61. AV #83237 - Video Cassette - The Theorem Of Pythagoras AV 83237 The theorem of pythagoras to introduce the mathematical problemsolved by the Greek mathematician Pythagoras how to use the known lengths of http://www.sfsu.edu/~avitv/avcatalog/83237.htm

AV# 83237 The Theorem of Pythagoras Video Cassette - 22 minutes - Color - 1988 Problems from real life are used to introduce the mathematical problem solved by the Greek mathematician Pythagoras - how to use the known lengths of two sides of a right triangle to determine the length of the third side. Pythagorean triples, the Chines e proof, the Euclidean proof and the Pythagorean theorem in three dimensions are also explained. Access Policy for this Title Search AV Library Titles for: Last modified on July 28, 2005 by av@sfsu.edu

62. Geometry 201 You will encounter the theorem of pythagoras and its applications in many othermath classes, 1, 10.1, The theorem of pythagoras, 115 Journal Entry http://www.math.ksu.edu/~mdd8191/Project/geometry.html

Mr. Smith's Home Page In an isosceles triangle, the sum of the square roots of the two equal sides is equal to the square root of the third side. The Scarecrow in The Wizard of Oz by L.Frank Baum Geometry 201 Course Information Course Overview Course Text and Supplies Assessment Current Unit:Chapter 10 (Pythagorean Theorem) ... Links to Geometry Course Overview Dear Geometry Explorer, Welcome to Geometry 201! The focus of this course is on the practical applications of geometry. It is also designed so that you have fun with geometry. In Geometry 210 you "learn by doing." You will learn the tools of geometry and to perform geometric investigations with them. Your investigations will lead you to geometric discoveries. Many of the geometric investigations are carried out in small cooperative groups in which you jointly plan and find solutions with your fellow students. When working cooperatively, you can accomplish much more than you can individually. Best of all, you will have less anxiety and a whole lot more fun. Additionally, you will use the technology provided by a graphing calculator and Geometer's Sketchpad to help in your investigations. Return to the top of page.

63. Bryn Mawr Classical Review 2004.09.21 Perhaps the fundamental error is to take the theorem of pythagoras as the canonical or the most developed version of this mathematical phenomenon, http://ccat.sas.upenn.edu/bmcr/2004/2004-09-21.html

Bryn Mawr Classical Review 2004.09.21 Corinna Rossi, Architecture and Mathematics in Ancient Egypt . Cambridge: Cambridge University Press, 2004. Pp. 280. ISBN 0-521-82954-2. $100.00. Word count: 2784 words Corinna Rossi's Architecture and Mathematics in Ancient Egypt is the revised version of the author's doctoral dissertation submitted to the University of Cambridge. The main purpose of the book is to analyze aspects of Egyptian architectural design in relation to select mathematical phenomena that are specifically Egyptian. Rossi maintains that scholars have mostly approached Egyptian architecture from modern mathematical perspectives rather than from the perspective of Egyptian mathematics itself. The other major error against which Rossi cautions time and again is the search by modern scholars for geometrical relations within plans of Egyptian monuments. The author argues that although many of these relations are possible to discover a posteriori from the plan, this does not necessarily mean that they were intended by the builders, or that they truly constituted the geometric bases of the designs. This is a problem that in fact pervades the study of ancient and medieval monuments in general. Rossi also very explicitly signals throughout the book that she does not intend to unfold 'mysteries' or 'secrets' about Egyptian monuments as many have tried to do since time immemorial, or provide formulae that will explain proportions in Egyptian architecture, arguing that whatever formulae or mathematical devices the Egyptians resorted to must have been very simple and straightforward rather than esoteric. Regardless of secrets and formulae, however, in a book with the present title, one still would have liked to see clearer elements of

64. Ask E.T.: E.T. Course Videos: Pythagorean Theorem And Viz-O-Matic They produced modules on the theorem of pythagoras, The Story of Pi, Similarity, The theorem of pythagoras uses animation and a witty voiceover for http://www.edwardtufte.com/bboard/q-and-a-fetch-msg?msg_id=00000w&topic_id=1

65. Have You Seen A widespread decorative motif and the theorem of pythagoras Pythagoras , similartriangles and the elephants defense pattern of the Bakuba http://www.ethnomath.org/resources/ISGEm/080.htm

Originally published in the International Study Group on Ethnomathematics (ISGEm) Newsletter , Volume 11, Number 1, December 1995. Located at: http://web.nmsu.edu/~pscott/isgem111.htm Article reproduced 2003 with permission of the ISGEm Newsletter editor for use in the Ethnomathematics Digital Library ( www.ethnomath.org ) developed by Pacific Resources for Education and Learning ( www.prel.org Have You Seen "Have You Seen" is a regular feature of the ISGEm Newsletter in which works related to Ethnomathematics can be reviewed. We encourage all those interested to contribute to this column. Gerdes, Paulus, African Pythagoras: A Study in Culture and Mathematics Education This translation of a 1992 Portuguese version includes the following chapters: Did ancient Egyptian artisans know how to find a square equal in area to two given squares? From woven buttons to the Theorem of Pythagoras From fourfold symmetry to 'Pythagoras' 'Pythagoras', similar triangles and the "elephants' defense" pattern of the Bakuba

66. Vlakke Meetkunde Afmetingen 40cm x 56cm. 4 posters+book The Pythagorean Theorem . Theorem ofPythagoras. poster theorem of pythagoras. Klik hier http://www.rhombus.be/contents/nl/d213.html

if(parent.wm)var wm=parent.wm targetFrame="self"; parentFrame1="toc"; parentFrame2="toc"; var tf=topFrame; Home Posters dw(ld('LD_PICK_CURRENCY','')) Vlakke meetkunde The circle dw(qandi(['P495','0.00','0','','1'])); Klik hier You can recognise a circle when you see one, but do you realise what a unique and special shape it is ? This very explicative four-colour poster illustrates all parts and properties of a circle and its relationship with the number pi. Afmetingen: 60cm x 80cm The Pythagorean Theorem poster set. dw(qandi(['P496','0.00','0','','1'])); Students study history and geometry as the explore four elegant proofs of the theorem from across the centuries.The book includes eight proofs with interesting facts, a brief biography and a list of concepts needed to understand the proofs. Afmetingen: 40cm x 56cm 4 posters+book "The Pythagorean Theorem" Theorem of Pythagoras dw(qandi(['P497','0.00','0','','1'])); Klik hier Taking literally the statement about the squares on the sides of a rectangular triangle, this poster illustrates the well known theorem in an instructive way. It also shows a simple trigonometrical proof and draws attention to the set of Pythagorean number-triples. Afmetingen: 60cm x 86cm Conic Sections dw(qandi(['P498','0.00','0','','1']));

67. SOME SELECTED PUBLICATIONS Another generalization of the theorem of pythagoras. Spectrum. The theoremof Pythagoras Generalizing from right triangles to right polygons. http://mzone.mweb.co.za/residents/profmd/publications.htm

SOME SELECTED PUBLICATIONS by Michael de Villiers Mathematical Articles International Journal for Mathematical Education in Science and Technology , 20(4), 585-603, August 1989. Imstusnews , 19, 15-16, November 1989. Spectrum , 28(2), 18-21, May 1990. Physics Teacher , 286-289, May 1991. Spectrum . International Journal for Mathematical Education in Science and Technology Mathematical Digest Imstusnews Spectrum International Journal for Mathematical Education in Science and Technology Australian Senior Mathematics Journal Pythagoras The Mathematical Gazette , 79(485), 374-378, July 1995. . Int. J. Math. Ed. Sci. Technol ., 26(2), 233-241, 1995. (Co-author: J. Meyer, UOFS). , 6(3), 169-171, Sept 1996. ). KZN AMESA Math Journal , Vol 3, No 1, 11-18. Mathematical Gazette , Nov. Mathematical Gazette , March 1999. Mathematics in School , March 1999, 18-21. Mathematics in College Mathematics Education Articles Mathematics Teacher , Vol.80, No.7, pp.528-532, October 1987. Pythagoras . 19, pp.27-30, April 1989. S.A. Tydskrif vir Opvoedkunde , 10(1), Feb 1990, 68-74 (co-author: E.C. Smith).

68. Historia Matematica Mailing List Archive: Re: [HM] Historiograp about the theorem of pythagoras (Heath s quotation marks) triangle theoremafter Pythagoras? In my opinion, the harm is extensive. http://sunsite.utk.edu/math_archives/.http/hypermail/historia/sep00/0142.html

Re: [HM] historiography of mathematics Subject: Re: [HM] historiography of mathematics From: Beatrice Lumpkin ( Bealumpkin@aol.com Date: Wed Sep 20 2000 - 16:59:32 EDT Next message: Bill Everdell: "Re: [HM] historiography of mathematics" Previous message: John Harper: "Re: [HM] Book: Revolutions in Mathematics" Next in thread: John Harper: "Re: [HM] historiography of mathematics" Next in thread: Bill Everdell: "Re: [HM] historiography of mathematics" Maybe reply: Beatrice Lumpkin: "Re: [HM] historiography of mathematics" Reply: John Harper: "Re: [HM] historiography of mathematics" Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Hello all, I am commenting on a comment: lambrou@itia.math.uch.gr Subject: Re: [HM] historiography of mathematics On 16 Sep 2000, Bill Everdell wrote: Lambrou Michael goes on to comment: The only problem is that this is NOT what the sources say! (They have two different stories, both a variant of the one mentioned). Some aspects of the misconceptions around the right-triangle theorem are not entirely harmless, especially in mathematics education. Heath says

69. Pythagorean Theorem And Its Many Proofs A collection of 43 proofs some interactive - of the Pythagorean theorem. http://www.cut-the-knot.org/pythagoras/index.shtml

Username: Password: Sites for teachers Sites for parents Awards Interactive Activities ... Sites for parents Pythagorean Theorem Let's build up squares on the sides of a right triangle. Pythagoras' Theorem then claims that the sum of (the areas of) two small squares equals (the area of) the large one. In algebraic terms, a + b = c where c is the hypotenuse while a and b are the sides of the triangle. The theorem is of fundamental importance in the Euclidean Geometry where it serves as a basis for the definition of distance between two points. It's so basic and well known that, I believe, anyone who took geometry classes in high school couldn't fail to remember it long after other math notions got solidly forgotten. Below is a collection of various approaches to proving the theorem. Some of the proofs are accompanied by Java illustrations, but most have been written in plain HTML. Remark The statement of the Theorem was discovered on a Babylonian tablet circa 1900-1600 B.C. Whether Pythagoras (c.560-c.480 B.C.) or someone else from his School was the first to discover its proof can't be claimed with any degree of credibility. Euclid's (c 300 B.C.) Elements furnish the first and, later, the standard reference in Geometry. In fact Euclid supplied two very different proofs: the Proposition I.47 (First Book, Proposition 47) and VI.31.

70. Pythagoras' Theorem - By Seth Y-Maxwell The History of pythagoras and his proof in 3D. Page includes Diagrams, History,Links, Guestbook, Test, Calculator, and a Joke all related to pythagoras and http://www.geocities.com/CapeCanaveral/Launchpad/3740/

By: Seth Yoshioka-Maxwell You can view one of the images by clicking once on the picture you want. Pythagoras was a great Mathematician who was the first to create the music scale of today. He also created theorems. One of his most famous theorem was: a +b =c Attention If You have any information on different proofs e-mail me. I would love to add more proofs to my site. Thank you. +b =c NEW ! Pythagorean Theorem Proof Calculator Pythagorean Theorem Joke President Garfield's Proof of the Pythagorian Theorem Main page ... Notify-mail Page and graphics designed by Seth Yoshioka-Maxwell

71. Babylonian Mathematics An overview of mathematics within this culture. Includes a description of the numerals used and a reference to pythagoras' theorem. http://www-history.mcs.st-andrews.ac.uk/Indexes/Babylonians.html

History Topics: Babylonian mathematics An overview of Babylonian mathematics Babylonian numerals Pythagoras's theorem in Babylonian mathematics A history of Zero ... Search Form JOC/EFR January 2004 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/Indexes/Babylonians.html

72. Pythagoras's Theorem -- From MathWorld SEE ALSO Irrational Number, pythagoras s Constant, Pythagorean theorem. PagesLinking Here. REFERENCES. Conway, JH and Guy, RK The Book of Numbers. http://mathworld.wolfram.com/PythagorassTheorem.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Number Theory Irrational Numbers Geometry ... Squares Pythagoras's Theorem Proves that the polygon diagonal of a square with sides of integral length cannot be rational . Assume is rational and equal to where and are integers with no common factors. Then so and , so is even. But if is even , then is even . Since is defined to be expressed in lowest terms, must be odd ; otherwise and would have the common factor 2. Since is even , we can let , then . Therefore, , and , so must be even . But cannot be both even and odd , so there are no and 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 SEE ALSO: Irrational Number Pythagoras's Constant Pythagorean Theorem [Pages Linking Here] REFERENCES: Conway, J. H. and Guy, R. K.

73. An Interactive Proof Of Pythagoras' Theorem Home page of the grand prize winner in Sun Microsystem's Java programming contest in 1995. http://sunsite.ubc.ca/LivingMathematics/V001N01/UBCExamples/Pythagoras/pythagora

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

74. Pythagoras Theorem Pythagorean theorem a la Friedrichs (by plane tesselation) http://www.cut-the-knot.org/pythagoras/PythLattice.shtml

Username: Password: Sites for teachers Sites for parents Awards Interactive Activities ... Sites for parents Pythagoras' Theorem This is a subtle and beautiful proof. It's quite easy to get an insight into why it works. The applet below is supposed to serve this purpose. The Pythagorean Theorem claims that a + b = c , where a and b are sides whereas c is the hypotenuse of a right-angled triangle. For the sake of the proof, we tasselate the plane into two grids. One is composed of the repeated pattern of two touching squares with sides a and b. The second grid consists of squares of side c parallel (and perpendicular) to the hypotenuse of the given triangle. These two grids have a common feature: they both are invariant under translation to the vector c parallel to the hypotenuse and of the same length. Note that this translation is equivalent to first translating the plane horizontally to the length of one side (say, a) and then vertically to the length of another (b). The insight might be gained when the two grids are superimposed as in the applet. Because of the above mentioned property the second grid cuts the first one into parts that may be combined in at least two different ways: to form two squares a + b or the bigger square c . (This is by no means a rigorous proof. See if you can fill in the details.) The applet may be in two states. In the first you modify a right-angled triangle. In the second you drag the second grid to observe various "proofs" of the Pythagorean Theorem. All the operations are performed by dragging the mouse.

75. The Pythagorean Theorem Lesson A lesson on the pythagorean theorem with the objective that the you will discover for yourself the actual theorem. http://www.arcytech.org/java/pythagoras/index.html

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. Pythagoras' Theorem pythagoras theorem asserts that for a right triangle with short sides of length a It contains 365 more or less distinct proofs of pythagoras theorem. 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

77. An Interactive Proof Of Pythagoras' Theorem Home page of the grand prize winner in Sun Microsystem s Java programming contestin 1995. 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

78. Pythagorean Theorem: Definition And Much More From Answers.com In mathematics, the Pythagorean theorem or pythagoras theorem, is a relation inEuclidean pythagoras perceived the theorem in this geometric fashion, http://www.answers.com/topic/pythagorean-theorem

showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Dictionary Science Wikipedia Best of Web Mentioned In Or search: - The Web - Images - News - Blogs - Shopping Pythagorean theorem Dictionary (Click to enlarge) Pythagorean theorem The Pythagorean theorem is: a b c (Academy Artworks) Pythagorean theorem n. The theorem that the sum of the squares of the lengths of the sides of a right triangle is equal to the square of the length of the hypotenuse. Science Pythagorean theorem (puh-thag-uh- ree -uhn, peye-thag-uh- ree -uhn) The theorem in geometry that, in a triangle with one right angle , usually called a right triangle , the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. The theorem is often expressed a b c The simplest whole number expression of this theorem is called the 3, 4, 5 triangle. In a right triangle, if one side measures three units, and the second side measures four units, the hypotenuse must measure five units because 3 ; that is, 9 + 16 = 25.

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

Pythagorean Theorem Information of Products

80. Nrich.maths.org::Mathematics Enrichment::NRICH pythagoras theorem shows that the hypotenuse of the isoceles triangle It s strange that there is no proof for the pythagoras theorem in the text book. http://nrich.maths.org/askedNRICH/edited/1963.html

Skip over navigation About Contact Mailing Lists ... maths finder past issues Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Welcome to NRICH. Pythagoras' proof of Pythagoras' Theorem? By Woon Khang Tang (P3742) on Monday, February 12, 2001 - 07:10 pm Can anyone tell me how does Pythagoras discovered his famous theorem - The Pythagoras Theorem? Does he discover it by drawing the triangle and measure it? Or just by guessing? I want to know because I haven't seen a proof for the theorem by Pythagoras himself; instead I have seen other proofs by other mathematician. By Anonymous on Monday, February 12, 2001 - 07:13 pm - Pythagoras didn't exist. - His theroem was known before the ancient greeks. By on Monday, February 12, 2001 - 07:22 pm Wow, I've never heard anyone claim Pythagoras didn't exist before. The way I understood it (but perhaps this is only one of many possibilities) the theorem was actually discovered/proven not by Pythagoras but by one of the Pythagoreans (those are the students of Pythagoras). In fact it is reputed that the discovery partly caused the collapse of his school. Because Pythagoras had built his model of the world in which all quantities are the ratio of two integers (so are called rational in today's terminology). Pythagoras theorem shows that the hypotenuse of the isoceles triangle with sides 1 and 1 is sqrt(2) - and no rational number squares to 2. Therefore rational numbers are insufficient to describe geometry, and so the Pythagoras world model in which rational numbers described everything fell apart.

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