhamma
 * G. E. M. Anscombe – Intention
 * Catherine Drinker Bowen – The Lion and the Throne: The Life and Times of Sir Edward Coke (1552–1634). Wins 1958 National Book Award for Nonfiction
 * Gerald Brenan – South from Granada: Seven Years in an Andalusian Village
 * M. Đilas – The New Class
 * Will Durant – The Reformation. Nominated for National Book Award for Nonfiction
 * Elisabeth Elliot – Through Gates of Splendor
 * Charles Evans – Kangchenjunga: The Untrodden Peak
 * Douglas Southall Freeman – George Washington: A Biography. Wins 1958 Pulitzer Prize for Biography; nominated for National Book Award for Nonfiction
 * Northrop Frye – Anatomy of Criticism: Four Essays
 * Patience Gray and Primrose Boyd – Plats du jour, illustrated by David Gentleman
 * Louis M. Hacker – Alexander Hamilton in the American. Nominated for National Book Award for Nonfiction
 * Bray Hammond – Banks and Politics in America. Won 1958 Pulitzer Prize for History
 * Gilbert Highet – Poets in a Landscape. Nominated for 1958 National Book Award for Nonfiction
 * Richard Hoggart – The Uses of Literacy
 * Eric John Holmyard – Alchemy
 * Stuart Holroyd – Emergence from Chaos
 * Ernst Kantorowicz – The King's Two Bodies
 * Henry Kissinger – Nuclear Weapons and Foreign Policy. Nominated for National Book Award for Nonfiction
 * Primo Levi – If This Is a Man (Se Questo è un Uomo)
 * Art Linkletter – Kids Say the Darndest Things
 * Christopher Lloyd – The Mixed Border
 * Mary McCarthy – Memories of a Catholic Girlhood. Nominated for National Book Award for Nonfiction
 * Tom Maschler (ed.) – Declaration (anthology)
 * Eliot Ness and Oscar Fraley – The Untouchables
 * Iris Origo – The Merchant of Prato (life and commercial career of Francesco di Marco Datini)
 * Walt Whitman Rostow & Max F. Milliken – A Proposal: Key to an Effective Foreign Policy. Nominated for National Book Award for Nonfiction
 * Jean-Paul Sartre – Search for a Method (Questions de méthode)
 * David Schoenbrun – As France Goes. Nominated for National Book Award for Nonfiction
 * Rodolfo Walsh – Operación Masacre
 * Ian Watt – The Rise of the Novel: Studies in Defoe, Richardson and Fielding
 * Alan Watts – The Way of Zen
 * K. A. Wittfogel – Oriental Despotism

Births

 * January 7 – Nicholson Baker, American novelist
 * January 16 – Stella Tillyard, English writer and historian
 * January 22 – Francis Wheen, English journalist and author
 * January 27 – Frank Miller, American comic-book cartoonist and scriptwriter
 * February 11 – Mitchell Symons, English writer and journalist
 * February 15 – Shahriar Mandanipour, Iranian writer
 * March 3 – Nicholas Shakespeare, English novelist and biographer
 * March 7 – Robert Harris, English novelist and current-affairs writer
 * March 20 – John Grogan, American journalist and non-fiction writer
 * March 23 – Ananda Devi, Mauritian francophone fiction writer and poet
 * March 26 – Paul Morley, English music journalist
 * March 29 – Elizabeth Hand, American science fiction and fantasy writer
 * April 3
 * Rainer Karlsch, German historian
 * Unni Lindell, Norwegian novelist
 * May 13 – Koji Suzuki, Japanese author and screenwriter
 * May 17 – Peter Høeg, Danish novelist
 * May 23 – Craig Brown, English satirist
 * June 8 – Scott Adams, American satirist
 * July 12 – Pino Quartullo, Italian actor, director, screenwriter and playwright
 * July 14 – Andrew Nicholls, English-born Canadian screenwriter
 * July 29 – Liam Davison, Australian novelist (died 2014 in air crash)
 * August 24 – Stephen Fry, English comedy performer, broadcast presenter and writer
 * August 25 – Simon McBurney, British actor, writer and theatre director
 * September 11 - James McBride, American writer and musician
 * September 22 – Nick Cave, Australian author and musician
 * October 9 – Herman Brusselmans, Belgian novelist, poet, playwright and columnist
 * October 28 - Catherine Fisher, British poet and children's writer
 * December 3 – Anne B. Ragde, Norwegian novelist
 * December 11 – William Joyce, American children's author
 * December 12 – Robert Lepage, Canadian playwright
 * unknown dates
 * Peter Armstrong, English poet and psychotherapist
 * John Doyle, Irish-born Canadian critic
 * Ana Santos Aramburo, Spanish national librarian
 * Melanie Rae Thon, American author

Deaths

 * January 10 – Gabriela Mistral, Chilean poet (born 1889)
 * January 13 – A. E. Coppard, English short story writer and poet (born 1878)
 * January 19 – Barbu Lăzăreanu, Romanian literary historian, poet, and communist journalist (heart attack, born 1881)
 * February 10 – Laura Ingalls Wilder, American author (born 1867)
 * March 7 – Wyndham Lewis, British novelist (born 1882)
 * March 9 – Rhoda Power, English children's writer and broadcaster (born 1890)
 * March 12 – John Middleton Murry, English critic (born 1889)
 * March 28 – Christopher Morley, American journalist, novelist and poet (born 1890)
 * March 29 – Joyce Cary, Irish novelist (born 1888)
 * April 22 – Roy Campbell, South African poet and satirist (born 1901)
 * June 17
 * May Edginton, English popular novelist (born 1883)
 * Dorothy Richardson, English novelist and journalist (born 1873)
 * June 26
 * Alfred Döblin, German novelist (born 1878)
 * Malcolm Lowry, English novelist and poet (born 1909)
 * July 10
 * Sholem Asch, Polish-Jewish novelist, dramatist and essayist (born 1880)
 * Julia Boynton Green, American author and poet (born 1861)
 * July 19 – Curzio Malaparte, Italian novelist, playwright, and journalist (cancer, born 1898)
 * July 21 – Kenneth Roberts, American historical novelist (born 1885)
 * July 23 – Giuseppe Tomasi di Lampedusa, Italian novelist (born 1896)
 * July 24 – Sacha Guitry, Russian-born French playwright, actor and director (b. 1885)
 * August 1 – Rose Fyleman, English writer and poet (born 1877)
 * August 21 – Mait Metsanurk, Estonian writer (born 1879)
 * August 25 – Leo Perutz, Austrian-born novelist and mathematician (born 1882)
 * September 2 – William Craigie, Scottish lexicographer (born 1867)
 * September 12 – José Lins do Rego, Brazilian novelist (born 1901)
 * September 22 – Oliver St. John Gogarty, Irish poet and memoirist (born 1878)
 * October 25 – Edward Plunkett, Baron Dunsany, Irish author (born 1878)
 * October 26 – Nikos Kazantzakis, Greek novelist (born 1883)
 * November 8 – Ernest Elmore (John Bude), English crime writer and theatre director (born 1901)
 * November 24 – Alfred Eckhard Zimmern, English historian and political scientist (born 1879)
 * December 15 – Mulshankar Mulani, Gujarati playwright (born 1867)
 * December 17 – Dorothy L. Sayers, English crime novelist (born 1893)
 * December 24 – Arturo Barea, Spanish journalist, broadcaster and writer (born 1897)
 * December 25 – Stanley Vestal, American writer, poet and historian (born 1877)

Awards

 * Carnegie Medal for children's literature: William Mayne, A Grass Rope
 * James Tait Black Memorial Prize for fiction: Anthony Powell, At Lady Molly's
 * James Tait Black Memorial Prize for biography: Maurice Cranston, Life of John Locke
 * Miles Franklin Award: Patrick White, Voss
 * Newbery Medal for children's literature: Virginia Sorenson, Miracles on Maple Hill
 * Nobel Prize for Literature: Albert Camus
 * Premio Nadal: Carmen Martín Gaite, Entre visillos
 * Prix Goncourt: Roger Vailland, La Loi
 * Pulitzer Prize for Drama: Eugene O'Neill, Long Day's Journey into Night
 * Pulitzer Prize for Fiction: no award given
 * Pulitzer Prize for Poetry: Richard Wilbur: Things of This World
 * Queen's Gold Medal for Poetry: Siegfried Sassoon

title: 1957 in literature


text:
Gherman Titov

Gherman Stepanovich Titov (Герман Степанович Титов; 11 September 1935 – 20 September 2000) was a Soviet and Russian cosmonaut who, on 6 August 1961, became the second human to orbit the Earth, aboard Vostok 2, preceded by Yuri Gagarin on Vostok 1. He was the fourth person in space, counting suborbital voyages of US astronauts Alan Shepard and Gus Grissom. A month short of 26 years old at launch, he is the youngest professional astronaut and was the youngest person to fly in space until 2021 when Oliver Daemen flew on Blue Origin NS-16 at the age of 18. Since Daemen flew a suborbital mission, Titov remains the youngest person to fly in Earth orbit.

Titov's flight finally proved that humans could live and work in space. He was the first person to orbit the Earth multiple times (a total of 17), the first to pilot a spaceship and to spend more than a day in space. He was also the first to sleep in orbit and to suffer from space sickness (becoming the first person to vomit in space).

Titov was the first human photographer from space: he made the first manual photographs from orbit, thus setting a record for modern first photos of Earth from space by a human (the first picture of the planet from space was shot by a V-2 rocket in 1946, launched from New Mexico). He also was the first person to film the Earth using a professional quality Konvas-Avtomat movie camera, which he used for ten minutes.

In his subsequent life Titov continued to work for the Soviet space program, and played a major role in the Spiral project where he trained to become the first pilot of an orbital spaceplane. However, after the death of Yuri Gagarin in a military aircraft accident in 1968, the Soviet government decided it could not afford to lose its second cosmonaut, and so Titov's career as test pilot ended.

Titov served in the Soviet Air Force, attaining the rank of colonel-general. In his final years in post-Soviet Russia he became a Communist politician. Despite having been chosen second, after Gagarin, to fly into space, it was Titov who later proposed the Soviet Government regularly celebrate Cosmonautics Day on April 12, the day of Gagarin's flight.

Biography
Titov was born in the village of Verkhneye Zhilino in the Altai Krai and went to school at the Stalingrad Military Aviation School. After graduating as an air force pilot, he was selected for cosmonaut training in 1960.

He flew the Vostok 2 mission launched on 6 August 1961. It lasted for 25.3 hours and he performed 17 orbits of the Earth. His call sign was Eagle (Орёл). He landed close to the town of Krasny Kut in Saratov Oblast, Russia. A month short of 26 years old at launch, he is the youngest Astronaut and remained the youngest person to fly in space until July 2021, when his record was surpassed by a Dutch teenager, Oliver Daemen. Titov was a member of the Communist Party of the Soviet Union, as were almost all the Soviet cosmonauts.

Titov was a fine sportsman, and keen on gymnastics:

"Service in the Air Force made us strong, both physically and morally. All of us cosmonauts took up sports and PT seriously when we served in the Air Force. I know that Yuri Gagarin was fond of ice hockey. He liked to play goal keeper. Gherman Titov was a gymnastics enthusiast, Andriyan Nikolayev liked skiing, Pavel Popovich went in for weight lifting. I don't think I am wrong when I say that sports became a fixture in the life of the cosmonauts."

- Valery Bykovsky

He was the first person to suffer from space sickness (motion sickness in space) and was also the first person to sleep in space. He slept for roughly one orbit and was surprised to wake with his arms floating in the air because of the absence of normal gravity. He returned to sleep after he had his arms under a security belt and slept 30 minutes more than predicted by the flight plan. He stated, "Once you have your arms and legs arranged properly, space sleep is fine.... I slept like a baby".

Though he had been suffering from space sickness during his orbit, Titov celebrated upon landing. His celebration is described as "a fit of euphoria" after landing, and on his return flight to Kubishev for debriefing, he alarmed the medical staff by opening and downing a beer, in complete violation of the rules.

After landing, Titov was sent to hospital for further testing to ensure that he was not sick. After his mission, he reportedly engaged in behaviours that could be considered unacceptable for someone working within the space programme. He is reported to have been enthralled in his love of women, excessive drinking, and fast cars, which caused some to theorise that his behaviour had potentially been another side effect of the space sickness he experienced from zero gravity. Further testing revealed that not to be the case.

During a widely-publicised 1962 visit to Seattle to tour the Century 21 World's Fair, Titov was asked by reporters how his space flight affected his philosophy of life. He replied: "Sometimes people are saying that God is out there. I was looking around attentively all day but I didn't find anybody there. I saw neither angels nor God". The utterance was used in Soviet anti-religion propaganda, but it was misattributed to Yuri Gagarin.

Following his space flight, Titov assumed various senior positions in the Soviet space programme until his retirement in 1992. In 1995, he was elected to the State Duma as a member of the Communist Party of the Russian Federation.

On 20 September 2000, he died of cardiac arrest in his sauna at the age of 65 in Moscow. He was buried in the Novodevichy Cemetery.

Awards and legacy
Gherman Titov was awarded the title Hero of the Soviet Union, two Orders of Lenin, and numerous medals and foreign orders. He was bestowed the title of the Hero of Socialist Labor of Bulgaria, Hero of Labour of Viet Nam and Hero of Mongolia. The Titov crater on the far side of the Moon and Titov Island in Ha Long Bay are named after him.

On 6 August 2011, the 50th anniversary of Titov's flight, the reconstructed and expanded Gherman Titov Museum was opened in his native village of Polkovnikovo, Altai Krai.

The Titov Space Centre is named after him.

Cultural references
In Arthur C. Clarke's 1982 book, 2010: Odyssey Two (and the 1984 film adaptation 2010), the opening scene features a conversation between Dimitri Moisevitch of the Soviet Space Council and Dr. Heywood Floyd. When Moisevitch informs Floyd that the Soviets will be travelling to Jupiter on their new spaceship the Cosmonaut Alexei Leonov, Floyd is puzzled, expecting that the ship was to be named after Gherman Titov. In the book, Moisevitch just mentions that it has been changed to Leonov; in the film, he comments without elaboration that Titov has fallen out of favour.

BBC Radio 4's Afternoon Play on 12 April 2011, Titanium, features Titov as narrator during the training and flight of Yuri Gagarin. It was part of a week to celebrate the 50th anniversary of Gagarin's flight.

Honours and awards

 * Russia and the USSR
 * Hero of the Soviet Union № 11158 (9 August 1961)
 * Order of Merit for the Fatherland, 3rd Class (7 September 1995) – for services to the state, achievements in work and significant contribution to strengthening friendship and cooperation between peoples
 * Two Orders of Lenin (17 June and 9 August 1961)
 * Order of the October Revolution (21 February 1985)
 * Order of the Red Banner of Labour (15 January 1976)
 * Lenin Prize (1988)
 * Medal "For the Development of Virgin Lands" (August 1961)
 * Honoured specialist of the Armed Forces of the USSR (15 August 1991) – for outstanding service to the Soviet state in the country's defence capacity and professional skill
 * Honoured Master of Sports (1961)
 * Pilot-cosmonaut of the Soviet Union (9 August 1961)
 * Honorary Citizen of Barnaul

Foreign awards

 * Hero of Labour of the Democratic Republic of Vietnam (21 January 1962)
 * Order of Ho Chi Minh (Vietnam)
 * Friendship Order (Vietnam)
 * Hero of Socialist Labour of the People's Republic of Bulgaria (27 September 1962)
 * Order of Georgi Dimitrov (Bulgaria, 27 September 1962).
 * Medal "25 Years of People's Power" (Bulgaria)
 * Medal "100th Anniversary of the Birth of Georgi Dimitrov" (Bulgaria, 14 February 1983)
 * Hero of the Mongolian People's Republic (10 December 1961)
 * Order of Sukhbaatar (Mongolia, 10 December 1961)
 * Medal "30 Years of Victory over Japan's militarist" (Mongolia, 8 January 1976)
 * Order of Karl Marx (East Germany, 1 September 1961)
 * Gold Medal "for exemplary work" (East Germany, 4 September 1961)
 * Star of the Republic of Indonesia, 2nd Class (9 January 1962)
 * Order of the Yugoslav Star with sash (19 September 1962)
 * Order of the Star of Romania, 1st Class (14 October 1961)
 * Order of the Star of the Republic of the Congo (Congo, 1965)
 * Order of Friendship and Cooperation (Syria, 1988)
 * Honour of the President of Ukraine (11 April 1995) – for outstanding contributions to the development of space rocket systems, the strengthening of international cooperation in space industry and in conjunction with the 10th anniversary of the first flight of the launch vehicle Zenit

title: Gherman Titov