61. Pythagorean Theorem - Encyclopedia Article About Pythagorean Theorem. Free Acces The theorem. The Pythagorean theorem or pythagoras theorem is namedafter and commonly attributed to the 6th century BC. (7th century http://encyclopedia.thefreedictionary.com/Pythagorean theorem

Dictionaries: General Computing Medical Legal Encyclopedia Pythagorean theorem Word: Word Starts with Ends with Definition In mathematics Mathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of 'figures and numbers'. In the formalist view, it is the investigation of axiomatically defined abstract structures using logic and mathematical notation; other views are described in Philosophy of mathematics. Mathematics might be seen as a simple extension of spoken and written languages, with an extremely precisely defined vocabulary and grammar, for the purpose of describing and exploring physical and conceptual relationships. Click the link for more information. , the Pythagorean theorem or Pythagoras' theorem , is a relation in Euclidean geometry In mathematics, Euclidean geometry is the familiar kind of geometry on the plane or in three dimensions. Mathematicians sometimes use the term to encompass higher dimensional geometries with similar properties. Euclidean geometry usually refers to geometry in the plane which is also called plane geometry . It is plane geometry which is the topic of this article. Euclidean geometry in three dimensions is traditionally called solid geometry. For information on higher dimensions see Euclidean space.

62. Pythagoras' Theorem - Encyclopedia Article About Pythagoras' Theorem. Free Acces encyclopedia article about pythagoras theorem. pythagoras theorem in Free onlineEnglish dictionary, thesaurus and encyclopedia. pythagoras theorem. http://encyclopedia.thefreedictionary.com/Pythagoras' Theorem

Dictionaries: General Computing Medical Legal Encyclopedia Pythagoras' Theorem Word: Word Starts with Ends with Definition In mathematics Mathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of 'figures and numbers'. In the formalist view, it is the investigation of axiomatically defined abstract structures using logic and mathematical notation; other views are described in Philosophy of mathematics. Mathematics might be seen as a simple extension of spoken and written languages, with an extremely precisely defined vocabulary and grammar, for the purpose of describing and exploring physical and conceptual relationships. Click the link for more information. , the Pythagorean theorem or Pythagoras' theorem , is a relation in Euclidean geometry In mathematics, Euclidean geometry is the familiar kind of geometry on the plane or in three dimensions. Mathematicians sometimes use the term to encompass higher dimensional geometries with similar properties. Euclidean geometry usually refers to geometry in the plane which is also called plane geometry . It is plane geometry which is the topic of this article. Euclidean geometry in three dimensions is traditionally called solid geometry. For information on higher dimensions see Euclidean space.

63. Pythagorean Theorem The Pythagorean theorem or pythagoras theorem is named after and commonly attributedto the 6th century BC Greek philosopher and mathematician pythagoras http://www.fact-index.com/p/py/pythagorean_theorem.html

Main Page See live article Alphabetical index Pythagorean theorem 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: 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: Given a right triangle, with legs of lengths a and b and hypotenuse of length c , then Proof: (see image, right) Draw a right triangle with sides a b , and c as above. Then take a copy of this triangle and place its a side in line with the b side of the first, so that their

64. 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

65. The Pythagorean Theorem The Pythagorean theorem is pythagoras most famous mathematical contribution.According to legend, pythagoras was so happy when http://jwilson.coe.uga.edu/emt669/Student.Folders/Morris.Stephanie/EMT.669/Essay

Department of Mathematics Education J. Wilson, EMT 669 The Pythagorean Theorem by Stephanie J. Morris The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. This famous theorem is named for the Greek mathematician and philosopher, Pythagoras. Pythagoras founded the Pythagorean School of Mathematics in Cortona, a Greek seaport in Southern Italy. He is credited with many contributions to mathematics although some of them may have actually been the work of his students. The Pythagorean Theorem is Pythagoras' most famous mathematical contribution. According to legend, Pythagoras was so happy when he discovered the theorem that he offered a sacrifice of oxen. The later discovery that the square root of 2 is irrational and therefore, cannot be expressed as a ratio of two integers, greatly troubled Pythagoras and his followers. They were devout in their belief that any two lengths were integral multiples of some unit length. Many attempts were made to suppress the knowledge that the square root of 2 is irrational. It is even said that the man who divulged the secret was drowned at sea. The Pythagorean Theorem is a statement about triangles containing a right angle. The Pythagorean Theorem states that:

66. An Interactive Proof Of Pythagoras' Theorem 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

67. 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

68. 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

69. Pythagoras' Theorem Click Here pythagoras theorem. pythagoras theorem allows us to find the lengthof the third side on a right angle triangle if we know the other two lengths. http://www.mathsisfun.com/pythagoras.html

HOME All Pages A - Z Listing Maths Menus Handling Data Miscellaneous Maths Help Discussion Forum Online Form Puzzles Calculators TI Calculators Computer Programs Winlogo Programs Links Add a link Maths links Online Shop Maths Books Contact Us Email Online Form About Mathsisfun Pythagoras' Theorem Pythagoras' Theorem allows us to find the length of the third side on a right angle triangle if we know the other two lengths. Bits to remember It only works on right angled triangles You need to know at least two other lengths. The formal definition is (ready for this) In a right angled triangle the sum of the square of the hypotenuse is equal to the sum of the squares of the other two sides. Algebraically a + b = c c is always the hypotenuse. Therefore 3 Which goes to 9 + 16 = 25 This can be used to find the length of an unknown side a + b = c = c c c = 13 a + b = c + b 81 + b Take 81 from both sides b b = 12 Related Links Right Angled triangles Triangles Pythagorean Triples

70. 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

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

Pythagorean Theorem Information of Products

72. 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

73. Euclid's Elements, Book I, Proposition 47 This proposition, I.47, is often called the Pythagorean theorem, called so by Proclusand others centuries after pythagoras and even centuries after Euclid. http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI47.html

Proposition 47 In right-angled triangles the square on the side opposite the right angle equals the sum of the squares on the sides containing the right angle. Let ABC be a right-angled triangle having the angle BAC right. I say that the square on BC equals the sum of the squares on BA and AC. Describe the square BDEC on BC, and the squares GB and HC on BA and AC. Draw AL through A parallel to either BD or CE, and join AD and FC. I.46 I.31 Post.1 Since each of the angles BAC and BAG is right, it follows that with a straight line BA, and at the point A on it, the two straight lines AC and AG not lying on the same side make the adjacent angles equal to two right angles, therefore CA is in a straight line with AG. I.Def.22 I.14 For the same reason BA is also in a straight line with AH. Since the angle DBC equals the angle FBA, for each is right, add the angle ABC to each, therefore the whole angle DBA equals the whole angle FBC. I.Def.22 Post.4 C.N.2 Since DB equals BC, and FB equals BA, the two sides AB and BD equal the two sides FB and BC respectively, and the angle ABD equals the angle FBC

74. 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 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? Answer: chi If the longer leg is 4 chi , and the hypotenuse is 5 chi , what is the shorter leg? Answer: chi The method of right triangles: Multiply the shorter leg and the longer leg each by itself, add, and extract the square root. This is the hypotenuse. Or: Multiply the longer leg by itself; subtract this from the product of the hypotenuse by itself; extract the square root of the difference. This is the shorter leg.

75. NOVA Online | The Proof | Pythagorean Puzzle 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

76. MathsNet: Interactive Pythagoras's Theorem MathsNet Interactive pythagoras s theorem a collection of resources foreducation, aimed at students, teachers and anyone else. part of geometry. http://www.mathsnet.net/dynamic/pythagoras/

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.

77. Pythagorean Philosophy: Simple Deduction Of Pythagoras Theorem Pythagorean theorem pythagoras Philosophy Pythagorean theorem Proofsfrom the Spherical Standing Wave Structure of Matter (WSM). http://www.spaceandmotion.com/Philosophy-Pythagoras-Pythagorean-Theorem.htm

Introduction: Pythagoras Theorem Links: Deducing Pythagoras' Theorem Search WSM Group ... Top of Page Philosophy / Pythagoras / Pythagorean Theorem Pythagorean Theorem Proofs from Spherical Standing Wave Structure of Matter (WSM) Pythagoras' Theorem is Caused by the Spherical shape of Matter as a Spherical Standing Wave in Space. Further, three dimensional space and spherical space are equivalent, as it takes three variables to describe the surface of a sphere. In fact the cause of both three dimensional space and Pythagoras' Theorem is simply that matter interacts spherically, as Albert Einstein realised. (Albert Einstein, 1934) From the latest results of the theory of relativity it is probable that our three dimensional space is also approximately spherical , that is, that the laws of disposition of rigid bodies in it are not given by Euclidean geometry, but approximately by spherical geometry .... According to the general theory of relativity , the geometrical properties of space are not independent, but they are

78. Pythagoras Theorem And Fibonacci Numbers pythagoras theorem AND FIBONACCI NUMBERS. pythagoras was born onthe island of Samos, Greece, in 569 BC.He excelled as a student http://milan.milanovic.org/math/english/Pythagoras/Pythagoras.html

PYTHAGORAS THEOREM AND FIBONACCI NUMBERS Pythagoras was born on the island of Samos, Greece, in 569 BC.He excelled as a student and, as a young man, he traveled widely . Tradition says that he explored from India in the East to Gaul in the West.Pythagoras traveled extensively through Egypt, learning maths, astronomy and music. Pythagoras left Samos in disgust for its ruler Polycrates. He moved on to the Greek city of Crotona, located on the southern shore of Italy. There he created a school where his followers lived and worked.It was a mystical learning community. At the heart of Pythagoras` teachings was the vision of the underlying harmony of the universe. This harmony had to be abstracted from the confusion of visible things and daily events. As a matter of fact this harmony existed in the abstract - in the same way as numbers and mathematical formulas are abstractions. Pythagoras believed in secrecy and communalism, so it is almost impossible distguishing his work from the work of his followers. Pythagoras and his followers contributed to music, astronomy and mathematics. He died about 500 BC in Metapontum, Lucania. Pythagoras` desire was to find the mathematical harmonies of all things. The study of of odd, even, prime and square numbers were among numerous mathematical investigations of the Pythagoreans. This helped them develop a basic understanding of mathematics and geometry to build their Pythagorean theorem.

79. 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.

80. Pythagoras' Theorem pythagoras theorem. Use the Pythagorgrams widget to undestand what pythagoras theorem says and why it works. Then try the pencil and paper problems. http://thejuniverse.org/Mathdesign/widgets/Pythagoras/

Pythagoras' Theorem Use the Pythagorgrams widget to undestand what Pythagoras' theorem says and why it works. Then try the pencil and paper problems. Pencil and Paper Problems 1. i) A right-angled triangle has shorter sides of lengths 2 and 5; how long is its hypotenuse? ii) A right-angled triangle has hypotenuse of length 4 and one side of length 2; how long is the other side? iii ) A triangle has two sides of lengths 5 and 6 and area 9. How long is the third side? [There are two possible answers.] 2. How long is the diagonal of a square with sides of length 1? Now, without using Pythagoras' theorem again , how long is the diagonal of a square with sides of length 13579? How long is the diagonal of a square with sides of length s? 3. How long is an altitude of an equilateral triangle with sides of length 2? Without using Pythagoras' theorem again, how long is an altitude of an equilateral triangle with sides of length 24680?

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