101. Euclid's Elements, Book I, Proposition 47 This proposition, I.47, is often called the Pythagorean theorem, called so byProclus and others centuries after pythagoras and even centuries after 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

102. NOVA Online | The Proof | Pythagorean Puzzle | Theorem How can I use the Pythagorean theorem to solve real problems? Andrew Wiles Math s Hidden Woman Pythagorean Puzzle http://www.pbs.org/wgbh/nova/proof/puzzle/theorem.html

Demonstrate the Pythagorean Theorem Think of each side of a right triangle as also being a side of a square that's attached to the triangle. The area of a square is any side multiplied by itself. (For example, a x a a On the diagram below, show that a b c , by moving the two small squares to cover the area of the big square. How can I use the Pythagorean theorem to solve real problems? Andrew Wiles Math's Hidden Woman Pythagorean Puzzle ... WGBH

103. Pythagoras Heath 7 gives a list of theorems attributed to pythagoras, (ii) The theoremof pythagoras for a right angled triangle the square on the hypotenuse http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pythagoras.html

Pythagoras of Samos Born: about 569 BC in Samos, Ionia Died: about 475 BC Click the picture above to see eleven larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing Pythagoras of Samos is often described as the first pure mathematician. He is an extremely important figure in the development of mathematics yet we know relatively little about his mathematical achievements. Unlike many later Greek mathematicians, where at least we have some of the books which they wrote, we have nothing of Pythagoras's writings. The society which he led, half religious and half scientific, followed a code of secrecy which certainly means that today Pythagoras is a mysterious figure. We do have details of Pythagoras's life from early biographies which use important original sources yet are written by authors who attribute divine powers to him, and whose aim was to present him as a god-like figure. What we present below is an attempt to collect together the most reliable sources to reconstruct an account of Pythagoras's life. There is fairly good agreement on the main events of his life but most of the dates are disputed with different scholars giving dates which differ by 20 years. Some historians treat all this information as merely legends but, even if the reader treats it in this way, being such an early record it is of historical importance. Pythagoras's father was Mnesarchus ([12] and [13]), while his mother was Pythais [8] and she was a native of Samos. Mnesarchus was a merchant who came from Tyre, and there is a story ([12] and [13]) that he brought corn to Samos at a time of famine and was granted citizenship of Samos as a mark of gratitude. As a child Pythagoras spent his early years in Samos but travelled widely with his father. There are accounts of Mnesarchus returning to Tyre with Pythagoras and that he was taught there by the Chaldaeans and the learned men of Syria. It seems that he also visited Italy with his father.

104. PYTHAGOREAN THEOREM CALCULATOR SOLVES FOR HYPOTENUSE OR LENGTH OF EITHER SIDE Pythagorean theorem Calculator That Can Solve For Hypotenuse length OR length ofeither of the sides. http://www.1728.com/pythgorn.htm

Pythagorean Theorem Calculator The Pythagorean Theorem is used for calculating the hypotenuse length of a right triangle. A right triangle with sides 6 and 8 will have a hypotenuse length of 10 because: 10 = Square Root Of ( 6 If you know the hypotenuse and the length of 1 side, the Pythagorean Theorem calculates the other side by: As an added bonus, all 3 angles will automatically be calculated. Do you want to solve for: or Click here to see a proof of the Pythagorean Theorem Significant Figures >>> Numbers are displayed in scientific notation with the amount of significant figures you specify. For easier readibility, numbers between .001 and 1,000 will not be in scientific notation but will still have the same precision. You may change the number of significant figures displayed by changing the number in the box above. Most browsers, will display the answers properly but if you are seeing no answers at all, enter a zero in the box above, which will eliminate all formatting but at least you will see the answers.

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