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Template:Introduction to .NET Framework 3.0

 Introduction to .NET Framework 3.0

Preface — An Overview — Advantages of .NET 3.0 — An Overview of Master Pages — Caching — Generics — Nullable Types — Windows Presentation Foundation — Windows Communication Foundation — Windows Cardspace — Windows Workflow Foundation — Features of IIS 7.0 — Windows Powershell


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Template:ASP.NET

 ASP.NET

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

title: Template:ASP.NET


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Template:A Beginner's Guide to D

A Beginner's Guide to D

title: Template:A Beginner's Guide to D


text:
A Beginner's Guide to D/Before We Begin...

 * 1) /Short Introduction to D/
 * 2) /D Compiler/
 * 3) /Editors Supporting D/


text: Category:Book:A Beginner's Guide to D

title: Category:Book:A Beginner's Guide to D


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User:Roger Pilgham

Roger Pilgham is the pseudonym of a Dutchman who, while living in the USA in the 1990's, discovered so many possible ways of misspelling his name that he is now convinced of the utter pointlessness of using it in international cyberspace. For the WikiWorld, he aptly (if exaggeratedly) chose the name of a fictional character known for boldly and cheerfully altering other people's brainchilds beyond their recognition. Read more about Roger Pilgham.

In real life, the user calling himself Roger Pilgham is a professional food writer and journalist, science fiction fan, amateur musician, travel nut, news addict and cat lover. He is fluent in English, French, German and his native Dutch, speaks reasonable Italian and Spanish and can crudely communicate in Russian, Turkish, Catalan, Norwegian and Mandarin Chinese--all of which did not keep him from flunking a bachelorship in comparative linguistics. He professes himself bewilderment incarnate when it comes to adding the graphic niceties to his profile that he has spotted with other WikiWorlders, but hopes to eventually expand on the pitiful tidbit that is his current excuse for a profile.

title: User:Roger Pilgham


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Template:Abnormal Sexual Psychology

Abnormal Sexual Psychology

title: Template:Abnormal Sexual Psychology


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User:AA1.Intelligence

= Contributions =
 * HTML
 * Forms
 * Hyperlinks

Subpages:

title: User:AA1.Intelligence


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Plato/Euthyphro

This is a short dialogue between Socrates and Euthyphro and is a very good introduction to typical aspects of Plato's thought and the Socratic method. The Greek language of Euthyphro is less difficult than that in longer works such the Symposium or the Republic. This dialogue is placed first in the Oxford Classical Texts 'Platonis Opera'. In general this is a good place to start with Plato if you have at least a year's worth of classical Greek.

Overall the piece is an interesting introduction to Greek theology and has an exact parallel in modern Christian theology, still being commented on in the twentieth century by writers such as C.S. Lewis as a live question. In essence the question put is, 'Does God command that we do or not do things because they are good or bad in themselves, or because God is good? And if the right commands are 'good' in themselves, does God obey these laws or does he make them?' Socrates has himself been summonsed to court by his political enemies and while waiting meets Euthyphro there, who is bringing a charge of manslaughter (of a slave) against his father. Socrates finds this remarkable, but Euthyphro maintains that 'a crime is a crime', and as family relations do not come into it, he is merely doing the right and proper thing. Socrates enquires how he is so sure of himself, and Euthyphro replies that he is an expert on morality as he understands piety toward the gods so well.

Socrates proceeds to tie poor Euthyphro up in knots with his gentle questions, which however amount to the typical Socratic skewering and dissection of self-proclaimed experts. He asks, 'are the gods themselves good and righteous and holy?' The religious and pious Euthyphro thinks so. He asks, 'are the gods to be emulated because they are good?'. The religious and pious Euthyphro thinks so. But, Socrates asks, 'why then, accoding to the poets, do the gods do so many things that we humans disapprove of - such as, stealing, making war, and adultery?' Euthyphro is at a loss to talk his way out of this fuzzy thinking and self-contradictions: he is left defeated but still defiant. The answers may not have been presented 'on a plate', but the clarity of the right question is now indisputable. This first dialogue strongly presages the 'Apology' of Socrates in which he defends himself against the charges brought in his famous court defence speech.

title: Plato/Euthyphro


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Wikibooks:Book donations

Donating Books
Many times in the past, people and organizations have offered to donate books to Wikibooks. Wikibooks will accept donations of books under certain conditions, and the copyright holder of the book must agree to follow Wikibooks copyright restrictions and policies. This page will discuss book donations, how a book is eligible to be donated, and what is the process to donate an eligible book.

Authors are responsible for ensuring that their books to be donated are acceptable under the Wikibooks inclusion criteria policy. Wikibooks is not a general purpose ebook host and books that do not conform to this policy, regardless of anything else written in this document, may be deleted from Wikibooks.

If you have a book that you wrote yourself, or that you own the copyright on, and understand what it means to release your work under a free license, you can skip to the donation checklist below.

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Once all the above steps are satisfied, you may begin to upload your book to Wikibooks. Make sure that your new book follows our Naming Conventions. If you need help, ask at the Reading Room. Once you have uploaded your book, or if you need additional help, post a notice in the assistance reading room.

title: Wikibooks:Book donations


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Talk:Latin/Lesson 4-Principal Parts

Untitled
Correct me if I'm wrong, but isn't mansum the fourth principal part of maneo? Wouldn't sum (esse fui futurus) be a better example of a verb that usually uses a future participle as its fourth p.p.? --Hieronymous85 16:16, 17 August 2007 (UTC)

title: Talk:Latin/Lesson 4-Principal Parts


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XQuery/Adder

Motivation
We would like to create a simple XQuery that takes two arguments and returns the sum of the two numbers.

Example Program Using URL Parameters (HTTP GET)
Call this like.

Accumulating Adder
To make this into an interactive application, we can extend the script to create an XHTML document containing a Form.

The script computes the new sum from the URL parameters (if any) and returns a minimal XHTML document containing a Form which both reports the sum and prompts for new inputs. Note the embedded XQuery expressions (in curly braces) which interpolates the computed values into the created XML element. The state of the computation, the value of the accumulator, is retained in a hidden input in the form.

Try this

Clearing the accumulator
To support the operation of clearing the accumulator, we can add a couple of submit buttons to the form. The presence of the 'Clear' action is used to set the inputs to zero.

Try this with

Example Using Session Variables
An alternative way of holding the state of this computation is in session variables. The session module in eXist provides the necessary functions.

Try this with

title: XQuery/Adder


text:
File:Drambuie bw.jpg

Source: http://www.beveragewarehouse.com

Non-free use rationale
This image meets the following non-free use criteria:
 * No free alternative possible
 * If this is a promotional image from the company, then any "user-supplied" image whose sole purpose was clearly to represent the same copyrighted box/item art (and nothing else, and with no significant artistic input- i.e. a "mechanical" reproduction, whether by scanner or camera) would likely have the same restrictions.
 * Is being used to demonstrate the product and/or its marketing
 * Serves to demonstrate the product being discussed rather than being used in a solely decorative manner.
 * Does not deprive company of ability to make money in any way
 * Is not being used in misleading or misrepresentative manner

Disclaimer

 * Use of this non-free image of a proprietary product is not an endorsement of that product nor of the internet business from which the image was obtained. This image was obtained from a manufacturer's website or an online business selling that product. The source of the file is listed under the image. The owners of the trademark and the image are acknowledged.

/Images

title: File:Drambuie bw.jpg


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Basic Algebra/Introduction to Basic Algebra Ideas/Exponents and Powers

Vocabulary

 * Exponent: A number written in superscript that denotes how many times the base will be multiplied by itself.
 * Base (or radix): The number to be multiplied by itself.

Example: $$5^2=25$$

In this example, the base is 5 and the exponent is 2.

Lesson
We use exponents to show when we're multiplying the same number more than one time.

 * $$ 3 \times 3 = 3^{2}$$
 * Three times three equals three to the second power (or three squared)

 * $$3 \times 3 \times 3 = 3^{3}$$
 * Three times three times three equals three to the third power (or three cubed)

 * $$3\times3\times3\times3= 3^{4}$$
 * Three times three times three times three equal three to the fourth power

 * $$2\times2\times2 = 2^{3}$$
 * Two times two times two equals two to the third power

Note that any nonzero number raised to the 0 power is always equal to 1.

 * $$2^{0} = 1$$
 * Two to the zero power equals one

We can also raise any number to a negative exponent. This is called the inverse exponent and places the number on the bottom of a fraction with a 1 on top:

 * $$2^{-2} = \frac{1}{2^{2}} = \frac{1}{4}$$
 * Two to the negative two equals one over two to the second power

Example Problems
Let's evaluate these expressions.

 * $$7^{2}$$
 * Seven to the second power equals forty-nine.

 * What is the area of a square with a side of 3 meters length?
 * So, the area of a square with a side length of 3 meters is 9 square meters.

 * $$c^{2}$$ where $$c = 6$$
 * So, c squared is 36.

 * $$x^{3}$$ where $$x = 10$$.
 * So, x to the third power is 1000.

 * $$y^{4}$$ where $$y = 2$$
 * So, y to the fourth is 16.

 * $$3^{-3}$$
 * So, three to the negative third power equals one twenty-seventh.

Practice Games

 * http://www.math.com/school/subject2/practice/S2U2L2/S2U2L2Pract.html
 * http://www.quia.com/pop/50485.html (scientific notation)
 * http://www.softschools.com/math/games/exponents_practice.jsp
 * http://www.quia.com/quiz/358716.html (King Kong Scientific Notation)
 * http://www.shodor.org/interactivate/activities/OrderOfOperationsFou/ (order of operations including exponents)

Practice Problems
Use  as the fraction line!  {Evaluate the following expressions:}

{ $$6^{2}=$${ 36_5 }
 * type="{}"}

{ $$2^{3}=$${ 8_5 }
 * type="{}"}

{ $$4^{2}=$${ 16_5 }
 * type="{}"}

{ $$5^{3}=$${ 125_5 }
 * type="{}"}

{ $$2^{4}=$${ 16_5 }
 * type="{}"}

{ $$9^{2}=$${ 81_5 }
 * type="{}"}

{ $$8^{2}=$${ 64_5 }
 * type="{}"}

{ $$5^{-3}=$${ 1/125|0.008_5 }
 * type="{}"}

{ $$6^{0}=$${ 1_5 }
 * type="{}"}

{ $$7^{2}=$${ 49_5 }
 * type="{}"}

{ $$12^{2}=$${ 144_5 }
 * type="{}"}

{ $$2^{4}=$${ 16_5 }
 * type="{}"}


text:
Basic Algebra/Introduction to Basic Algebra Ideas/Chapter Test

 {== Section A (5 marks) == Evaluate the following expressions.}

{ $$24 \div 6 - 7 =$${ -3_2 }
 * type="{}"}

{ $$(5 + 3) \times 6=$${ 48_2 }
 * type="{}"}

{ $$\frac{16+14}{5} - 3=$${ 3_2 }
 * type="{}"}

{ $$\frac{36}{4 - (-2)}+5=$${ 11_2 }
 * type="{}"}

{ $$\left(\frac{2 \times 27}{9}\right)^2=$${ 36_2 }
 * type="{}"}

{== Section B (5 marks) == Evaluate the following expressions.}

{ $$9+3^2=$${ 18_2 }
 * type="{}"}

{ $$3+ \frac{20}{2^2} =$${ 8_2 }
 * type="{}"}

{ $$\frac {2(3+4)}{94^0}=$${ 14_2 }
 * type="{}"}

{ $$20 - 2 \left(\frac{96}{4^2}\right)=$${ 8_2 }
 * type="{}"}

{ $$-4 + 5 \left(\frac{56+7}{3^2}\right) - 1 =$${ 30_2 }
 * type="{}"}

{== Section C (5 marks) == Evaluate the following expressions when $$w=4$$, $$x=5$$, $$y=6$$ and $$z=7$$.}

{ $$3x+2y+z=$${ 34_2 }
 * type="{}"}

{ $$\frac{w^2}{y+2}+2z=$${ 16_2 }
 * type="{}"}

{ $$2 \left(\frac{x^2+3}{w}\right)-(2y-z)=$${ 9_2 }
 * type="{}"}

{ $$(6-3)\left(\frac{2w-x}{z-4}\right)+(3y-4)=$${ 17_2 }
 * type="{}"}

{ $$3^2(2w^0)\left(\frac{wx}{y-2}\right)-z=$${ 83_2 }
 * type="{}"}

{== Section D (6 marks)== Evaluate the value of $$x$$ in the following equations with the given value of $$y$$.}

{$$4x+3y=18$$ (given $$y=2$$) $$x=$${ 3_2 }
 * type="{}"}

{$$\frac{2x}{y+1}+4=20$$ (given $$y=3$$) $$x=$${ 32_2 }
 * type="{}"}

{$$2 \left(\frac{2x-2}{y-3}\right)+8=6^2$$ (given $$y=7$$) $$x=$${ 29_2 }
 * type="{}"}

{$$3^3+2^0+3x-2y \left(\frac{18}{2}\right)=97$$ (given $$y=3$$) $$x=$${ 41_2 }
 * type="{}"}

{$$[5(2x-3)]^2=y+6$$ (given $$y=19$$) $$x\in\{$${ 1_2 },{ 2_2 }$$\}$$
 * type="{}" coef="2"}


text:
Talk:Basic Algebra/Introduction to Basic Algebra Ideas/Order of Operations

I forsee a potential problem in explaining Order of Operations: None of the preceeding lessons define an "Operation". Should we explain binary (+,- for subtraction,*,/,^) and unary (- for negatives,square root) functions? I don't think that is a good idea if we haven't really introduced functions yet. I am not an educator; perhaps someone with experience could explain how they introduce order of operations to their students?

 * "Operations" are now (maybe already were) explained in lesson 1, not rigorously, but I think well enough for the purposes here. We can probably talk about unitary operations (and their precedence) once we get to them. Zahlen 04:40, 19 January 2007 (UTC)


text:
Talk:Basic Algebra/Introduction to Basic Algebra Ideas/Simple Operations

A Basic English Matter
We should use the gerund form for the names of operations (adding instead of addition, multiplying instead of multiplication). It is easier for a non-native speaker to understand. --Ezrakatz 05:58, 28 January 2007 (UTC)

The Minus Sign
The minus sign (in the font used for this page) is difficult to recognize. In this font, a dash would be a better choice than the hyphen.


text:
Basic Algebra/Introduction to Basic Algebra Ideas/Simple Operations

Vocabulary

 * Operation
 * Equals Sign
 * Adding
 * Subtracting
 * Multiplying
 * Dividing

Lesson
An operation is a thing you do to numbers. You use signs like: +, –, ×, or ÷ for operations.

The equals sign is not an operation. You use the " = " sign for the equals sign. It is a special sign that you put between two things that are the same.

Adding
Adding is a way to put two numbers together. You use the " + " sign for the adding operation. If you have 5 apples and a friend has 6 apples, you and your friend have 11 apples. This is 5 + 6 = 11 using the signs of Mathematics, and is read "five plus six equals eleven".

Order is not important when adding. 2 + 3 is the same as 3 + 2.

Subtracting
Subtracting is a way of taking a number from another number. It is the opposite of adding. You use the " – " sign for the subtracting operation. If you have 5 apples and give 3 to a friend, you then have 2 apples left. This is 5 – 3 = 2 using the signs of Mathematics, and is read "five minus three equals two".

Order is important when subtracting. 3 – 2 is not the same as 2 – 3.

Multiplying
Multiplying is a way of adding a number many times. You use the " × ", " • " or " * " sign for the multiplying operation. If you have 4 apple trees and every tree has 25 apples, you have 100 apples. This is 4 × 25 = 100 or 25 + 25 + 25 + 25 = 100 in the signs of Mathematics. The first way is shorter and easier to use.

Multiplying 25 by 4 is the same as adding 25, 4 times or adding 4, 25 times.

4 x 25 = 100 should be read "four times twenty-five equals one hundred".

Order is not important when multiplying. 2 × 3 is the same as 3 × 2.

Dividing
Dividing is a way of subtracting a number many times. It is the opposite of multiplying. You use the " ÷ " or " / " sign for the dividing operation. If 3 friends take an equal part of a bag of 12 apples, every friend gets 4 apples. Or, you may take away (subtract) 3 apples from the bag of 12 apples, exactly 4 times until the bag is empty. This is 12 ÷ 3 = 4 or 12 – 3 – 3 – 3 – 3 = 0 in the signs of Mathematics.

12 ÷ 3 = 4 should be read "twelve divided by three equals 4".

Order is important when dividing. 3 ÷ 2 is not the same as 2 ÷ 3.

Example Problems

 * 3 + 4 = 7
 * 5 – 3 = 2
 * 6 × 2 = 12
 * 13 + 14 = 27
 * 21 – 9 = 12
 * 8 × 3 = 24

Practice Games

 * Arcademics Grand Prix (Multiplication)
 * Arcademics Jet Ski (Addition)
 * Arcademics Sailboat (Subtraction)
 * Arcademics Drag Race (Division)

Practice Problems
 {Evaluate the following expressions:}

{ 6 + 8 = { 14_2 }
 * type="{}"}

{ 3 + 4 = { 7_2 }
 * type="{}"}

{ 10 + 15 = { 25_2 }
 * type="{}"}

{ 28 + 13 = { 41_2 }
 * type="{}"}

{ 12 - 5 = { 7_2 }
 * type="{}"}

{ 16 - 3 = { 13_2 }
 * type="{}"}

{ 7 × 5 = { 35_2 }
 * type="{}"}

{ 8 × 4 = { 32_2 }
 * type="{}"}

{ 6 × 6 = { 36_2 }
 * type="{}"}

{ 14 ÷ 7 = { 2_2 }
 * type="{}"}

{ 15 ÷ 3 = { 5_2 }
 * type="{}"}

{ 40 ÷ 5 = { 8_2 }
 * type="{}"}


text:
Basic Algebra/Introduction to Basic Algebra Ideas/Solving Equations Using Properties of Mathematics

Vocabulary

 * Associative Property of Addition
 * Associative Property of Multiplication
 * Commutative Property of Addition
 * Addition Property of Equality
 * Subtraction Property of Equality

Lesson
It is very important to show math in the simplest way. For example, $$\frac{5}{10}$$ is the same as $$\frac{1}{2}$$, but $$\frac{1}{2}$$ is better because it is easier to understand. The simplest answer is usually the best.

Associative Properties mean that you can do the problem in any order, and the answer will always be the same.

Commutative Properties mean that you can change the order of numbers around, and the answers will always be the same.

Equality Properties state that if two numbers on either side of the equation are equal, and the operation processed is the same, as well having the same variables in the operations, the result will be the same for both sides of the equation. Read the section devoted to the Addition and Subtraction Properties of Equality for more information.

Associative Property of Addition
The associative property of addition shows us that when adding multiple values together, the outcome will always be the same. You can group numbers together in parenthesis, and it will still end up having the same outcome. For example, $$3 + (4 + 5) = (3 + 4) + 5$$. The order remains the same, but the grouping has changed. The result, however, is consistent.

Associative Property of Multiplication
The associative properties work for both addition and multiplication. Think of grouping $$3 \times 3$$ together. You end up with 9. What about $$3 \times (3 \times 4)$$? If we change the grouping here, the result will be the same. Try to visualize why this is. When multiplying, you're often building objects in rows and columns.

For example, a 2 inch $$\times$$ 4 inch block will be 2 inches across, and 4 downward. If you had a block 4 inches across and 2 inches downward, it would be the same size overall. When you put objects in parenthesis, remember to do those operations first. You may end up with certain "sides" of the operation or object being larger or smaller, but the total area will always have the same outcome.

Commutative Property of Addition
The commutative property of addition shows that no matter what order numbers are in when we add them, the result will always be the same. For example, $$x + y = y + x$$, just how $$3 + 4 = 4 + 3$$. Even though the order in which we added has shifted, the result doesn't change, and the statements on both sides of the equal sign remain true.

Addition Property of Equality
The addition property of equality states that if two variables or numbers are equal to each other on each side of the equation, and the operation they go through is alike, the resulting sum will be the same. If for example, both $$x$$ and y are 6, and you add $$z$$ to each of them, that is,

if $$x = y$$ then $$x + z = y + z$$

or if $$6 = 6$$ then $$6 + z = 6 + z$$

Subtraction Property of Equality
The subtraction property of equality states that if two variables or numbers are equal to each other on each side of the equation, and the operation they go through is alike, the resulting difference will be the same. If for example, both $$x$$ and y are 6, and you subtract $$z$$ from each of them, that is,

if $$x = y$$ then $$x - z = y - z$$

or if $$6 = 6$$ then $$6 - z = 6 - z$$

Example Problems
Find $$x$$ where $$y=6$$.

 * $$\frac{x+y}{2}=14$$

 * $$(x-3y) + 2x = 15$$

 * $$\frac{15-y}{x}=y^2$$

Practice Games

 * http://www.math.com/school/subject2/S2U3Quiz.html
 * http://www.quia.com/rr/4096.html

Practice Problems
Answer should be correct to two decimals - round up or down accordingly until the answer is correct to two decimals  {Find $$x$$ where $$y=9$$}

{$$x=8\left(\frac{y}{3}\right)$$ Answer:{ 24_6 }
 * type="{}"}

{$$x-4=8+y$$ Answer:{ 21_6 }
 * type="{}"}

{$$\frac{14+x}{y}=3$$ Answer:{ 13_6 }
 * type="{}"}

{$$\frac{15-y}{x}=y^2$$ Answer:{ 0.07_6 }
 * type="{}"}

{$$\frac{1+y^2}{x-4}=17-y^2$$ Answer:{ 2.72_6 }
 * type="{}"}

{$$x+7-(y-9)=43y+3x-y^2$$ Answer:{ -149.5_6 }
 * type="{}"}

{$$\frac{12-x(45-y)}{y^2-67}=84$$ Answer:{ -32.33_6 }
 * type="{}"}


text:
Basic Algebra/Introduction to Basic Algebra Ideas/The Ideas of Algebra

Algebra is a way of working with numbers and signs to answer a mathematics problem (a question using numbers). You use Algebra in life.

It answers, for example, questions like these:

If I have 10 coins and need 25 coins to get a book, how many more coins do I need to get the book?

If you have 6 bottles of milk and you drink 2 bottles in a day, how many days will your milk last?

If you start running a race at a speed of 10 kilometers an hour, and your friend starts running 10 minutes later at a speed of 15 kilometers an hour, when will your friend catch up to you?

Algebra helps answer questions when building houses, making food, and doing science work.

This book will help you learn how to do mathematics using Algebra. It has chapters (parts of the book) with lessons (parts of the chapter about one idea).

A lesson has five parts:

 * 1) Vocabulary - lists special words you need for the lesson.
 * 2) Lesson - explains a new idea and how to use this idea.
 * 3) Example Problems - demonstrates the steps to complete problems using the new idea.
 * 4) Practice Games - provides entertaining challenges in which you complete math problems.
 * 5) Practice Problems - You practice your skills while completing problems.


text:
Basic Algebra/Introduction to Basic Algebra Ideas/Variables and Expressions

Vocabulary

 * Variable
 * Term
 * Operation
 * Expression
 * Evaluate
 * Substitute

Lesson
A variable is a letter or symbol that takes place of a number in Algebra. Common symbols used are $$a$$, $$x$$, $$y$$, $$\theta$$ and $$\lambda$$. The letters x and y are commonly used, but remember that any other symbols would work just as well.

Variables are used in algebra as placeholders for unknown numbers. If you see "3 + x", don't panic! All this means is that we are adding a number who's value we don't yet know.

Some examples of variables in use:
 * $$3x$$ -- three times of $$x$$.
 * $$5 - y$$ -- five minus $$y$$
 * $$2 \div s$$ or $$\frac {2}{s}$$-- 2 divided by $$s$$

A term is a number or a variable or a cluster of numbers and variables multiplied and or divided separated by addition and subtraction.

Examples of terms:
 * $$3 + 5$$ The terms are 3 and 5.
 * $$\frac {6}{x}$$  The term is $$6/x$$, 6 over $$x$$ is one term, because the operation is division.
 * $$6x + 5$$  The terms are 6$$x$$ and 5, 6$$x$$ and 5 are separate terms because they are separated by a addition or subtraction.

An operation is a thing you do to numbers, like add, subtract, multiply, or divide. You use signs like +, –, *, or / for operations.

An expression is one or more terms, with operations between all terms.

Examples of expressions:

 * $$3 \div 6$$
 * $$8 \times x$$
 * $$x \times 6 + y$$
 * $$a \times b \times c \times d$$

To evaluate an expression, you do the operations to the terms of an expression.

Examples of evaluating expressions:

 * $$3 + 4$$ evaluates to 7.
 * $$18 \div 3$$ evaluates to 6.
 * $$4 \times 5 - 3$$ evaluates to 17.

To evaluate an expression with variables, you substitute (put a thing in the place of an other thing) numbers for the variables.

Examples of substituting: (Substitute 3 for x in these examples.)
 * $$x + 4$$ is $$3 + 4$$.
 * $$18 \div x$$ is $$18 \div 3$$.
 * $$4 \times 5 - x$$ is $$4 \times 5 - 3$$.

Example Problems
Evaluate the following expressions

Practice Games

 * Evaluating expressions
 * Advanced Expression Evaluator

Practice Problems
remember order of operations

 {Evaluate each expression if $$a$$ = 1, $$b$$ = 2, $$c$$ = 3, and $$d$$ = 5.}

{ $$5 \times b=$${ 10_2 }
 * type="{}"}

{ $$9 \times c=$${ 27_2 }
 * type="{}"}

{ $$c-2=$${ 1_2 }
 * type="{}"}

{ $$d-5=$${ 0_2 }
 * type="{}"}

{ $$\frac{b}{2}=$${ 1_2 }
 * type="{}"}

{ $$\frac{36}{c}=$${ 12_2 }
 * type="{}"}

{ $$b \times c + 2=$${ 8_2 }
 * type="{}"}

{ $$b \times c \times d - 5=$${ 25_2 }
 * type="{}"}

{Evaluate each expression if $$x$$ = 4, $$y$$ = 2, and $$z$$ = 3.}

{ $$x+y=$${ 6_2 }
 * type="{}"}

{ $$2z=$${ 6_2 }
 * type="{}"}

{ $$xz=$${ 12_2 }
 * type="{}"}

{ $$x+y+z=$${ 9_2 }
 * type="{}"}

{ $$xy+z=$${ 11_2 }
 * type="{}"}

{ $$yz-x=$${ 2_2 }
 * type="{}"}

{ $$\frac{6}{y}+z=$${ 6_2 }
 * type="{}"}

{ $$\frac{2x}{2+y}=$${ 2_2 }
 * type="{}"}

{More harder questions:

Evaluate each expression if $$x$$ = 5, $$y$$ = 8, and $$z$$ = 9.}

{ $$(2+x) \times y=$${ 56_2 }
 * type="{}" coef="2"}

{ $$\frac {3y-9}{5}=$${ 3_2 }
 * type="{}" coef="2"}

{ $$\frac {27}{x+4} - (y-5)=$${ 0_2 }
 * type="{}" coef="2"}

{ $$\frac {z+12}{2x-3} + y=$${ 11_2 }
 * type="{}" coef="2"}

{ $$\left(\frac {6x}{2+y} - z\right)+\left(x- \frac{z}{3}\right)=$${ -4_2 }
 * type="{}" coef="2"}


text:
Talk:Basic Algebra/Introduction to Basic Algebra Ideas/Variables and Expressions

Let's not use "plugging in" as a metaphor for substitution. In a primitive environment, I don't know if it has the same familiarity. Use "put it in" instead.

Heheh, ok, but in a primitive environment, they won't have a computer... unless you are imagining some school in the middle of the african bush which happens to have internet connection and jotters and pencils but no workbooks, which i suppose makes some kind of sense. Can I ask, don't you think we need some kind of video perhaps introducing the topic? --213.217.194.176 13:49, 18 November 2006 (UTC)

Greek letters
I saw in the page that Greek letters are used as names of variables. Maybe it's a good idea to give an overview of the Greek alphabet in appendix or something. Here it is: α alpha β beta γ gamma δ delta ε epsilon ζ dzeta η eta θ theta ι iota κ kappa λ lambda μ mu ν nu ξ xi ο omicron π pi ρ rho ς sigma (end of a word, not used as a mathematical variable) σ sigma τ tau υ upsilon φ phi χ chi ψ psi ω omega

 * I don't think they're commonly introduced at an elementary level. They also aren't used so far in the examples for the first few lessons. I think it would be better to avoid their use altogether for this textbook. Zahlen 03:35, 19 January 2007 (UTC)

Answers in parentheses
Would it not make sense to show the solution for the first couple of problems only, and then to LINK to the solutions? Ideally the link would automatically open a new window (provided the code for that is compatible with simple browsers and low bandwidth).

 * I'm guessing this, or something similar will be implemented in the HSTutorial's static version. I don't think we need to worry too much about formatting for now. Zahlen 03:44, 19 January 2007 (UTC)

Expressions with more than 1 operation and Precedence
Should we be introducing long expressions like 6 x 3 - 4 in this lesson before precedence is introduced in lesson 3? As a mathematician, I'd say no, but I don't have experience teaching such topics to young children. Presently, I've edited the examples and problems so that operators with higher precedence are on the left, i.e no ambiguity arises between evaluating left to right and evaluating in order of precendence.

If we do decide to keep long expressions in this lesson, I think it would be a good idea to break up the evaluation process into steps, e.g. first evaluating 6 x 3 - 4 to 18 - 4, then finally to 14. Zahlen 03:44, 19 January 2007 (UTC)

Game
The lesson links to a game at http://www.quia.com/cm/29771.html. This game uses expressions like 7(9) to mean 7 * 9, which hasn't been taught (yet). We might still want to keep the link, if we can't find better games. (Will HSTutorials be making any games of their own?) Zahlen 04:16, 19 January 2007 (UTC)

Problem with definitions
I was just reading through this material to brush up on my own algebra. I don't know the definition of an expression but the definition here seems flawed to me. First a term is defined and we see that 6/x is one term. Expressions are defined next: "An expression is two or more terms, with operations between all terms.". Yet the list of example expressions starts with "3/4" and "8*n". By the definition of expressions above they are not expressions because they only consist of one term. My belief is that the examples are correct and the definition of expressions is wrong. But on the other hand teaching mathematics is not my field. --Tobbe


text:
Basic Algebra/Introduction to Basic Algebra Ideas/Working With Negative Numbers

Vocabulary

 * Positive
 * Negative

Negative Numbers
A positive number is a number greater than zero.

A negative number is a number less than zero. You make a negative number by doing the negative operation on a positive number. You use the " – " sign for the negative operation. This sign is the same you use for subtracting.

Adding and Subtracting
Adding a negative number is the same as subtracting a positive number.
 * $$ 7 + (-4) = 7 - 4$$
 * $$ x + (-y) = x - y$$

Subtracting a negative number is the same as adding a positive number.
 * $$ 7 - (-4) = 7 + 4$$
 * $$ x - (-y) = x + y$$

Multiplying and Dividing
Multiplying a negative number by a positive number, or a positive number by a negative number makes the result negative.
 * $$ (-2) \times 3 = -6$$
 * $$ 2 \times (-3) = -6$$

Multiplying a negative number by a negative number makes the result positive.

 * $$ (-2) \times (-3) = 6$$

You do the same for dividing.
 * $$ (-6) \div 3 = -2$$
 * $$ 6 \div (-3) = -2$$
 * $$ (-6) \div (-3) = 2$$

Exponentiating
Exponentiating a negative number to an even (a number you can divide by two) power makes the result positive.
 * $$ (-3)^2 = 9$$
 * $$ (-x)^2 = (-x) \times (-x) = x^2$$

Exponentiating a negative number to an odd (a number you can not divide by two) power makes the result negative.
 * $$ (-2)^3 = -8$$
 * $$ (-x)^3 = (-x) \times (-x) \times (-x) = x^2 \times (-x) = -x^3$$

Order of Operations
The negative operation has the same precedence as multiplying and dividing.

 * $$ 3 + 8 \div 4 = 3 + 2 = 5$$
 * $$ -3^2 = -(3 \times 3) = -9$$
 * $$ (-3)^2 = (-3) \times (-3) = 9$$

Example Problems

 * $$4 + (-4) = 0$$
 * $$4 + (-7) = -3$$
 * $$0 + (-2) = -2$$
 * $$-5 + 7 - 2 \times (-4) = 10$$

Practice Problems
 { $$6 + (-3) =$${ 3_3 }
 * type="{}"}

{ $$3 + (-9) =$${ -6_3 }
 * type="{}"}

{ $$-4 \times 4 = $${ -16_3 }
 * type="{}"}

{ $$ 4 \times (-9) = $${ -36_3 }
 * type="{}"}

{ $$-2 \times (-4) = $${ 8_3 }
 * type="{}"}

{ $$ \frac{-25}{5^2} = $${ -1_3 }
 * type="{}"}

{ $$-4 \div 2= $${ -2_3 }
 * type="{}"}


text:
Basic Algebra/Introduction to Basic Algebra Ideas/Order of Operations

Vocabulary

 * Order of Operations
 * The order of operations is the rule at which you apply operations within a mathematical formula. There are two common mnemonics.

In mathematics, we use BODMAS:

 * Brackets
 * Orders (e.g. exponents)
 * Division
 * Multiplication
 * Addition
 * Subtraction

In the United States, you may also see PEMDAS:

 * Parentheses
 * Exponents
 * Multiplication
 * Division
 * Addition
 * Subtraction

Other variations exist, but the rules for order of operations remain the same.

Lesson
Evaluate the expression $$3 + 4 \times 5$$.

1st solution - If you multiply first, it is $$3 + 20$$ and evaluates to 23.

2nd solution - If you add first, it is $$7 \times 5$$ and evaluates to 35.

Is the first or second answer correct?

With no order of operations, both answers would be expected, but if an expression evaluates to more than one answer, math becomes ambiguous and does not work. For math to work there is only one order of operations to evaluate a mathematical expression.

The order of operations is Parenthesis, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This can be remembered in two ways: "Please Excuse My Dear Aunt Sally" or PEMDAS. Please note that for Multiplication and Division and Addition and Subtraction you do whichever one comes first going from left to right, and that is why both PEMDAS and BODMAS work. The following list, from top to bottom, is the order of operations in Algebra. Operations at the top of the list are completed first, and operations on the same line are completed from left to right.

 * Parenthesis
 * Exponent ^
 * Multiply $$\times$$, Divide $$\div$$
 * Add $$+$$, Subtract $$-$$

Parenthesis is a special operation that has the most precedence. You use the ( and ) signs to make a separate expression from a group of terms. You evaluate an expression in parenthesis first. You use parenthesis if you need to do an operation with less precedence first. If the term in parenthesis is juxtaposed to a variable with no multiplication, then you treat this implicit multiplication the same as any other multiplication. (example: In $$1/2x$$, the $$2x$$ is a juxtaposed, implicit multiplication, so it means the same as $$1/2 \times x$$, and multiplication does not take precedence over the division in the Order of Operations. If you want $$2x$$ to be a proper term, you should write $$1/(2x)$$)

Example problems
Let's evaluate these expressions.

Back to the first problem: Evaluate the expression $$3 + 4 \times 5$$.

There is only one answer, 23, because we multiply first.

If we want to add first, we can use parentheses.

If we write $$(3 + 4) \times 5$$, then we add first, and get 35.

Practice games

 * http://www.quia.com/cm/11715.html
 * http://regentsprep.org/regents/math/orderop/orderPrac.htm

Practice problems
 {Evaluate the following expressions:}

{ 62 × (8 – 6) ={ 72_2 }
 * type="{}"}

{ 8 + 6 × 32 ={ 62_2 }
 * type="{}"}

{ 32 / 23 + 4 ={ 8_2 }
 * type="{}"}

{ 8 + 32 / 16 ={ 10_2 }
 * type="{}"}

{ 6 +(4 / 2)2 × 8={ 38_2 }
 * type="{}"}


text:
File:Anisette mb bevmax.jpg

Source: http://www.bevmax.com

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Disclaimer

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/Images

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text:
File:Arak wardy missionliquor.jpg

Sourcez: http://www.missionliquor.com

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 * If this is a promotional image from the company, then any "user-supplied" image whose sole purpose was clearly to represent the same copyrighted box/item art (and nothing else, and with no significant artistic input- i.e. a "mechanical" reproduction, whether by scanner or camera) would likely have the same restrictions.
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Disclaimer

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/Images

title: File:Arak wardy missionliquor.jpg


text:
File:Xtabentún argonaut.jpg

Source: http://www.argonautliqors.vom

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Disclaimer

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/Images

title: File:Xtabentún argonaut.jpg


text:
Cookbook:Mirepoix

In French cuisine, mirepoix is a mixture of finely diced vegetables used as a base for stocks, soups and stews. Typically it consists of two parts onion, and one part each of celery and carrot gently fried in butter or olive oil until soft. Leeks, bacon or herbs can sometimes be added.

title: Cookbook:Mirepoix


text:
User talk:Correctordj~enwikibooks

Hello and welcome to Wikibooks!

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 * Explore, be bold in editing pages, and have fun!

You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Staff lounge, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be an idea if you add this page to your "watchlist" so that you can see when any new information is posted there.

I see you have been doing some editing to the Muggles' Guide of late. Thank you for that, and if you have any questions at all, please feel free to contact me.

Good luck! Chazz (talk) 19:00, 17 August 2007 (UTC)

Your account will be renamed
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The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Correctordj. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Correctordj~enwikibooks that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

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title: User talk:Correctordj~enwikibooks


text:
User talk:AA1.Intelligence

Welcome
Hello, welcome to Wikibooks!

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Come introduce yourself at the new users page. If you have any questions, you can ask there or you cancontact me personally on my talk page. Just hit the "+" sign on the top of either page, and enter your question! Urbane  (Talk)   (Contributions)  20:21, 17 August 2007 (UTC)

title: User talk:AA1.Intelligence


text:
User talk:Jack2121~enwikibooks

Welcome
Hello, welcome to Wikibooks!

 * Wikibooks is a collection of open-source textbooks. Find out what this means.
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Explore, be bold in editing pages, and have fun!

Come introduce yourself at the new users page. If you have any questions, you can ask there or you cancontact me personally on my talk page. Just hit the "+" sign on the top of either page, and enter your question! Urbane  (Talk)   (Contributions)  20:23, 17 August 2007 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Jack2121. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Jack2121~enwikibooks that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:19, 17 March 2015 (UTC)

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title: User talk:Jack2121~enwikibooks


text:
File:Patxarana prodspain.jpg

Source: http://www.productsfromspain.com

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title: File:Patxarana prodspain.jpg


text:
File:Salmiakki Koskenkorva02.jpg

Source: http://upload.wikimedia.org/wikipedia/commons/a/ad/Salmiakki_Koskenkorva.jpg

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Disclaimer

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text:
User talk:Roger Pilgham

Welcome message
Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally.

You might also be interested to read our Cookbook policy page and talk to other Cookbook editors. Webaware talk 00:08, 18 August 2007 (UTC)

title: User talk:Roger Pilgham


text:
Cookbook:Welsh Fruit Bread (Bara Brith) I

| Welsh cuisine

Bara brith, sometimes known as "speckled bread" (the literal meaning of the original Welsh-language name), is a fruit bread which originated in Wales. It is traditionally made with raisins, Zante currants and candied peel. In Wales the fruit is traditionally soaked overnight in cold tea.

In Argentina, bara brith, which was brought to the country by the Welsh settlers who started arriving in Chubut province in 1865, is known as torta negra ("black cake") and is a traditional food item there.

There are many different recipes for this bread, which is baked and sold commercially in some parts of Wales. This recipe is adapted from Delia Smith’s Complete Cookery Course and Delia Smith's Illustrated Complete Cookery Course.

The bread has a limited shelf life and is best eaten as soon as possible.

Ingredients

 * 8 fl oz (225 ml) milk
 * 2 oz (50 g) brown sugar, plus 1 teaspoon
 * 4 level teaspoons dried yeast
 * 1 lb (450 g) strong plain flour
 * 1 level teaspoon salt
 * 3 oz (75 g) butter or margarine
 * 1 level teaspoon mixed spice
 * 1 egg, beaten
 * 12 oz (350 g) mixed dried fruit
 * Clear honey, to glaze
 * 2 lb (900 g) loaf tin, well greased

Procedure

 * 1) Warm the milk in a small pan until hand-hot. Put it into a bowl with 1 teaspoon of sugar and the yeast. Leave it in a warm place for about 15 minutes until a froth appears.
 * 2) Sift the flour and place in a large bowl with 2 oz (50 g) sugar and the salt. Rub the fat into the flour until it resembles fine breadcrumbs, then stir in the mixed spice. Add the egg and frothed yeast. Mix to a dough in the bowl before turning it out onto a floured surface. Knead until smooth and elastic. Place back into a bowl and cover with plastic film or a damp cloth. Leave it to rise in a warm place for about 90 minutes.
 * 3) After it has been left to stand, 'knock down' the dough and knead again, adding the fruit slowly.
 * 4) Place into a bread tin and put the tin into an oiled plastic bag. Leave to rise for about 35–40 minutes and preheat the oven to gas mark 5, 190°C (375°F).
 * 5) When the dough has risen and springs back when pressed, take the tin out of the bag and bake in the centre of the oven for about 30 minutes.
 * 6) Cover the top of the loaf tin with aluminium foil to stop it burning and bake for another 30 minutes.
 * 7) Take out of the oven and tap the bottom of the loaf, which should sound hollow—if not, bake it for another 5 minutes.
 * 8) Brush the honey onto the top of the loaf and cool it on a wire rack. Slice it thinly and serve buttered.


text:
User:Quasarstrider/Universal Religion Proposal

Hypothesis

 * We were originally shaped by a Supreme Entity.
 * Its Science was so advanced to us, eons ago, that it still seems like Magic.
 * Our original genetic code was seeded across the Universe.
 * Our mentors were a Triad Of Supreme Entities, asexual, thinking as One God in Order.
 * The Supreme Entities have many faces and are masters of disguise.
 * They show themselves in the shape most suited to convince the people they are speaking with.
 * They speak in the manner most fitting for the people of their time.
 * They wish to guide us in our path, using their Invisible Hand, inspiring people across the ages into great leaders: in times of chaos, distress, despair, and fear.

One acts as Father (hard, tends towards egoist)

 * Egyptian: Set/Anubis
 * Christians: Devil
 * Hindu: Khali/Shiva
 * Greek: Mars/Poseidon/Hades
 * Taoism: Yang

Plays Bad Cop.

Uses all means possible towards victory.

Father got impatient on sinful people. It started to make people fight themselves in ever greater wars. It stopped listening to Justice. Its blood lust got insatiable. Was punished for bad behavior and got softer with time.

One acts as Mother (soft, tends towards altruist)

 * Egyptians: Isis
 * Christians: Son; or rather, (as in the Greek Orthodox Church) the female Sophia ('Wisdom', a feminine name in Greek), already mentioned in book of Ecclesiates.
 * Hindu: Vishnu
 * Greek: Aphrodite/Hera/Athena
 * Taoism: Yin

Plays Good Cop.

Rallies people under the banner of Justice. Loves all creatures. Mother is growing weary of sinful people.

One acts as Judge (law giver)

 * Egyptians: Osiris
 * Christians: Father/Holy Spirit
 * Hindu: Brahma
 * Greek: Zeus

Creator of the Universe. Law giver. Arbiter of Father and Mother.

Conclusion
Other peoples believed in a Triad of Supreme Beings. Like the Daoists, Hindus, Norse and Hittites; and above all the Neo-Platonists, from whom the Christians shamelessly plagiarized their Trinity.

Our collective genetic memory, imprinted on all beings in this planet is:
 * 1) Survive
 * 2) Multiply
 * 3) Spread
 * 4) Use the least mass, energy and time possible

'''Our cardinal sin is the sin of pride, also named hubris. The arrogance of believing ourselves to be better than others. It blinds us, deafens us and weakens us all. The human genetic code is similar.'''

The Cardinal Sin of Man
 The cardinal sin of mankind is to believe that the Supreme Being must be a liar or a weakling, or even perhaps an ogre.
 * Liar: Christianity stakes the claim that either God the Son was a liar, pretending to be too weak to hinder humans from arresting him, etc.; or else a
 * Weakling: Alternatively, for Christians, God the Son was such a weakling that he could be easily taken prisoner by humans, easily tortured to death by humans, etc.; and even an
 * Ogre: As Son of the Christian God who sought in a typically ogrish fashion to condemn humans just for being human, Jesus Christ as his Son is a member of a family of treacherous ogres; and is, therefore, completely untrustworthy.


title: User:K1000~enwikibooks


text:
User talk:K1000~enwikibooks

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title: User talk:K1000~enwikibooks


text:
General Relativity/Introduction

General relativity (GR) is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915. According to general relativity, the observed gravitational attraction between masses results from the warping of space and time by those masses.

Before the advent of general relativity, Newton's law of universal gravitation had been accepted for more than two hundred years as a valid description of the gravitational force between masses. Under Newton's model, gravity was the result of an attractive force between massive objects. Although even Newton was bothered by the unknown nature of that force, the basic framework was extremely successful at describing motion.

However, experiments and observations show that Einstein's description accounts for several effects that are unexplained by Newton's law, such as minute anomalies in the orbits of Mercury and other planets. General relativity also predicts novel effects of gravity, such as gravitational waves, gravitational lensing and an effect of gravity on time known as gravitational time dilation. Many of these predictions have been confirmed by experiment, while others are the subject of ongoing research. For example, although there is indirect evidence for gravitational waves, direct evidence of their existence was also achieved by team of scientists in experiments such as the LIGO.

General relativity has developed into an essential tool in modern astrophysics. It provides the foundation for the current understanding of black holes, regions of space where gravitational attraction is so strong that not even light can escape. Their strong gravity is thought to be responsible for the intense radiation emitted by certain types of astronomical objects (such as active galactic nucleus or microquasars). General relativity is also part of the framework of the standard Big Bang model of cosmology.

Although general relativity is not the only relativistic theory of gravity, it is the simplest such theory that is consistent with the experimental data. Nevertheless, a number of open questions remain: the most fundamental is how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity.

In ordinary three-dimensional space the formula for distance in Cartesian coordinates is

$$ds^2 = dx^2 + dy^2 + dz^2 \,$$.

Now one can change the coordinate systems if one wants. If one rotates the coordinate system or stretches or shrinks it, the values for x, y, and z may change, but the distances will not. We can even conceive of more radical changes, like going into spherical coordinates where

$$ds^2 = dr^2 + r^2\sin^2{\theta}d\phi^2 + r^2d\theta^2 \,$$.

In special relativity we learned that physics is described by another invariant in which

$$ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2 \,$$.

Again, we are free to change the coordinates of x, y, z and t to anything we want, but the underlying geometry and distances don't change.

The next step is to incorporate gravity into this picture. While the mathematical details can be complex, the basic idea is that the effects of gravity are equivalent to the effects of acceleration on an observer. From this equivalence principle, Einstein was able to show that what matter does is to change the rules for distances. The formula we showed above is strictly true only when matter is not present; when matter is present, the rules for determining distances change, and the effect of these changes is to produce the effects of gravity we all know.

This picture of gravity is powerfully simple and elegant. However, there is one problem with it; in order for it to be usable, it is necessary to learn many new mathematical concepts to understand how this picture works.

In our daily lives, we have become very familiar with the properties of three-dimensional Euclidean space because that is the world we live in. In order to do anything such as walking, moving, or catching balls, our brains have to deal with 3-space and so we have a great deal of intuitive knowledge about how this sort of geometry works. Even when we are doing mathematics in three-dimensional space, we are helped by the fact that our minds have this sort of knowledge built in. However when we discuss other types of space, our normal intuition fails us, and we are forced to follow the much more difficult path of trying to figure out what happens by describing the situation through precise mathematical statements, and this involves learning several new mathematical concepts and techniques.

To give an example of the mathematical techniques we will have to learn. Imagine you are on the surface of a flat plane. One formula for distance is

$$ds^2 = dx^2 + dy^2 \,$$.

Another formula for distance in the plane in polar coordinates is

$$ds^2 = dr^2 + r^2d\theta^2 \,$$.

Now these two formula look quite different, but they are really two different descriptions of the same situation.

On the surface of a cylinder

$$ds^2 = dz^2 + r^2 d\theta^2 \,$$

we again have a formula which looks very similar to the distance in the plane expressed in polar coordinates: locally, the cylinder cannot be distinguished from the plane. Later on, we will give this a name: we call these flat surfaces.

However if we were on the surface of a sphere, then the distance for small changes in φ and θ is

$$ds^2 = r^2\sin^2{\phi}d\theta^2 + r^2d\phi^2 \,$$.

Now in this situation, the difference in the distance formula is not merely one in which we are using different coordinates to talk about the same thing, the thing that we are talking about is actually different. So this brings up a lot of questions. How do we know if the differences in distance formulas are real or are just differences in coordinate systems? Can we talk about distance formulas in a way that lets us naturally distinguish between real differences rather than ones that are the result of our descriptions? How can we classify different geometries? All of this may be intuitively obvious when we are talking about three-dimensional spaces or two-dimensional objects such as spheres embedded in three dimension space. However, in order to talk about the behavior of four-dimensional space-time geometries, we need to rely on mathematical statements to get us answers.

Fortunately, mathematicians such as Riemann worked this all out in the start of the 19th century. However to understand how to deal with weird geometries, we will need to learn a few more concepts, such as the concept of a tensor.

title: General Relativity/Introduction


text:
Talk:GIMP/Toolbox

Page
I started to update it last time. Maybe table in every section? Maybe just one row but it could look better. Look here. Soeb (talk) 17:49, 27 March 2008 (UTC)
 * Doesn't matter anymore. Should be as it is. Soeb (talk) contrib 17:52, 18 November 2008 (UTC)

Actually got a new idea. The page would be one table. You can see some concept in my first sandbox. Notice that the links to images are wrong on purpose. If the moving would actually happen, new naming should be used. Also the page is not finished when I'm writing this. Although it will be soon. Soeb talk|contribs 14:54, 5 February 2009 (UTC)

 * Great idea, Soeb. I didn't actually see this post until you notified me, I don't have many pages on watchlist. I think you should go ahead with your idea. Be bold. It is a wiki, after all. --Chelseafan528 (talk) 17:03, 9 February 2009 (UTC)

 * Thanks, I'll finish the page and update it here to the new design. And this was actually a drastic change to the overall look of the article, so I wanted to confirm if it is going to be accepted. Soeb talk|contribs 19:17, 9 February 2009 (UTC)

Done Soeb talk|contribs 20:44, 3 April 2009 (UTC)

Use tool names as links
The user interaction for getting more information is broken, when you see a title for information, you mark it as a link... when someone wants more information for the 'foreground select tool' they should select the text 'foreground select tool' NOT 'here' —Preceding unsigned comment added by StephenG (discuss • contribs) 2009-05-04T12:20:14
 * Sorry for such a late response. I fully agree with this and I'll update it right now. Soeb talk|contribs 07:23, 6 June 2010 (UTC)

title: Talk:GIMP/Toolbox


text:
User talk:JTL~enwikibooks

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. -- Herby talk thyme 10:29, 18 August 2007 (UTC)

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title: User talk:JTL~enwikibooks


text:
Bartending/Mixers/Simple syrup

Simple syrup is a solution of sugar dissolved in water used to sweeten cocktails (to balance tart citrus or similar). Many older cocktail recipes call for regular sugar to be added, but it is difficult to make sugar dissolve in a cold cocktail, often resulting in a grainy texture or unincorporated sugar resting at the bottom of the glass, both of which are usually undesirable. Simple syrup incorporates much more easily, and thus is a useful ingredient to have on hand.

This can be made in many ways, but is most often made by heating a 1:1 ratio of standard refined sugar and water until it begins to simmer, then removing it from heat and continuing to stir until all the sugar has dissolved. It is also possible to do the same with raw sugars such as demerara, which will result in a much more rich, caramel-like solution. Also, if one continues to heat a simple syrup solution, the sugars will break down into component sugars, resulting in a different flavour. Feel free to experiment with varieties and ratios to find the formula appropriate for your tastes and what cocktails you are making.

Regardless, it is an important ingredient to have on hand, as many cocktails call for it, and it can help greatly in rounding out and bringing together flavours.

Rock candy syrup and gomme are sugar syrups like simple syrup, though they are supersatured and thus have a much higher sugar content. Additionally, gomme contains gum arabic to help keep the sugar in solution. In practice, the three syrups can be used interchangeably with proper adjustment to the drink recipe.

title: Bartending/Mixers/Simple syrup


text:
Talk:Macroeconomics/Math Review

Very interesting topic. I wonder why is this under Macroeconomics? This is the point that is not clear for me yet and would be delighted to learn. Laz 12:18, 18 August 2007 (UTC)
 * This is background for intertemporal utility maximization, which is the basis for much of the type of freshwater macro done by people like Prescott and Sargent et al. Smmurphy (talk) 16:26, 7 September 2009 (UTC)

This is quite absurd, in context. It is not in any way relevant to the introductory MacroEconomics presented.

title: Talk:Macroeconomics/Math Review


text:
User talk:77.99.118.67

You are doing excellent work on the Muggles' Guide.

Please create an ID for yourself, so we can welcome you properly and recognize you if your IP address changes.

Thank you. Chazz (talk) 17:11, 18 August 2007 (UTC)

title: User talk:77.99.118.67


text:
User:JTL~enwikibooks

www.hartech.cn

title: User:JTL~enwikibooks


text:
User talk:Deepthought~enwikibooks

Hello and welcome to Wikibooks!

Here are some tips to help you get started:
 * You should sign your name on Talk and vote pages using four tildes, like this: ~~~~.
 * Remember to conduct any editing experiments in the sandbox.
 * If you're a Wikipedian, see Wikibooks for Wikipedians for a primer on how things work here (it's a little different).
 * If you want to base your work here on materials from Wikipedia, please use WB:RFI to bring the material over in compliance with the GFDL.
 * If you're an instructor and plan on using wikibooks for a class project, see Guidelines for class projects
 * Please say hello at the Staff Lounge with any questions or ideas.
 * Eventually, you might want to read the Manual of Style and Policies and Guidelines.
 * Please take a look at Naming policy before starting a new book.
 * Remember to maintain a Neutral point of view.
 * Explore, be bold in editing pages, and have fun!

You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Staff lounge, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be an idea if you add this page to your "watchlist" so that you can see when any new information is posted there.

Meanwhile, I note that you are editing in the Muggles' Guide quite a lot. I do appreciate the commentary you are putting in there; you do seem to have quite the handle on what is going on in the series. If you have any questions, please feel free to ask me at any time. And good luck... Chazz (talk) 18:28, 18 August 2007 (UTC)

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title: User talk:Deepthought~enwikibooks


text:
Talk:Programming Mac OS X with Cocoa for Beginners/Containers - arrays, and dictionarys

Spelling
Shouldn't it be dictionaries?

Yes. It should. I can't figure out how to fix that. Zav


text:
Arabic/definiteArticle

The definite article ("the" in English) is "al" (spelled ال alif, la'm). It is pronounced with the same sound as the name of the letter "L" (i.e. el). It basically does what the word "the" does; it goes before a definite noun. But it has two extra jobs, because in Arabic, small words like "of" and "is" are not used. To illustrate: the striked-out words in the following English sentences would not translate into an Arabic word once the sentence is translated. The boy is on the roof. The sky is blue. The girls are here. I am going away. We are there. The book of the boy is here. Luckily, the definite article helps indicate where "is/are/am", and "of" would be. Whenever there are two words, one definite (i.e. starts with "L") and one indefinite (starts without "L"), if the first is definite then you know that "is/are/am" is implied between the two words. If the first is indefinite then you know that "of" is implied between the two words.

Summary
(Y) means some noun (Z) means some other noun → means "translates to" l- indicates the Arabic definite article l-(Y)      →  the (Y) l-(Y) (Z)  →  the (Y) is (Z) (Y) l-(Z)  →  the (Y) of the (Z)

Translation Exercise
book  كِتابُ keetaab airport مَطارُ Mataar restaurant مَطعَمُ mat3am title/address عُنوانُ unwan big كَبيرُ kabeer small صَغيرُ sagheer

ا
 * 1) الكتاب،al ketaab
 * 2) المطار، al mataar
 * 3) المطعم،al mat3am
 * 4) الكتاب صغير.al ketaab sagheer
 * 5) المطار كبير.al mataar kabeer
 * 6) المطعم صغير.al mat3am sagheer
 * 7) عنوان المطار
 * 8) عنوان المطعم
 * 9) عنوان الكتاب.

Key

 * 1) The book.
 * 2) The airport.
 * 3) The restaurant.
 * 4) The book is small.
 * 5) The airport is big.
 * 6) The restaurant is small.
 * 7) The address of the airport.
 * 8) The address of the restaurant.
 * 9) The title of the book.

title: Arabic/definiteArticle


text:
User talk:Alsalamah

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. Mattb112885 (talk to me) 10:24, 19 August 2007 (UTC)

title: User talk:Alsalamah


text:
User talk:Cjbonk

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. -- Herby talk thyme 10:47, 19 August 2007 (UTC)

The Practice of Learning Theories
Hello Cjbonk. I've seen you create two new pages recently: How can we end the POLT?, and Introducing the POLT. Am I right in assuming that these pages are supposed to be part of The Practice of Learning Theories? If so, they are not properly named, and need to be moved. I can help, if this is the case. Please let me know. You can leave the answer here, I will read this page waiting for a reply. --Whiteknight (Page) (Talk) 02:35, 12 December 2007 (UTC)
 * I notice that you've added your email in plaintext. While there's policy which says this is wrong, we discourage it because it makes that email susceptible to spam. MediaWiki (the software Wikibooks runs on) has an integrated email feature; you can set an email in your preferences where you can be reached. This also doesn't show your email to those sending you emails through the wiki, so it has added privacy. You can link to the email interface like this: Special:Emailuser/Username . Happy editing! – Mike.lifeguard  | talk 05:02, 12 December 2007 (UTC)

title: User talk:Cjbonk


text:
User talk:Sebastian~enwikibooks

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title: User talk:Sebastian~enwikibooks


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User talk:LJG59

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title: User talk:LJG59


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User talk:Frj1947~enwikibooks

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The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

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title: User talk:Frj1947~enwikibooks


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User talk:Griffcb~enwikibooks

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title: User talk:Griffcb~enwikibooks


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User talk:Cuneo~enwikibooks

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The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

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title: User talk:Cuneo~enwikibooks


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User talk:Kier07

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title: User talk:Kier07


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User talk:Hieronymous85

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title: User talk:Hieronymous85


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User talk:AnessaPJ

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title: User talk:AnessaPJ


text:
User talk:Dlaz

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title: User talk:Dlaz


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User talk:Safiyu

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title: User talk:Safiyu


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User talk:Rkrish67

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title: User talk:Rkrish67


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User talk:ConradPino

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title: User talk:ConradPino


text:
User talk:Brequinda~enwikibooks

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. -- Herby talk thyme 10:47, 19 August 2007 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Brequinda. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Brequinda~enwikibooks that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:00, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 04:42, 19 April 2015 (UTC)

title: User talk:Brequinda~enwikibooks


text:
User talk:Yael~enwikibooks

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. -- Herby talk thyme 10:47, 19 August 2007 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Yael. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Yael~enwikibooks that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:54, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 05:39, 19 April 2015 (UTC)

title: User talk:Yael~enwikibooks


text:
User talk:Collinpark

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. -- Herby talk thyme 10:47, 19 August 2007 (UTC)

title: User talk:Collinpark


text:
User talk:Angelas

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. -- Herby talk thyme 10:47, 19 August 2007 (UTC)

title: User talk:Angelas


text:
User talk:Max0x7ba

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. -- Herby talk thyme 10:47, 19 August 2007 (UTC)

title: User talk:Max0x7ba


text:
User talk:Guitarist Nick

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. -- Herby talk thyme 10:47, 19 August 2007 (UTC)

title: User talk:Guitarist Nick


text:
User talk:Hudsontng

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. -- Herby talk thyme 10:47, 19 August 2007 (UTC)

title: User talk:Hudsontng


text:
User talk:Longelegantlegs

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. -- Herby talk thyme 10:48, 19 August 2007 (UTC)

title: User talk:Longelegantlegs


text:
User talk:Jillskor

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. -- Herby talk thyme 10:48, 19 August 2007 (UTC)

title: User talk:Jillskor


text:
User talk:Openelfar

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. -- Herby talk thyme 10:48, 19 August 2007 (UTC)

Hi!
Yes! Yes! Yes!

Sorry I did not respond to your message earlier. I am very excited to at last have someone on board. I was feeling too lonely and have hardly made any contribution to this book in the last year.

Good to know that you have some material to contribute. The best way to discuss about this project would be on the discussion page of a particular topic. The page on Orthopaedic surgery would suit me fine. Otherwise you could contact me at: bduttabaruah[at]gmail.com

Lets get something, anything for that matter, started on this project and I am sure we can gather more as we roll along. BDB 05:16, 24 October 2007 (UTC)

title: User talk:Openelfar


text:
User talk:Ajedony

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. -- Herby talk thyme 10:48, 19 August 2007 (UTC)

title: User talk:Ajedony


text:
User talk:AndyCunningham

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. -- Herby talk thyme 10:48, 19 August 2007 (UTC)

title: User talk:AndyCunningham


text:
User talk:Sonofkirby

Welcome
Hello, welcome to Wikibooks!

 * Wikibooks is a collection of open-source textbooks. Find out what this means.
 * To sign your name (on talk pages), use four tildes, like this: ~~~~
 * For help in using the wiki, see the editing guide.
 * Explore, be bold, and have fun!
 * For site news, see the Bulletin board.

Explore, be bold in editing pages, and have fun!

Come introduce yourself at the new users page. If you have any questions, you can ask there or you cancontact me personally on my talk page. Just hit the "+" sign on the top of either page, and enter your question! Urbane  (Talk)   (Contributions)  12:58, 19 August 2007 (UTC)

title: User talk:Sonofkirby


text:
User talk:Alwaybepreparedcom

Welcome
Hello, welcome to Wikibooks!

 * Wikibooks is a collection of open-source textbooks. Find out what this means.
 * To sign your name (on talk pages), use four tildes, like this: ~~~~
 * For help in using the wiki, see the editing guide.
 * Explore, be bold, and have fun!
 * For site news, see the Bulletin board.

Explore, be bold in editing pages, and have fun!

Come introduce yourself at the new users page. If you have any questions, you can ask there or you cancontact me personally on my talk page. Just hit the "+" sign on the top of either page, and enter your question! Urbane  (Talk)   (Contributions)  12:58, 19 August 2007 (UTC)

title: User talk:Alwaybepreparedcom