81. Unit 3 Section 1 : Pythagoras' Theorem Unit 3 Section 1 pythagoras theorem. pythagoras theorem relates thelengths of the sides in a rightangled triangle. A right-angled http://www.ex.ac.uk/cimt/mepres/book8/bk8i3/bk8_3i1.htm

Unit 3 Section 1 : Pythagoras' Theorem Pythagoras' Theorem relates the lengths of the sides in a right-angled triangle. A right-angled triangle has one angle of 90°. The side opposite the right angle is always the longest side, and is called the hypotenuse The diagram on the left shows a right-angled triangle. The lengths of the sides are 3cm, 4cm and 5cm. The hypotenuse is the 5cm side because it is opposite the right-angle and it is the longest side Now look at the diagram on the right. A square has been drawn on each of the sides of the triangle above. We are going to examine the areas of each of the squares. Shorter sides The square on the 3cm side has an area of 3cm × 3cm = 9cm². The square on the 4cm side has an area of 4cm × 4cm = 16cm². Hypotenuse The square on the 5cm side has an area of 5cm × 5cm = 25cm². How they are related If you add together the areas of the squares on the two shorter sides, you get 25cm². This is the same as the area of the square on the hypotenuse. Pythagoras' Theorem Pythagoras' theorem states that if you square the two shorter sides in a right-angled triangle and add them together, you

82. The Pythagorean Theorem turned this rose into a briar. Unfortunately, nobody knows how pythagoras originally proved the theorem, but here are three ways. http://www.perseus.tufts.edu/GreekScience/Students/Tim/Pythag'sTheorem.html

The Pythagorean Theorem The Pythagorean Theorem is one of Euclidean Geometry's most beautiful theorems. It is simple, yet obscure, and is used continuously in mathematics and physics. In short, it is really cool. Evidence of the theorem can be traced far back into Egyptian history with the help of the Rhind Papyrus(1788-1580 BC). The Rhind Papyrus itself claims to be a copy of an earlier work, possibly dating as far back as 2000 BC. The use of the 3-4-5 triangles(9+16=25) to construct perfect right angles, indeed seems to have been a very common practice, long ago. Unfortunately, little information predates the Greeks, so this will probably remain another mystery of the Egyptians. Traditionally, however, the theorem has been credited[in western culture] to Pythagoras of Samos . The legend has it that he was so excited by its proof that he sacrificed a bull for the occasion, even though Pythagoreans were against animal sacrifice. Unfortunately, there are only legends. The Pythagorean School, which gets its name from its founder, was a secret cult. They regarded their knowledge as something to be kept from all outsiders. Thus, they did not write things down until the cult began to lose prominence several generations later, leaving posterity with a void where the life of Pythagoras should have been. Consequently, classicists do not know if Pythagoras was actually responsible for the first proof. How does one prove this enigma? The geometry books I have had experience with turned this rose into a briar. Unfortunately, nobody knows how "Pythagoras"

83. ThinkQuest : Library : Go Forth & Multiply: A Mathematics Adventure pythagoras theorem. pythagoras theorem. The pythagoras theorem is one of the mostimportant mathematical contributions. The pythagoras theorem states that. http://library.thinkquest.org/C0110248/trigonometry/pythagoras.htm

Index Education Want to learn more about the world of mathematics? Then go forth, and enter the wildest math adventure you've ever been! Learn new math concepts and refresh your knowledge for those you've already known. Understand how the formulae you use were derived from. Or, you can take a step back into the past and read about how mathematics and its concepts originated. Go forth and multiply! Visit Site 2001 ThinkQuest Internet Challenge Awards Achievement Award Students Teow Lim Raffles Junior College, Singapore, Singapore Vee San Raffles Girls' School (Secondary), Singapore, Singapore Coaches Poh Kheng Pioneer Junior College, Singapore, Singapore Jee Wah Raffles Girls' School (Sec), Hougang, Singapore Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site. Privacy Policy

84. Learn.co.uk - Learning Resources For The National Curriculum, Online Lessons, GC Other units Introduction. Applications. Introduction, pythagoras theorem. pythagoras theorem states In any rightangled triangle http://www.learn.co.uk/default.asp?WCI=Unit&WCU=36566

85. BBC - Education Scotland - Standard Grade Bitesize Revision - Maths I - Pythagor Index page for pythagoras s theorem, Trigonometry and Angles within the subject MathsI. Standard Grade Bitesize is the easy to use online revision service for http://www.bbc.co.uk/scotland/education/bitesize/standard/mathsI/pythagoras/inde

@import url('/includes/tbenh.css') ; Home TV Radio Talk ... A-Z Index SUNDAY 6th June 2004 Text only BBC Homepage Scotland Credits ... Help Like this page? Send it to a friend! B Home Maths I Pythagoras's Theorem, Trigonometry and Angles Biology Chemistry Computing Studies English French Geography History Maths I Maths II Modern Studies Physical Education Physics Discover our full range of revision videos and books! Pythagoras Trigonometry Angles Involved with Circles Angle and Line Facts http://www.bbc.co.uk/scotland/education/bitesize Print Back to top

86. Pythagoras' Theorem Friberg, a leading authority on Babylonian mathematics, presented convincing evidencethat the old Babolonians were aware of the pythagoras theorem around 1800 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. Is this the oldest proof? This proof is sometimes referred to as the Chinese square proof , or just the Chinese proof . It is supposed to have appeared in the Chou pei suan ching (ca. 1100 B.C.E.), according to Ralph H. Abraham [see ``Dead links'' below,] who attributes this information to the book by Frank J. Swetz and T. I. Kao, Was Pythagoras Chinese? . See also Development of Mathematics in Ancient China According to David E. Joyce 's A brief outline of the history of Chinese mathematics , however, the earliest known proof of Pythagoras is given by Zhoubi suanjing (The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven) (c. 100 B.C.E.-c. 100 C.E.) In the The MacTutor History of Mathematics archive there is a section devoted to Chinese mathematics . The overview section at that section also mentions the Zhoubi suanjing is a proof as well. I have been told that this proof, with the exclamation `Behold!', is due to the Indian mathematician Bhaskara II (approx. 1114-1185). A web page at the

87. Pythagoras --  Encyclopædia Britannica Internet Guide. , pythagoras Haven Northern Illinois University Interactivedemonstration of pythagoras theorem. , pythagoras Think http://www.britannica.com/eb/article?eu=63648

88. 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). Click here for GCSE maths coursework online Page by: Richard Tang Click here for GCSE forums! HOME GCSE bookshop GCSE Forums ... Matthew Woollard 2001

89. Chapter 11, 12 Pythagoras And His Theorem But to the initiate who first heard it, the theorem also partook of a mystical revelation.Tradition says that pythagoras himself celebrated the occasionly a http://www.anselm.edu/homepage/dbanach/pyth1.htm

Selections from Julia E. Diggins String, Straightedge, and Shadow Viking Press, New York 1965. (Illustrations by Corydon Bell) Now back in print for purchase at http://wholespiritpress.com/string.htm 11. PYTHAGORAS AND HIS FOLLOWERS The early story of Greek geometry is strangely different from its founding in Miletus . Most of what we know is a mixture of myth and magic, shapes and rules, all revolving around the fabulous figure of Pythagoras. The "divine" Pythagoras-that was what he was called, not only after his death but even in his own lifetime. For the latter part of the 6th century B.C. was still a time of superstition. The Ionian "physiologists" had only tried to find an orderly pattern in nature. Most men continued to believe that gods and spirits moved in the trees and the wind and the lightning. And cults were popular all over the Greek world-"mysteries," they were called-that promised to bring their members close to the gods in secret rites. Some were even headed by seers. Pythagoras was one of these. A native of the island of

90. 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).

91. Proof Of Pythagoras' Theorem - Mathematics At Apronus.com THE PROOF OF pythagoras theorem. pythagoras theorem If ABC is a triangleand )ACB is the right angle then AC ^2 + BC ^2 = AB ^2. http://www.apronus.com/geometry/pythagoras.htm

Apronus Home Mathematics Geometry THE PROOF OF PYTHAGORAS' THEOREM Pythagoras Theorem If ABC is a triangle and Proof Take any triangle ABC with <)ACB right. Let DECA, CFGB, ABKH be squares. Let C'C be the altitude of triangle ACB. And let <)C''C'B be right. The area of a square is the second power of the length of its side. Then it is enough to show that the sum of the areas of DECA and CFGB is equal to the area of ABKH. Hence it is enough to show that the sum of the areas of triangles DEA and FGB is equal to half of the area of ABKH. DE is the altitude of triangle DEA. Since <)ACB is right, segments AD and EB are parallel. Hence triangels DBA and DEA have the same length of altitudes and the same base. So the area of triangle DBA is equal to the area of triangle DEA. <)DAB = 90 degrees + <)CAB = <)CAH. Hence the area of triangle CHA is equal to the area of triangle DBA. Since C'C is the altitude of triangle ACB and FG is the altitude of triangle FGB. Since <)ACB is right, segments BG and AF are parallel. Hence triangels FGB and AGB have the same length of altitudes and the same base. So the area of triangle FGB is equal to the area of triangle AGB.

92. Pythagorean Theorem From MathWorld Pythagorean theorem from MathWorld For a right triangle with legs a and b and hypotenuse c, a^2+b^2=c^2. Many different proofs exist for this most fundamental of all geometric theorems. The http://rdre1.inktomi.com/click?u=http://mathworld.wolfram.com/PythagoreanTheorem

93. Pythagoras' Haven - In Deutsch Translate this page Der Lehrsatz des pythagoras a 2 + b 2 = c 2 wird bewiesen. Die Schalter NEXT, BACKund RESET erlauben einen Gang durch den Beweis. Der Satz des pythagoras. http://didaktik.physik.uni-wuerzburg.de/~pkrahmer/java/pythago/pythago.html

Der Lehrsatz des Pythagoras a + b = c wird bewiesen. Die Schalter NEXT, BACK und RESET erlauben einen Gang durch den Beweis. Zum JAVA Applet: Original Applet von Jim Morey (morey@math.ubc.ca) (deutscher Text von mm-physik). Der S atz des P ythagoras mm-physik

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

China India West Asia Greece ... Religion The Web Just H4K H4K Lesson Plans for Teachers Parents' Corner H4K Crafts and Projects Pythagoras Pythagoras lived in the 400'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 never married , but 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

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