21. Project MATHEMATICS!--Theorem Of Pythagoras Contents. The program begins with three reallife situations that lead to the same mathematical problem Find the length of one side of a right triangle if the lengths of the http://www.projectmathematics.com/pythag.htm

The Theorem of Pythagoras Video Segments Three questions from real life Discovering the Theorem of Pythagoras Geometric interpretation Pythagoras Applying the Theorem of Pythagoras Pythagorean triples The Chinese proof Euclid's elements Euclid's proof A dissection proof Euclid's Book VI, Proposition 31 The Pythagorean Theorem in 3D Contents The program begins with three real-life situations that lead to the same mathematical problem: Find the length of one side of a right triangle if the lengths of the other two sides are known. The problem is solved by a simple computer-animated derivation of the Pythagorean theorem (based on similar triangles): In any right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs. The algebraic formula a + b = c is interpreted geometrically in terms of areas of squares, and is then used to solve the three real-life problems posed earlier. Historical context is provided through stills showing Babylonian clay tablets and various editions of Euclid's Elements . Several different computer-animated proofs of the Pythagorean theorem are presented, and the theorem is extended to 3-space.

22. The Theorem Of Pythagoras ... Key To Proof The theorem states that the area of the large white square (square of the hypoteneuse) in the following diagram http://www.math.uwaterloo.ca/navigation/ideas/grains/pythagoras-key.shtml

/* Changed to use separate display and positioning CSS March 28 2007 */ @import url("/coreTemplates/CSSFiles/layout/positioning2Col.css"); @import url("/coreTemplates/CSSFiles/display/fontDefaults.css"); @import url("/coreTemplates/CSSFiles/display/MathExtraFonts.css"); @import url("/coreTemplates/CSSFiles/print/MathPrint.css") print; @import url("/coreTemplates/CSSFiles/mobile/MathMobile.css") handheld; Search Math uwaterloo.ca Math Home About Math Depts,Schools and Programs Graduate Studies and Research ... UW Home The key to the proof of the theorem of Pythagoras The theorem states that the area of the large white square (square of the hypoteneuse) in the following diagram is equal to the sum of the areas of the two squares (of the two sides) in the next diagram It's important to notice that the orange triangle in both pictures is the same one, just rotated to better show the squares (and to match the animation). The proof begins by changing the solid white square to a blue one outlined in white. Then the same orange triangle is placed at each side of the square. The inside edges of the four triangles form the hypoteneus square. The outside edges of these four triangles form a large outer square.

23. The Pythagorean Theorem Note If your WWW browser cannot display special symbols, like ² or 2 or ±, then click here for the alternative Pythagorean Theorem page. http://www.jimloy.com/geometry/pythag.htm

Return to my Mathematics pages Go to my home page The Pythagorean Theorem click here for the alternative Pythagorean Theorem page The Pythagorean Theorem states: Proof #1: The simplest proof is an algebraic proof using similar triangles ABC, CBX, and ACX (in the diagram): This proof is by Legendre, and was probably originally devised by an ancient Hindu mathematician. Euclid's proof is quite a bit more complicated than that. It is actually surprising that he did not come up with a proof similar to the above. But, his proof is clever, as well. Proof #2: Here is another nice proof: We start with a right triangle (in gold, in the diagram) with sides a, b, and c. We then build a big square, out of four copies of our triangle, as shown at the left. We end up with a square, in the middle, with sides c (we can easily show that this is a square). We now construct a second big square, with identical triangles which are arranged as in the lower part of the diagram. This square has the same area as the square above it. We now sum up the parts of the two big squares: These two areas are equal: Proof #3: This diagram might look familiar. I've just drawn the squares on the sides of our right triangle. And, I've drawn a line from the right angle of the triangle, perpendicular to the hypotenuse, through the square which is on the hypotenuse. The idea is to prove that the little square (in blue) has the same area as the little rectangle (also in blue). I've named the width of this rectangle, x.

24. THE THEOREM OF PYTHAGORAS POSTER - GEYER Instructional Aids THE THEOREM OF PYTHAGORAS POSTER THEOREM OF PYTHAGORAS POSTER (24 inches x 34 inches The Theorem of Pythagoras PosterTaking literally the statement about the squares on the http://www.geyerinstructional.com/325cc78de2db96ab09c7aab023259b1a.item

Home Contact Us About Us Search for Store Math Department POSTERS GENERAL MATH POSTERS THE THEOREM OF PYTHAGORAS POSTER The Theorem of Pythagoras Poster Taking literally the statement about the squares on the hypotenuse and the other two sides, this poster llustrates the well known theorem in a colorful and instructive way. It also shows a simple trigonometrical proof and draws attention to the special sets of numbers known as Pythagorean triples. There is also a nice pointer to other geometrical representations of the theorem. 24½ x 34½. THE THEOREM OF PYTHAGORAS POSTER Price: $12.00 QTY THEOREM OF PYTHAGORAS POSTER (24 inches x 34 inches Main Contact Us Request Catalog Index of Complete Catalog ... About Us United States or Canada orders only.

25. Pythagoras' Theorem It contains 365 more or less distinct proofs of Pythagoras Theorem. The total effect is perhaps a bit overwhelming, and the quality of the figures is very http://www.sunsite.ubc.ca/DigitalMathArchive/Euclid/java/html/pythagoras.html

Pythagoras' Theorem Pythagoras Theorem asserts that for a right triangle with short sides of length a and b and long side of length c a + b = c Of course it has a direct geometric formulation. For many of us, this is the first result in geometry that does not seem to be self-evident. This has apparently been a common experience throughout history, and proofs of this result, of varying rigour, have appeared early in several civilizations. We present a selection of proofs, dividing roughly into three types, depending on what geometrical transformations are involved. The oldest known proof Proofs that use shears (including Euclid's). These work because shears of a figure preserve its area. Some of these proofs use rotations, which are also area-preserving. Proofs that use translations . These dissect the large square into pieces which one can rearrange to form the smaller squares. Some of these are among the oldest proofs known. Proofs that use similarity . These are in some ways the simplest. They rely on the concept of ratio, which although intuitively clear, in a rigourous form has to deal with the problem of incommensurable quantities (like the sides and the diagonal of a square). For this reason they are not as elementary as the others. References Oliver Byrne

26. On The Theorem Of Pythagoras transcription http://www.cs.utexas.edu/users/EWD/ewd09xx/EWD975.PDF

27. Math Forum: A Proof Of The Pythagorean Theorem and we know that the Babylonians knew about the Pythagorean theorem about 1000 years before the time of Pythagoras (born in 572 B.C.). http://mathforum.org/isaac/problems/pythagthm.html

The Pythagorean Theorem A Math Forum Project Table of Contents: Famous Problems Home The Bridges of Konigsberg The Value of Pi Prime Numbers ... Links The Pythagorean theorem is one of the most famous in all of mathematics. It states: Theorem: The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the legs. There are many different proofs of the theorem (even one supplied by President Garfield in 1876!), and we know that the Babylonians knew about the Pythagorean theorem about 1000 years before the time of Pythagoras (born in 572 B.C.). Nonetheless, a rigorous, general proof of the theorem requires the development of deductive geometry, and thus it is thought that Pythagoras probably supplied the first proof. Most math historians credit him with a proof by dissection, which relies on the use of two squares, one inscribed inside the other. The Indian astronomer Bhaskara (1114-1185) developed this proof: to Probability: Summary and Problems to a Proof that e is irrational Home The Math Library Quick Reference Search ... Help http://mathforum.org/

28. Theorem Of Pythagoras A*a + B*b = C*c NTNUJAVA Virtual Physics Laboratory Physics Simulations to help you enjoy the fun of physics! http://www.phy.ntnu.edu.tw/~hwang/abc/Pythagoras.html

NTNUJAVA Virtual Physics Laboratory Physics Simulations to help you enjoy the fun of physics! October 31, 2010, 03:06:58 PM Welcome, Guest . Please login or register Did you miss your activation email? 1 Hour 1 Day 1 Week 1 Month Forever Login with username, password and session length News : This site host hundreds of physics related java simulations under create common license. All registered user will be able to get files for offline use when user login and view the simulation. Switch to this new system on 2007/02/14. (previous system ) ,Check out Chinese forum to find more simulations and resources in Chinese. This topic This board Entire forum Home Help Search Login ... Register Youe can not help men permanently by doing for them what they could and should do for themselves. ..."Abraham Lincoln(1809-1865, US President 1861-1865" NTNUJAVA Virtual Physics Laboratory Physics Simulations to help you enjoy the fun of physics! JDK1.0.2 simulations (1996-2001) Misc ... Theorem of Pythagoras a*a + b*b = c*c Pages: [ Go Down Print Author Topic: Theorem of Pythagoras a*a + b*b = c*c (Read 31385 times) Members and 1 Guest are viewing this topic.

29. Pythagoras Theorem - Homepage Most people have heard of Pythagoras and know that is something to do with geometry but not much else? Many of the things that we take for granted such as http://www.pythagorastheorem.co.uk/

Pythagoras Theorem > Home > Resources > Contact Useful Links sites for parents sites for teachers Sponsored Links Introduction to Pythagoras Most people have heard of Pythagoras and know that is something to do with geometry but not much else? Many of the things that we take for granted such as satellite navigation, mobile telephones and air travel all use the principles that Pythagoras proved over two thousand year ago. What is Pythagoras? Pythagoras He also founded a religious movement called Pythagoreanism which had many followers. Pythagoreans believed that many things in life could be explained by mathematics. Pythagoras is best known for proving the Pythagorean Theorem , as it is known in the US , or Pythagoras Theorem in the UK , which has been used by scientists, students, mathematicians and engineers in their daily lives ever since. Many things which we take for granted nowadays would not be possible if it was not for Pythagoras Theorem. What's Pythagoras Theorem? Pythagoras' theorem states that in any right angled triangle , the square of the hypotenuse is equal to the sum of the squares of the other two sides.

30. Theorem Of Pythagoras In cases where you might need assistance with algebra and in particular with logarithmic or functions come pay a visit to us at Mathisradical.com. We have got a large amount of http://www.mathisradical.com/theorem-of-pythagoras.html

Algebra Tutorials! Sunday 31st of October Home Exponential Decay Negative Exponents Multiplying and Dividing Fractions 4 ... Angles and Degree Measure Theorem of Pythagoras With Applications The so-called Theorem of Pythagoras states that for a right triangle, it is always true that c = a + b Recall that in a right triangle, the longest side, opposite the right angle, is called the hypotenuse . Thus the Theorem of Pythagoras states that for right triangles the square of the length of the hypotenuse = the sum of the squares of the lengths of the other two (shorter) sides If the lengths of any two sides of a right triangle are known, then the length of the remaining third side can be computed using this formula. (In the examples that follow, we will observe the convention that for right triangles, the right angle is always labelled C, and the other two angles are labelled A and B. The labels for the sides are the lower-case characters of the angles opposite. So, the side opposite the right angle vertex is always labelled c, the side opposite vertex A is always labelled a, and the side opposite vertex B is always labelled b. These symbols are somewhat loosely used simply as names of these parts of the triangle, and as well, in formulas, they represent the sizes of the parts. Thus b is a label for the side opposite vertex B, but in a formula, the symbol b stands for the length of that side. Similarly, the symbol B is a label for a vertex, but also, in formulas represents the size of the angle at the vertex, in some appropriate unit of measurement such as degrees.)

31. Cabdev Montessori - Montessori Materials & Supplies - Economy Line - Mathematics Theorem of Pythagoras Cabdev Montessori has been supplying Montessori Materials throughout Canada and the United States since 1972. http://www.cabdevmontessori.com/product.php?productid=21857

32. Pythagoras Theorem File Format PDF/Adobe Acrobat Quick View http://www.haeseandharris.com.au/samples/ibmyp5plus-2_04.pdf

33. History Of Pythagorean Theorem The Pythagorean theorem got its name from ancient Greek mathematician Pythagoras , who was considered to be first to give proof of this theorem. http://www.buzzle.com/articles/history-of-pythagorean-theorem.html

Home World News Latest Articles Escape Hatch ... Endless Buzz History of Pythagorean Theorem The Pythagorean theorem got its name from the ancient Greek mathematician Pythagoras, who was considered to be the first to give proof of this theorem. But it is believed that people noticed the special relationship between the sides of a right triangle long before Pythagoras... The Pythagorean theorem plays a significant role in many fields related to mathematics . For example, it forms the basis of trigonometry, and in its arithmetic form, it combines both to geometry and algebra. The theorem is a relation in Euclidean geometry among the three sides of a right triangle. It states that ' the sum of the squares of the lengths of the two other sides of any right triangle will equal the square of the length of the hypotenuse Mathematically, the theorem is usually written as: a + b = c - where a and b represent the lengths of the two other sides of the triangle and c represents the length of the hypotenuse. History The history of the Pythagorean theorem can be divided as: knowledge of Pythagorean triples, the relationship among the sides of a right triangle and their adjacent angles, and the proofs of the theorem. Around 4000 years ago, the Babylonians and the Chinese were aware of the fact that a triangle with the sides of 3, 4 and 5 must be a right triangle. They used this concept to construct right angles and designed a right triangle by dividing a long string into twelve equal parts, such that one side of the triangle is three, the second side is four and the third side is five sections long.

34. Famous Theorems Of Mathematics/Pythagoras Theorem - Wikibooks Jul 16, 2010 The Pythagoras Theorem or the Pythagorean theorem, named after the Greek . Like most of the proofs of the Pythagorean theorem, http://en.wikibooks.org/wiki/Famous_Theorems_of_Mathematics/Pythagoras_Theorem

35. Theorem Of Pythagoras Video Introduction. You are going to investigate the Theorem of Pythagoras using two interactive tools that will help you understand the relationship between the areas of the http://www.blackgold.ab.ca/ict/divison3/pythagoras/

Video Introduction You are going to investigate the Theorem of Pythagoras using two interactive tools that will help you understand the relationship between the areas of the squares on each side of a right triangle. This theorem has many practical uses, particularly in the area of architectural design. In this activity you will: Explore Square Roots Investigate the Theorem of Pythagoras Use the Theorem of Pythagoras to Solve Problems You should save a copy of the tables and questions to complete as you use the tools.

36. MathsNet: Interactive Pythagoras's Theorem MathsNet Interactive Pythagoras s Theorem a collection of resources for education, aimed at students, teachers and anyone else. http://www.mathsnet.net/dynamic/pythagoras/index.html

part of This is the Interactive Pythagoras's Theorem website Pythagoras Most, if not all, of the facts about Pythagoras are disputed by historians. He did not write anything himself so all information has been provided by others - either his followers or later historians. The following is agreed by many to be approximately true! Pythagoras was born about 569 BC in Samos, Ionia and died about 475 BC. Pythagoras argued that there are three kinds of men. The lowest consists of those who come to buy and sell, and next above them are those who come to compete. Best of all are those who simply come to look on. These pages explain the famous mathematical result known as Pythagoras's Theorem , give you various interactive proofs of the theorem, problems based on the theorem, and mathematical things related to the theorem.

37. Theorem Of Pythagoras | Facebook Welcome to a Facebook Page about Theorem of Pythagoras. Join Facebook to start connecting with Theorem of Pythagoras. http://www.facebook.com/pages/Theorem-of-Pythagoras/128560520988

Theorem of Pythagoras 65 people like this. to connect with Wall Info Fan Photos Theorem of Pythagoras + Others Theorem of Pythagoras Just Others Theorem of Pythagoras edited their Members Genre and Hometown August 29, 2009 at 3:56am Theorem of Pythagoras External: Theorem of Pythagoras - The Weekly Theorem #2 August 29, 2009 at 3:45am Theorem of Pythagoras Theorem spielt am 11. September in langen weißen Mänteln auf der Bühne vorm Slobos/Stadtmühle Winzerfest August 29, 2009 at 3:42am See More Posts English (US) Español More… Download a Facebook bookmark for your phone. Login Facebook ©2010

38. Pythagorean Theorem Pythagoras, for whom the famous theorem is named, lived during the 6th century B.C. on the island of Samos in the Aegean Sea, in Egypt, in Babylon and in http://scidiv.bellevuecollege.edu/math/pythagoras.html

The Pythagorean Theorem Pythagoras, for whom the famous theorem is named, lived during the 6th century B.C. on the island of Samos in the Aegean Sea, in Egypt, in Babylon and in southern Italy. Pythagoras was a teacher, a philosopher, a mystic and, to his followers, almost a god. His thinking about mathematics and life was riddled with numerology. The Pythagorean Theorem exhibits a fundamental truth about the way some pieces of the world fit together. Many mathematicians think that the Pythagorean Theorem is the most important result in all of elementary mathematics. It was the motivation for a wealth of advanced mathematics, such as Fermat's Last Theorem and the theory of Hilbert space. The Pythagorean Theorem asserts that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: a b c The figure above at the right is a visual display of the theorem's conclusion. The figure at the left contains a proof of the theorem, because the area of the big, outer, green square is equal to the sum of the areas of the four red triangles and the little, inner white square: c ab a b ab a ab b a b Math Homepage BCC Homepage

39. The Theorem Of Pythagoras The theorem of Pythagoras is one of the earliest and most important results in the history of mathematics. It has immense practical value and led to the discovery of irrational http://www.stats.uwaterloo.ca/~rwoldford/pythagoras.html

Pythagoras (fl. 500 BCE) The theorem of Pythagoras is one of the earliest and most important results in the history of mathematics. It has immense practical value and led to the discovery of irrational numbers - a right triangle with unit sides leads via Pythagoras to the square root of 2! For further history: St. Andrews' history of Mathematics site Theorem of Pythagoras Given any right angle triangle, if one forms a square on each side of that triangle then the area of the largest square (that of the hypoteneuse) is equal to the sum of the areas of the two smaller squares (those which are formed on the sides about the right or 90 degree angle). Proof of the theorem is demonstrated through the following Quicktime animation. Use the controls to animate the movie. Notes on the demonstration: Textual details of the proof are intentionally absent from the movie. This encourages the student to work through why this is in fact a proof and how they might produce a formal proof based on the demonstration. Alternatively an instructor might like to fill in these details before/during/after the demonstration.

40. Unit 3 Section 1 : Pythagoras' Theorem Pythagoras Theorem relates the lengths of the sides in a rightangled triangle Pythagoras theorem states that if you square the two shorter sides in a http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i3/bk8_3i1.htm

Unit 3 Section 1 : Pythagoras' Theorem Pythagoras' Theorem relates the lengths of the sides in a right-angled triangle. A right-angled triangle has one angle of 90°. The side opposite the right angle is always the longest side, and is called the hypotenuse The diagram on the left shows a right-angled triangle. The lengths of the sides are 3cm, 4cm and 5cm. The hypotenuse is the 5cm side because it is opposite the right-angle and it is the longest side Now look at the diagram on the right. A square has been drawn on each of the sides of the triangle above. We are going to examine the areas of each of the squares. Shorter sides The square on the 3cm side has an area of 3cm × 3cm = 9cm². The square on the 4cm side has an area of 4cm × 4cm = 16cm². Hypotenuse The square on the 5cm side has an area of 5cm × 5cm = 25cm². How they are related If you add together the areas of the squares on the two shorter sides, you get 25cm². This is the same as the area of the square on the hypotenuse. Pythagoras' Theorem Pythagoras' theorem states that if you square the two shorter sides in a right-angled triangle and add them together, you

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