41. The Theorem Of Pythagoras (in VSCCAT) ENC Online Curriculum Resources The theorem of pythagoras (ENC Skip Navigation, You Are Here ENC Home Curriculum Resources The theoremof Pythagoras (ENC000896, Research Reviews). The theorem of pythagoras. http://scolar.vsc.edu:8005/VSCCAT/ABW-2835

The Theorem of Pythagoras Title: The Theorem of Pythagoras [videorecording] / creator and writer, Tom M. Apostol ; produced by Project Mathematics! Author: Apostol, Tom M. Hibbs, Albert R. California Institute of Technology. Project Mathematics. Published: Pasadena, CA : California Institute of Technology, c1988. Subject: Pythagorean theorem. Series: Mathematics Mathematics. Material: 1 videocassette (VHS) (26 min.) : sd., col. ; 1/2 in. + 1 guide (30 p. : ill.) Note: Produced by Project Mathematics and the JPL Computer Graphics Laboratory. Guide includes: outline of program, script, illustrations, study questions, and index. Narrator, Al Hibbs. Math tutorial explains the Pythagorean theorem, discusses history, proof, and uses. LC Card no: System ID no: ABW-2835 Holdings: Lyndon State College CALL NUMBER: [Video] 516.22 T343 Videocass Available CALL NUMBER: [Video] 516.22 T343 Booklet Book Available/Notes Vermont Technical College CALL NUMBER: [Video] 516.22 T34 Videocass Available CALL NUMBER: [Video] 516.22 T34 c2 Videocass Available

42. Theorem Of Pythagoras Translate this page Teorema de Pitágoras a 2 + b 2 = c 2. Este applet java mostra a você (automaticamente- passo a passo) Como o povo Chinês antigo descobriu o mesmo teorema. http://www.cepa.if.usp.br/fkw/abc/Pythagoras.html

Teorema de Pitágoras a + b = c Este applet java mostra a você (automaticamente - passo a passo) Como o povo Chinês antigo descobriu o mesmo teorema. (muito antes de Pitágoras). Você pode mudar o intervalo delta T (em segundos, valor original = 2 segundos). Clique no botão do mouse para obter o modo de controle manual: Clique no botão esquerdo: mostra o passo seguinte Clique no botão direito: mostra o passo anterior Quando você atingir o último passo, pressione o botão reiniciar para recomeçar applets java relacionados a Pitágoras Suas sugestões serão muito apreciadas! Por favor clique hwang@phy03.phy.ntnu.edu.tw Autor Fu-Kwun Hwang Dept. of physics National Taiwan Normal University Última modificação:

43. The Theorem Of Pythagoras Is Said To Have Many Proofs. I Ve Found The theorem of pythagoras is said to have many proofs. alexl@daemon.cna.tek.com(Alexander writes The theorem of pythagoras is said to have many proofs. http://www.ics.uci.edu/~eppstein/junkyard/pytho.html

From: alexl@daemon.cna.tek.com (Alexander Lopez) Newsgroups: sci.math Subject: Pythagorean theorem - proofs on the WWW? Date: 19 Apr 1996 15:40:51 -0700 Organization: Tektronix, Inc., Redmond, OR Reply-To: alexl@daemon.cna.tek.com The theorem of Pythagoras is said to have many proofs. I've found four on the WWW (used with the Geometers SketchPad). Are there any sites with more, or sites with historical background on the proofs? Alexander Lopez Software Engineering alexl@daemon.CNA.TEK.COM From: eppstein@ics.uci.edu (David Eppstein) Date: 19 Apr 1996 22:26:48 -0700 Newsgroups: sci.math Subject: Re: Pythagorean theorem - proofs on the WWW? alexl@daemon.cna.tek.com http://www.ics.ici.edu/~eppstein/junkyard/ ), reformatted somewhat from the original HTML: Euclid's Elements ( http://www.columbia.edu/~rc142/Euclid.html ). Online, in interesting colors, without all those annoying proofs. Also see D. Joyce's Java-animated version ( http://aleph0.clarku.edu/~djoyce/java/elements/elements.html ), and a manuscript excerpt from a copy in the Bodleian library made in the year 888 ( http://www.lib.virginia.edu/science/parshall/elementsamp.html

44. Pythagoras And The Pythagoreans `Geometry has two great treasures one is the theorem of pythagoras;the other, the division of a line into extreme and mean ratio. http://www.math.tamu.edu/~don.allen/history/pythag/pythag.html

Next: About this document Pythagoras and the Pythagoreans Historically, Pythagoras means much more that the familiar theorem about right triangles. The philosophy of Pythagoras and his school has impacted the very fiber of mathematics and physics, even the western tradition of liberal education no matter what the discipline. Pythagorean philosophy was the prime source of inspiration for Plato and Aristotle; the influence of these philosophers is without question and is immeasurable. Pythagoras and the Pythagoreans Little is known of his life. Pythagoras (fl 580-500, BC) was born in Samos on the western coast of what is now Turkey. He was reportedly the son of a substantial citizen, Mnesarchos. There he lived for many years under the rule of the tyrant Polycrates, who had a tendency to switch alliances in times of conflict which were frequent. He met Thales, likely as a young man, who recommended he travel to Egypt. It seems certain that he gained much of his knowledge from the Egyptians, as had Thales before him. Probably because of continual conflicts and strife in Samos, Pythagoras settled in Croton, on the eastern coast of Italy, a place of relative peace and safety.

45. 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 his theorem. 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 This theorem shown in 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

46. Pythagorean Theorem And Its Many Proofs right triangle. pythagoras theorem then claims that the sum of (theareas of) two small squares equals (the area of) the large one. http://www.cut-the-knot.org/pythagoras/index.shtml

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site 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. I plan to present several geometric proofs of the Pythagorean Theorem. An impetus for this page was provided by a remarkable Java applet written by Jim Morey . This constitutes the first proof on this page. One of my first Java applets was written to illustrate another Euclidean proof. Presently, there are several Java illustrations of various proofs, but the majority have been rendered in plain HTML with simple graphic diagrams. 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.)

47. Pythagoras' Playground (by The Event Inventor) We will use the amazing properties of the Pythagorean theorem to explore the world around us. http://www.kyes-world.com/pythagor.htm

HOME TELESCOPES SITE MAP From this site, we will use the amazing properties of the Pythagorean Theorem to explore the world around us. 2500 years ago, Pythagoras of Samos and his students developed the first proof that, for a right triangle, a + b = c (the sum of the squares of the two legs of a triangle is equal to the square of the hypotenuse) as well as being responsible for many other important developments in mathematics, astronomy and music. Many of the ideas used and instruments we will be making were originally employed by the Babylonians, 1000 years before Pythagoras proved on paper why they worked! During the Dark Ages, the Arabs nurtured the science of astronomy and developed the primitive quadrant into a more advanced tool, called an ASTROLABE. The first brave mariners that dared to leave sight of land in their sailing ships did so with the help of these instruments, making it possible for them to determine their position on the Earth to within a few degrees of accuracy; close enough to find land again! Here are some investigations to help you discover the secrets that these explorers used, to enjoy the world around us:

48. Pythagorean Theorem And Its Many Proofs pythagoras' theorem. 43 proofs of the Pythagorean theorem. on the sides of a right triangle. pythagoras' theorem then claims that the sum of (the areas of The statement of the theorem was discovered on a Babylonian tablet circa http://www.cut-the-knot.com/pythagoras

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site 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. I plan to present several geometric proofs of the Pythagorean Theorem. An impetus for this page was provided by a remarkable Java applet written by Jim Morey . This constitutes the first proof on this page. One of my first Java applets was written to illustrate another Euclidean proof. Presently, there are several Java illustrations of various proofs, but the majority have been rendered in plain HTML with simple graphic diagrams. 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.)

49. Pythagorean Theorem Pythagorean theorem This Internet site presents the Pythagorean theorem as a fundamental theorem of Euclidian geometry that plays an important role in the field of mathematics. The site offers http://rdre1.inktomi.com/click?u=http://www.cut-the-knot.org/pythagoras/index.sh

50. Pythagoras Theorem pythagoras theorem. Applet by Jim Morey (Euclid s Elements I.47). Copyright ©19962004 Alexander Bogomolny 9586635. Google Web Search. Latest on CTK Exchange. http://www.cut-the-knot.org/pythagoras/morey.shtml

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site Pythagoras' Theorem Applet by Jim Morey (Euclid's Elements I.47) Alexander Bogomolny G o o g l e Web Search Latest on CTK Exchange Math Glossary on CTK website Posted by 1mathworld24 1 messages 03:34 PM, Mar-01-04 Conversions Posted by Raelynn 2 messages 11:26 AM, May-25-04 Reuleaux's triangle Posted by David 1 messages 08:28 PM, May-29-04 property of power of 2 Posted by japam 0 messages 02:05 PM, May-30-04 trouble with page load Posted by dimoskon 1 messages 11:31 AM, May-22-04 Ratio of even and odd numbers Posted by Rob 14 messages 06:48 AM, May-30-04

51. Babylonian Mathematics An overview of mathematics within this culture. Includes a description of the numerals used and a reference to pythagoras' theorem. http://www-groups.dcs.st-and.ac.uk/~history/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

52. 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

53. 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

54. 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

Pythagoras's theorem in Babylonian mathematics Babylonian index History Topics Index Pythagoras's theorem in Babylonian mathematics In this article we examine four Babylonian tablets which all have some connection with Pythagoras 's theorem. Certainly the Babylonians were familiar with Pythagoras 's theorem. A translation of a Babylonian tablet which is preserved in the British museum goes as follows:- is the length and the diagonal. What is the breadth Its size is not known. times is times is You take from 25 and there remains What times what shall I take in order to get times is is the breadth. All the tablets we wish to consider in detail come from roughly the same period, namely that of the Old Babylonian Empire which flourished in Mesopotamia between 1900 BC and 1600 BC. Here is a map of the region where the Babylonian civilisation flourished. The article Babylonian mathematics gives some background to how the civilisation came about and the mathematical background which they inherited. The four tablets which interest us here we will call the Yale tablet YBC 7289, Plimpton 322 (shown below), the Susa tablet, and the Tell Dhibayi tablet. Let us say a little about these tablets before describing the mathematics which they contain. The Yale tablet YBC 7289 which we describe is one of a large collection of tablets held in the Yale Babylonian collection of Yale University. It consists of a tablet on which a diagram appears. The diagram is a square of side 30 with the diagonals drawn in. The tablet and its significance was first discussed in [5] and recently in [18].

55. Pythagorean Theorem - Wikipedia, The Free Encyclopedia In mathematics, the Pythagorean theorem or pythagoras theorem, is a relationin Euclidean geometry between the three sides of a right triangle. http://en.wikipedia.org/wiki/Pythagorean_theorem

Pythagorean theorem From Wikipedia, the free encyclopedia. In mathematics , the Pythagorean theorem or Pythagoras' theorem , is a relation in Euclidean geometry between the three sides of a right triangle. The theorem is named after and commonly attributed to the 6th century BC Greek philosopher and mathematician Pythagoras , although the facts of the theorem were known by Indian and Greek mathematicians well before he lived. Table of contents 1 The theorem 2 A visual proof 3 The converse 4 Generalisations ... edit The theorem The Pythagorean theorem states: 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 a triangle with one right angle ; the legs are the two sides that make up the right angle, and the hypotenuse is the third side opposite the right angle. In the picture below, a and b are the legs of a right triangle, and c is the hypotenuse: Pythagoras perceived the theorem in this geometric fashion, as a statement about areas of squares: The sum of the areas of the blue and red squares is equal to the area of the purple square.

56. Pythagoras - Wikipedia, The Free Encyclopedia Whether or not we attribute the Pythagorean theorem to pythagoras, it seems fairlycertain that he had the pioneering insight into the numerical ratios which http://en.wikipedia.org/wiki/Pythagoras

Pythagoras From Wikipedia, the free encyclopedia. Pythagoras 582 BC 496 BC Greek Ionian ... mathematician and philosopher , known best for the Pythagorean Theorem Bust of Pythagoras Pythagoras, known as "the father of numbers", made influential contributions to Greek philosophy and religious teaching in the late 6th century BC. Because legend and obfuscation cloud his work even more than with the other pre-Socratics , one can say little with confidence about his life and teachings. Pythagoras was born on the island of Samos , off the coast of Asia Minor . As a young man he left his native city for Croton in Southern Italy to escape the tyrannical government of Polycrates . Many writers credit him with visits to the sages of Egypt and of Babylon before going west; but such visits feature stereotypically in the biographies of Greek wise men, and may express legend rather than fact. In any case, Pythagoras undertook a reform of the cultural life of Croton, urging the citizens to follow virtue and forming an elite circle of followers around himself. Very strict rules of conduct governed this cultural center. He opened his school to men and women students alike. According to Iamblichus , the Pythagoreans followed a structured life of common meals, exercise, reading and philosophical study. We may infer from this that participants required some degree of wealth and leisure to join the inner circle. Music featured as an essential organizing factor of this life: the disciples would sing hymns to

57. 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

58. 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

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Geometry Plane Geometry Squares ... 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 ... search Conway, J. H. and Guy, R. K.

59. 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

60. 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.

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