61. Template Theorem of Pythagoras a 2 + b 2 = c 2. This java applet shows you (automatically step by step) How ancient Chinese http://www.phys.hawaii.edu/~teb/java/ntnujava/abc/Pythagoras.html

Theorem of Pythagoras a + b = c This java applet shows you (automatically - step by step) How ancient Chinese people discovers the same theorem. (much earlier than Pythagoras). You can change the interval delta T (in second, default value = 2 second). Click mouse button for manual control mode : Click right mouse button : show the following step Click left mouse button : show the previous step When you reach the last step, Press reset button to restart related Pythagoras java applet Your suggestions are highly appreciated! Please click hwang@phy03.phy.ntnu.edu.tw Author¡G Fu-Kwun Hwang Dept. of physics National Taiwan Normal University Last modified :¡@

62. Surprising Uses Of The Pythagorean Theorem | BetterExplained Oct 24, 2007 The Pythagorean theorem is a celebrity if an equation can make it into the Simpsonshttp//www.snpp.com/episodes/1F08.html, I d say its. http://betterexplained.com/articles/surprising-uses-of-the-pythagorean-theorem/

@import url( http://betterexplained.com/wp-content/themes/be-v8/style.css ); BetterExplained Learn Right, Not Rote. Home All Posts About FAQ ... Surprising Uses of the Pythagorean Theorem The Pythagorean theorem is a celebrity: if an equation can make it into the Simpsons , I'd say its well-known. But most of us think the formula only applies to triangles and geometry. Think again. The Pythagorean Theorem can be used with any shape and for any formula that squares a number Read on to see how this 2500-year-old idea can help us understand computer science, physics, even the value of Web 2.0 social networks. Understanding How Area Works I love seeing old topics in a new light and discovering the depth there. For example, I realize I didn't have a deep grasp of area until writing this article. Yes, we can rattle off equations, but do we really understand the nature of area? This fact may surprise you: The area of any shape can be computed from any line segment squared . In a square, our "line segment" is usually a side, and the area is that side squared (side 5, area 25). In a circle, the line segment is often the radius, and the area is pi * r^2 (radius 5, area 25 pi). Easy enough. We can pick any line segment and figure out area from it: every line segment has an "area factor" in this universal equation: Shape Line Segment Area Area Factor Square Side [s] s Square Perimeter [p] 1/16 p Square Diagonal [d] 1/2 d Circle Radius [ r ] pi r pi (3.14159...)

63. Pythagoras Of Samos Biography Theorem The famous Pythagoras Theorem concerning right angled triangles holds that the square of Hypotenuse (i.e. the length of the long line opposite the right http://www.age-of-the-sage.org/greek/philosopher/pythagoras_biography.html

pytagoras, samos, philosophy, biography Pythagoreans, life, works, Theorem, Pythagorean school Home Ancient Greece > Pythagoras of Samos biography Site Map Popular Pages Slide Shows Guest Book ... Support Us Pythagoras of Samos an outline biography   The famous Greek philosopher mathematician Pythagoras was born circa 570 B.C. on Samos an island lying off the western coast of Asia Minor. Samos was at this time one of the colonies that had been developed by the city states of ancient Greece centred upon Asia Minor and the islands lying off its coasts. Such colonisation had been encouraged moreso by population pressures and political turmoils in ancient Greece rather than by the prospect of trading opportunities.   At this remove it is difficult to be precise about Pythagoras and his background, 570 B.C. is rather a long time ago and records were not really maintained even about prominent or controversial figures.   It is suggested that his mother came from amongst the colonial Greeks of Samos but that his father was a Phoenician craftsperson from Tyre who worked with precious metals and who had been granted citizenship rights after bringing corn to Samos at a time of famine.   Pythagoras seems to have had an impressive birthmark on his thigh that, amongst his fellows, was held to be a mark of divine favour - he was considered to have had a "Golden Thigh."

64. Education Interactive • Theorem Of Pythagoras Our Promises We have extensive experience in teaching and teacher training, so you can be confident that all of our products have been carefully selected. http://www.education-interactive.co.uk/shop/pr-107.html

Home Contact Us Number Partners Running School Maths Days ... 24 Game Tournaments Our Promises: We have extensive experience in teaching and teacher training, so you can be confident that all of our products have been carefully selected. We want you to make the right choices. So if you are not sure what to buy, give us a call and we will be happy to advise. We aim to despatch orders on the day we receive them. Schools, LAs and organisations working with Number Partners can be invoiced. Choose the invoice option at the checkout. We can provide bespoke packages for schools to meet pupil and budget requirements. We are committed to providing a service to you that is fast, friendly and first class! In your basket at the moment No items Schools, LAs and organisations working with Number Partners can be invoiced. Choose the invoice option at the checkout. Featured A complete 10 session maths course for gifted and talented mathematicians. Wondermaths provides schools, home educators and other learning organisations with a fully prepared and resourced KS2 maths course. Each session folder contains comprehensive teaching notes, all handouts / activity sheets, resources needed for the session and a further challenge sheet. Used by pupils across the country, this is a fantastic resource created by the highly experienced teachers in our team.

65. Pythagorean History Legend has it that upon completion of his famous theorem, Pythagoras sacrificed 100 oxen. Although he is credited with the discovery of the famous theorem, http://www.geom.uiuc.edu/~demo5337/Group3/hist.html

A Brief History of the Pythagorean Theorem Just Who Was This Pythagoras, Anyway? Pythagoras (569-500 B.C.E.) was born on the island of Samos in Greece, and did much traveling through Egypt, learning, among other things, mathematics. Not much more is known of his early years. Pythagoras gained his famous status by founding a group, the Brotherhood of Pythagoreans, which was devoted to the study of mathematics. The group was almost cult-like in that it had symbols, rituals and prayers. In addition, Pythagoras believed that "Number rules the universe,"and the Pythagoreans gave numerical values to many objects and ideas. These numerical values, in turn, were endowed with mystical and spiritual qualities. Eudoxus developed a way to deal with these unutterable numbers. The sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse. This relationship has been known since the days of the ancient Babylonians and Egyptians, although it may not have been stated as explicitly as above. A portion of a 4000 year old Babylonian tablet (c. 1900 B.C.E.), now known as Plimpton 322 , (in the collection of Columbia University, New York), lists columns of numbers showing what we now call Pythagorean Triplessets of numbers that satisfy the equation a^2 + b^2 = c^2 Hands On Activity It is known that the Egyptians used a knotted rope as an aid to constructing right angles in their buildings. The rope had 12 evenly spaced knots, which could be formed into a 3-4-5 right triangle, thus giving an angle of exactly 90 degrees. Can you make a rope like this? Now use your knotted rope to check some right angles in your room at school or at home.

66. - Mathematics :: Fraction Material :: Theorem Of Pythagoras Theorem Of Pythagoras This set of material represents three cases of the theorem of Pythagoras. In the fi rst, two sides of the triangle are equal; in the second, the sides of the http://www.nienhuis.com/mathematics/fraction-material/theorem-of-pythagoras-1.ht

67. Pythagoras' Theorem Pythagoras Theorem was discovered by Pythagoras, a Greek mathematician and philosopher who lived between approximately 569 BC and 500 BC. http://www.mathsteacher.com.au/year10/ch14_measurement/01_pythag/18pythag.htm

Year 10 Interactive Maths - Second Edition Pythagoras' Theorem Pythagoras' Theorem was discovered by Pythagoras, a Greek mathematician and philosopher who lived between approximately 569 BC and 500 BC 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: 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 AD. Applications of Pythagoras' Theorem To solve a word problem, read the problem and draw a diagram. Then write the given information on the diagram and identify any right-angled triangle(s). Use Pythagoras' Theorem to form an equation and solve the equation thus obtained. Translate the solution into a worded answer. Example 1 A ship sails 80 km due east and then 18 km due north. How far is the ship from its starting position when it completes this voyage?

68. Theorem Of Pythagoras This java applet shows you (automatically step by step) How ancient Chinese people discovers the same theorem. (much earlier than Pythagoras). http://physci.kennesaw.edu/javamirror/ntnujava/abc/Pythagoras.html

Theorem of Pythagoras a + b = c This java applet shows you (automatically - step by step) How ancient Chinese people discovers the same theorem. (much earlier than Pythagoras). You can change the interval delta T (in second, default value = 2 second). Click mouse button for manual control mode : Click right mouse button : show the following step Click left mouse button : show the previous step When you reach the last step, Press reset button to restart related Pythagoras java applet Your suggestions are highly appreciated! Please click hwang@phy03.phy.ntnu.edu.tw Author¡G Fu-Kwun Hwang Dept. of physics National Taiwan Normal University Last modified :¡@

69. Pythagoras Theorem And Fibonacci Numbers Pythagoras Theorem and Fibonacci numbers. Pythagoras Theorem and Lucas numbers. 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.

70. Lesson 9.1•The Theorem Of Pythagoras Lesson 9.4•Story Problems Name Period Date 1. A 20 ft ladder reaches a window 18 ft high. How far is the foot ofthe ladder from the base ofthe building? http://www.keymath.com/documents/dg4/PracticeYourSkills/DG4PS_893_09.pdf

71. Pythagorean Philosophy: Simple Deduction Of Pythagoras Theorem Pythagorean Theorem Pythagoras Philosophy Pythagorean Theorem Proofs from the Spherical Standing Wave Structure of Matter (WSM). http://www.spaceandmotion.com/Philosophy-Pythagoras-Pythagorean-Theorem.htm

Philosophy Eastern Philosophy Wisdom Quotes Ancient Greek Philosophy Heraclitus Logos Dynamic Unity Socrates Wisdom Truth Apology Plato's Republic Greek Philosopher Aristotle Unity Metaphysics Marcus Aurelius Stoic Meditations Benedict Spinoza Ethics in Motion Gottfried Leibniz One Monadology George Berkeley Idealism Mind God David Hume Problem Causation Immanuel Kant Pure Reason Friedrich Nietzsche Quotes Good Evil Political Science Global Politics Ed. Philosophy Education of Truth Philosophy of Art Famous Artists Philosophy of Mind Idealism Realism Postmodernism Modern Definition! Philosophy Site Map Subjects Truth Reality (Home) Simple Science Metaphysics Substance Mathematical Physics Einstein Relativity Quantum Physics Cosmology Space Philosophy Truth Theology Religion Evolution Ecology Health Nutrition Education Wisdom Politics Utopia The Spherical Standing Wave Structure of Matter (WSM) in Space Site Introduction (2010): Despite several thousand years of failure to correctly understand physical reality (hence the current postmodern view that this is impossible ) there is an obvious solution.

72. Theorem Of Pythagoras - Gives A Geometric Proof Of The Rule For Measuring The Si Science Central 502059 - Proof of Pythagoras Theorem. Related sites WebMath (Popularity ) A set of tutorials on various topics in introductory mathematics, as well as http://www.sciencecentral.com/site/502059

73. Pythagoras' Theorem Jul 21, 2005 Disclaimer I have learned quite a bit about this and other proofs of the Pythagoras theorem since last time I edited this page. http://www.math.ntnu.no/~hanche/pythagoras/

Behold! The above picture is my favourite proof of Pythagoras' theorem. Filling in the details is left as an exercise to the reader. I have learned quite a bit about this and other proofs of the Pythagoras theorem since last time I edited this page. I now know that much of what you read below is wrong or misguided. Until I can find the time to improve the page, you should read this with a skeptical eye. (Always good advice anyhow.) It's not all wrong, of course. But to give just one example of the wrongness, the Chou pei suan ching and Zhoubi suanjing are one and the same: They are just transliterations of the Chinese phrase in, respectively, the and the pinyin Is this the oldest proof? This proof is sometimes referred to as the Chinese square proof , or just the Chinese proof . The righthand picture above appears in the Chou pei suan ching (ca. 1100 B.C.E.), for the special (3,4,5) pythagorean triple. See also Development of Mathematics in Ancient China According to David E. Joyce

74. About "The Theorem Of Pythagoras" A videotapeand-workbook module that explores a basic topic in high school mathematics in ways......Author Project MATHEMATICS!, California Institute of Technology http://www.mathforum.org/library/view/7534.html

The Theorem of Pythagoras Library Home Full Table of Contents Suggest a Link Library Help Visit this site: http://www.projectmathematics.com/pythag.htm Author: Project MATHEMATICS!, California Institute of Technology Description: A videotape-and-workbook module that explores a basic topic in high school mathematics in ways that cannot be done at the chalkboard or in a textbook. Several animated proofs of the Pythagorean theorem are presented, with applications to real-life problems and to Pythagorean triples. The theorem is extended to 3-space, but does not hold for spherical triangles. Levels: High School (9-12) Languages: English Resource Types: Multimedia Video Lesson Plans and Activities Textbooks Math Topics: Higher-Dimensional Geometry Triangles and Other Polygons Math Ed Topics: Audiovisual/Multimedia Curriculum/Materials Development Home The Math Library ... Help http://mathforum.org/ The Math Forum is a research and educational enterprise of the Goodwin College of Professional Studies

75. Babylonian Pythagoras Certainly the Babylonians were familiar with Pythagoras s theorem. A translation of a Babylonian tablet which is preserved in the British museum goes as http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Babylonian_Pythagoras.htm

Pythagoras's theorem in Babylonian mathematics Babylonian index History Topics Index Version for printing 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.

76. YouTube - Theorem Of Pythagoras Proof of the theorem of pythagoras using similar triangles. http://www.youtube.com/watch?v=E_41-NV_NY4

77. Pythagoras - History For Kids! Oct 21, 2010 Pythagoras himself is best known for proving that the Pythagorean Theorem was true. The Sumerians, two thousand years earlier, already knew http://www.historyforkids.org/learn/greeks/science/math/pythagoras.htm

Pythagoras for Kids - the ancient Greek mathematician Pythagoras and the Pythagorean Theorem Pythagoras Pythagoras lived in the 500's BC , and was one of the first Greek mathematical thinkers. He spent most of his life in the Greek colonies in Sicily and southern Italy. He had a group of followers (like the disciples of Jesus ) who followed him around and taught other people what he had taught them. The Pythagoreans were known for their pure lives (they didn't eat beans , for example, because they thought beans were not pure enough). They wore their hair long, and wore only simple clothing , and went barefoot. Both men and women were Pythagoreans. Pythagoreans were interested in philosophy , but especially in music and mathematics , two ways of making order out of chaos. Music is noise that makes sense, and mathematics is rules for how the world works. Pythagoras himself is best known for proving that the Pythagorean Theorem was true. The Sumerians , two thousand years earlier, already knew that it was generally true, and they used it in their measurements, but Pythagoras is said to have proved that it would always be true. We don't really know whether it was Pythagoras that proved it, because there's no evidence for it until the time of Euclid , but that's the tradition. Some people think that the proof must have been written around the time of Euclid, instead.

78. The Pythagorean Theorem. Topics In Trigonometry. (A theorem is a statement that can be proved). Credit for this theorem goes to the Greek philosopher Pythagoras, who lived in the 6th century B. C. http://www.themathpage.com/atrig/pythagorean-theorem.htm

79. YouTube - Theorem Of Pythagoras Live @ Villa Nachttanz live http://www.youtube.com/watch?v=L0IRI1S6cDA

80. BBC - KS3 Bitesize: Maths - Pythagoras' Theorem - Introduction A key stage 3 revision and recap resource for maths, covering using Pythagoras Theorem to find the length of the hypotenuse, another side and a segment. http://www.bbc.co.uk/schools/ks3bitesize/maths/shape_space/pythagoras_theorem/re

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