61. An Interactive Proof Of Pythagoras' Theorem Home page of the grand prize winner in Sun Microsystem's Java programming contest in 1995.Category Computers Programming Contests Personal Pages......UBC Mathematics Department http//www.math.ubc.ca/. An Interactive Proofof pythagoras' theorem. This Java applet was written by Jim Morey. http://www.sunsite.ubc.ca/LivingMathematics/V001N01/UBCExamples/Pythagoras/pytha

UBC Mathematics Department http://www.math.ubc.ca/ An Interactive Proof of Pythagoras' theorem This Java applet was written by Jim Morey . It won grand prize in Sun Microsystem's Java programming contest in the Summer of 1995. http://www.math.ubc.ca/ Return to Interactive Mathematics page

62. Pythagoras' Theorem pythagoras' theorem. pythagoras theorem asserts that for a right triangle withshort sides of length a and b and long side of length c a 2 + b 2 = c 2. 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

63. Pythagoras' Haven The following window shows a geometrical proof of pythagoras' theorem. The threebuttons, NEXT, BACK, RESTART, allow you to go through the steps of the proof. http://java.sun.com/applets/archive/beta/Pythagoras/

The following window shows a geometrical proof of Pythagoras' Theorem. The three buttons, NEXT, BACK, RESTART, allow you to go through the steps of the proof. As well, if you would like to repeat the action of the diagram simply click on the image. (The text can be retyped by clicking on the text box). Good luck understanding the proof. This will hopefully turn into a place for geometric proofs of the Pythagorean Theorem the square of the hypotenuse of a right angle triangle is equal to the sum of the squares of the other two sides. Take a look at the poorly documented program and its helpers Banner and fillTriangle this hacked from the hotjava people my home page

64. Babylonian Pythagoras pythagoras's theorem in Babylonian mathematics. pythagoras's theorem in Babylonianmathematics This shows a nice understanding of pythagoras's theorem. http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Babylonian_Pythagoras.html

65. Pythagorean Theorem Pythagorean theorem. Information of Products. http://www.ies.co.jp/math/java/geo/pythagoras.html

Pythagorean Theorem Information of Products

66. Pythagoras Theorem(2) pythagoras theorem(2). pythagoras theorem. Applet. How to use this applet. Drag thered point. Reference pythagoras theorem OYA,Shinichi, 1975, Tokai univ. Press http://www.ies.co.jp/math/java/samples/pytha2.html

Pythagoras Theorem(2) Pythagoras Theorem Applet How to use this applet Drag the red point. Press "Define" button. Drag five pieces of quadrilaterals to fit in the square below. Reference "Pythagoras Theorem" OYA,Shinichi, 1975, Tokai univ. Press

67. Pythagorean Theorem Rotates around the opposite vertex. move, Drag the central red point. Reference pythagoras theorem OYA, Shinichi, 1975, Tokai University Press. http://www.frontiernet.net/~imaging/pythagorean.html

Pythagorean Theorem Java applet can't run : Your browser is not Java enabled. Java applet can't run : Your browser is not Java enabled. Drag the red point. Press "Define" button. Drag five pieces of quadrilaterals to fit in the square below. Select a rectangle by clicking on the "green" or "pink" radio button. Select the transformation from "shift", "rotate", and "move". shift Drag the red points on the sides. rotate Drag the red points on the vertices. Rotates around the opposite vertex. move Drag the central red point. Reference "Pythagoras Theorem" OYA, Shinichi, 1975, Tokai University Press. The above applets, images, and text were created by IES Inc (International Education Software ), a producer of educational software in Japan. Manipula Math with Java is a collection of more than 70 applets illustrating mathematical concepts including Trigonometry and Calculus created by IES Inc. "Imaging the Imaginged" (this site) mirrors these two applets, presenting them as excellent examples of using graphics, interaction, and Java for providing an enhanced educational experience efficiently and effectively using the combined power of the internet, Java, and the machine you are now using. I've written an Interactive Quadric Surface Rendering I've mirrored these applets to facilitate faster access to them for users here in the United States and to present them in the slightly modified context with a greater emphasis on the the advantages of using graphics and interaction

68. NOVA Online | The Proof | Pythagorean Puzzle A fun look at the man and one of his bestknown equations. Includes Shockwave demonstration. From Category Kids and Teens School Time Math Mathematicians pythagoras...... who lived over 2,000 years ago during the sixth century BCE pythagoras spent a putit another way Check it outyou can show that the Pythagorean theorem works http://www.pbs.org/wgbh/nova/proof/puzzle/

Pythagorean Puzzle Here's the deal; there was this Greek guy named Pythagoras, who lived over 2,000 years ago during the sixth century B.C.E. Pythagoras spent a lot of time thinking about math, astronomy, and music. One idea he came up with was a mathematical equation that's used all the time, for example in architecture, construction, and measurement. His equation is simple: a b c Or, to put it another way: Check it outyou can show that the Pythagorean theorem works. Shockwave version (Get Shockwave here non-Shockwave version Andrew Wiles Math's Hidden Woman ... WGBH

69. Pythagorean Theorem pythagoras, for whom the famous theorem is named, lived during the 6th centuryBC on the island of Samos in the Aegean Sea, in Egypt, in Babylon and in http://scidiv.bcc.ctc.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

70. Pythagorean Theorem - Wikipedia The Pythagorean theorem or pythagoras' theorem is named for and attributed to the6th century BC Greek philosopher and mathematician pythagoras, though the http://www.wikipedia.org/wiki/Pythagorean_theorem

Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help Other languages: Deutsch Polski Pythagorean theorem From Wikipedia, the free encyclopedia. The Pythagorean theorem or Pythagoras' theorem is named after and commonly attributed to the 6th century BC Greek philosopher and mathematician Pythagoras , though the facts of the theorem were known before he lived. The theorem states a relationship between the areas of the squares on sides of a right triangle The sum of the areas of the squares on the legs of a right triangle is equal to the area of the square on the hypotenuse. (A right triangle is one with a right angle ; the legs are the two sides that make up the right angle; the hypotenuse is the third side opposite the right angle; the square on a side of the triangle is a square, one of whose sides is that side of the triangle). Since the area of a square is the square of the length of a side, we can also formulate the theorem as:

71. Pythagoras's Theorem -- From MathWorld pythagoras's theorem, Pappas, T. Irrational Numbers the pythagoras theorem. TheJoy of Mathematics. San Carlos, CA Wide World Publ./Tetra, pp. 9899, 1989. http://mathworld.wolfram.com/PythagorassTheorem.html

Geometry Plane Geometry Squares Number Theory ... Irrational Numbers Pythagoras's Theorem Proves that the polygon diagonal d of a square with sides of integral length s cannot be rational . Assume is rational and equal to where p and q are integers with no common factors. Then so and , so is even. But if is even , then p is even . Since is defined to be expressed in lowest terms, q must be odd ; otherwise p and q would have the common factor 2. Since p is even , we can let , then . Therefore, , and , so q must be even . But q cannot be both even and odd , so there are no d and s such that is rational , and must be irrational In particular, Pythagoras's constant is irrational . Conway and Guy (1996) give a proof of this fact using paper folding, as well as similar proofs for (the golden ratio ) and using a pentagon and hexagon Irrational Number Pythagoras's Constant Pythagorean Theorem References Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 183-186, 1996. Gardner, M. The Sixth Book of Mathematical Games from Scientific American. Chicago, IL: University of Chicago Press, p. 70, 1984. Pappas, T. "Irrational Numbers & the Pythagoras Theorem."

72. A Proof Of The Pythagorean Theorem By Liu Hui A proof of the Pythagorean theorem by Liu Hui (third century AD).Historia mathematica, 1985, 12, pp. 713. In this Web version I http://www.staff.hum.ku.dk/dbwagner/Pythagoras/Pythagoras.html

A proof of the Pythagorean Theorem by Liu Hui (third century AD) Historia mathematica , pp. 71-3. In this Web version I have included Chinese characters, which were not in the published version. Some statements here are no longer up to date, but I have not made any major changes. Donald B. Wagner Reverdilsgade 3, 1.th DK-1701 Copenhagen V Denmark dbwagner@hum.ku.dk If your e-mail is rejected by our server, please check www.orbs.org and try this address instead: dbwagner@spam.hum.ku.dk Department of Asian Studies University of Copenhagen Leifsgade 33 DK-2300 Copenhagen S Denmark Fax +45-3532 8835 The Jiuzhang suanshu (Arithmetic in nine chapters) is a Chinese mathematical book, probably of the first century A.D. Chapter 9, on right triangles, consists of 24 problems together with algorithms for their solution, with no explanation. The Pythagorean Theorem is introduced by the first three problems: If [the length of] the shorter leg [of a right triangle] is 3 chi , and the longer leg is 4 chi , what is the hypotenuse? Answer: chi If the hypotenuse is 5 chi , and the shorter leg is 3 chi , what is the longer leg?

73. Theorem 12 (Pythagoras) opposite the longest side. theorem 12 is also called the theorem ofpythagoras although it was known before pythagoras was even born! http://www.teachnet.ie/tbrophy/theorem12.html

Theorem 12: In a right-angled triangle, the square of the length of the side opposite to the right angle is equal to the sum of the squares of the lengths of the other two sides. The converse, that means the opposite, of this theorem is also true. In other words Theorem 13: If the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle has a right angle and this is opposite the longest side. Theorem 12 is also called the Theorem of Pythagoras although it was known before Pythagoras was even born! To demonstrate this we will make use of Theorem 8 . This theorem tells us that if we have a triangle whose base is x units long and whose height is y units then it has an area given by one half of xy

74. Proofs Of The Pythagorean Theorem The Choupei, an ancient Chinese text, also gives us evidence that the Chinese knewabout the Pythagorean theorem many years before pythagoras or one of his http://jwilson.coe.uga.edu/EMT668/EMT668.Student.Folders/HeadAngela/essay1/Pytha

Pythagorean Theorem by Angie Head This essay was inspired by a class that I am taking this quarter. The class is the History of Mathematics . In this class, we are learning how to include the history of mathematics in teaching a mathematics. One way to include the history of mathematics in your classroom is to incorporate ancient mathematics problems in your instruction. Another way is to introduce a new topic with some history of the topic. Hopefully, this essay will give you some ideas of how to include the history of the Pythagorean Theorem in the teaching and learning of it. We have been discussing different topics that were developed in ancient civilizations. The Pythagorean Theorem is one of these topics. This theorem is one of the earliest know theorems to ancient civilizations. It was named after Pythagoras, a Greek mathematician and philosopher. The theorem bears his name although we have evidence that the Babylonians knew this relationship some 1000 years earlier. Plimpton 322 , a Babylonian mathematical tablet dated back to 1900 B.C., contains a table of Pythagorean triples. The Chou-pei , an ancient Chinese text, also gives us evidence that the Chinese knew about the Pythagorean theorem many years before Pythagoras or one of his collegues in the Pythagorean society discovered and proved it. This is the reason why the theorem is named after Pythagoras.

75. The Pythagorean Theorem Lesson The Pythagorean theorem. This lesson will allow you to figure out the Pythagoreantheorem all by yourself. Go ahead and click on the preface link. http://www.arcytech.org/java/pythagoras/

The Pythagorean Theorem This lesson will allow you to figure out the Pythagorean Theorem all by yourself. Go ahead and click on the preface link. Preface Objective of this lesson Quick review Tip Number 1 ... Lesson Description (for teachers) Acknowledgments Last Updated: Sunday, 25-Mar-2001 03:00:44 GMT Arcytech Java Home Page Provide ... Feedback

76. The History Of Pythagoras And His Theorem The History of pythagoras and his theorem. Even though the theorem was known longbefore his time, pythagoras certainly generalized it and made it popular. http://www.arcytech.org/java/pythagoras/history.html

The History of Pythagoras and his Theorem In this section you will learn about the life of Pythagoras and how it is that the theorem is known as the Pythagorean Theorem. Be aware that there are no good records about the life of Pythagoras, so the exact dates and other issues are not known with certainty. In addition, the names of some of the people as well as the places where Pythagoras lived may have different spellings. Pythagoras was born in the island of Samos in ancient Greece . There is no certainty regarding the exact year when he was born, but it is believed that it was around 570 BC That is about 2,570 years ago! Those were times when a person believed in superstitions and had strong beliefs in gods, spirits, and the mysterious. Religious cults were very popular in those times. Pythagoras of Samos Pythagoras' father's name was Mnesarchus and may have been a Phoenician. His mother's name was Pythais. Mnesarchus made sure that his son would get the best possible education. His first teacher was Pherecydes, and Pythagoras stayed in touch with him until Pherecydes' death. When Pythagoras was about 18 years old he went to the island of Lesbos where he worked and learned from Anaximander, an astronomer and philosopher, and Thales of Miletus, a very wise philosopher and mathematician. Thales had visited Egypt and recommended that Pythagoras go to Egypt. Pythagoras arrived in Egypt around 547 BC when he was 23 years old. He stayed in Egypt for 21 years learning a variety of things including geometry from Egyptian priests . It was probably in Egypt where he learned the theorem that is now called by his name.

77. Pythagoras' Theorem pythagoras' theorem. pythagoras' theorem states that Proof of pythagoras'theorem. Cut out four congruent rightangled triangles. http://www.mathsteacher.com.au/year9/ch04_pythagoras/01_hypotenuse/pythag.htm

Year 9 Interactive Mathematics Teacher™ www.mathsteacher.com.au 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. That is: Pythagoras' Theorem was discovered by Pythagoras, a Greek mathematician and philosopher who lived between approximately 569 B.C. and 500 B.C. Proof of Pythagoras' Theorem Cut out four congruent right-angled triangles. Place them as shown in the following diagram. The figure ABCD is a square with side length a + b , and it consists of the four congruent right-angled triangles and a square, EFGH , with side length c This proof was devised by the Indian mathematician, Bhaskara, in 1150 A.D. Applications of Pythagoras' Theorem Pythagoras' Theorem is used to find the length of the third side of a right-angled triangle when the lengths of two other sides are known. Finding a Hypotenuse Example 1 Find the length of the hypotenuse of the right-angled triangle shown in the diagram.

78. Pythagoras' Theorem GCSE Maths Shape and space pythagoras' theorem pythagoras' theorem connects thelengths of two sides of a rightangled triangle with the length of the third http://www.projectgcse.co.uk/maths/pythagoras.htm

Click here for GCSE coursework! G C S E subject: English Maths Biology Chemistry ... Shape and space Pythagoras' theorem connects the lengths of two sides of a right-angled triangle with the length of the third side. It only works with right-angled triangles Pythagoras' theorem is r = x + y Where r is always the side opposite the right angle, and x and y are the other two sides. Phythagoras' theorem can be rearranged to find any of the three sides of a triangle. Remember that the length is not r but it is r (i.e. don't forget to root the answer). HOME GCSE bookshop Take a break GCSE coursework ... Click here! Page by: Richard Tang

79. Pythagoras' Theorem Home Java - pythagoras theorem. pythagoras' theorem. by Jim Morey fromthe University of British Columbia (scroll down for instructions). http://pirate.shu.edu/~wachsmut/Java/Pythagoras/Pythagoras.html

Home Java Pythagoras' Theorem by Jim Morey from the University of British Columbia (scroll down for instructions).

80. Pythagoras' Theorem pythagoras' theorem. pythagoras's theorem In any rightangled triangle, the squareof the hypotenuse is equal to the sum of the squares of the other two sides. http://www.revision-notes.co.uk/revision/742.html

RevisionNotes.Co.Uk - Free Revision and Course Notes for UK Students Home GCSE Maths Trigonometry : Pythagoras' Theorem Revision Notes GCSE A-Level University IB User Options Search My Revision Notes Bookmark Page Contribute Contribute Work Other Sites Essay Bank Coursework.Info Custom Research Pythagoras' Theorem Save this page for later viewing View Saved Pages Pythagoras's Theorem In any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. i.e.: c² = a² + b² in the following diagram: from revision-notes.co.uk Example Find AC in the diagram below. AB² + AC² = BC² AC² = BC² - AB² AC = revision-notes.co.uk Other Notes in this Category Bearings Congruency Intercept Theorem Pythagoras' Theorem ... Sine and Cosine Formulae Didn't find this useful? Visit Coursework.Info for over 14,000 GCSE, A-Level and University Essays

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