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Pythagorean Theorem

Pythagorean Theorem. By Jane Doe. Pythagoras. The Man Who Made the Theory. Pythagoras: His Early Life. Born in about 569 B.C. Born in Somos, Ionia Father was Mnesarchus Mother was Pythais Mnesarchus was a merchant Pythagoras traveled with father Striking birthmark on thigh

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Pythagorean Theorem

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  1. Pythagorean Theorem By Jane Doe

  2. Pythagoras The Man Who Made the Theory

  3. Pythagoras: His Early Life • Born in about 569 B.C. • Born in Somos, Ionia • Father was Mnesarchus • Mother was Pythais • Mnesarchus was a merchant • Pythagoras traveled with father • Striking birthmark on thigh • Two or three brothers

  4. Pythagoras: Influential People • Among his teachers, three people were to influence him most • Pherekydes, a philosopher who is often described as his teacher • Thales, an old philosopher and master of Anaximander • Anaximander, a philosopher, pupil, and lecturer on Miletus

  5. Pythagoras: Egypt • Went to Egypt with letter of introduction by tyrant ruler of Samos • Picked up traditions there he kept for rest of life: • Secrecy of Priests • Aversion to Beans • Refusal to Animal Skin Clothing • Porphyry claims he learnt Geometry from Egyptians

  6. Pythagoras: Egypt (continued) • Tyrant ruler of Samos had alliance with Egypt • Tyrant ruler joined Persians to invade Egypt • Persia won • Pythagoras taken prisoner and taken to Babylon • Escaped and returned to Samos

  7. Pythagoras: Schools • Founded a school called “semicircle” • Traveled to Croton and founded a school • Beliefs by Pythagoras were: • That at its deepest level, reality is mathematical in nature • That philosophy can be used for spiritual purification • That the soul can rise to union with the divine • That certain symbols have a mystical significance • That all brothers of the order should observe strict loyalty and secrecy.

  8. Pythagoras: Music • Noticed that strings with ratios of integers produced specific sounds and harmonious tones • Noticed that these strings could be extended to other music

  9. Pythagoras: Death • Pythagoras is said to have been involved in a dispute between Croton and Sybaris. • Pythagoras’ school got attacked by a Croton noble • Pythagoras flees to Metapontium, and most say he died there. Some evidence has been found to suggest that Pythagoras returned to Croton. No one knows for sure.

  10. The Pythagorean Theorem The Famous Theory for a Right Triangle

  11. Pythagorean Theorem: Origin • May have been known to Babylonian’s before Pythagoras’ time • Pythagoras’ school is credited with the first proof of the Theorem • It is now known as the Pythagorean Theorem after Pythagoras

  12. Pythagorean Theorem: Explanation • The official Pythagorean Theorem is: A²+B²=C² • The sides squared are really squares. • It really means that the squares on the legs (A and B) equal the square on the hypotenuse (C)

  13. Pythagorean Theorem: Proof • There are over 100 proofs for the Pythagorean Theorem. Some are located in the Geometry textbook, written by Larson, Boswell, and Stiff, and published by McDougal Littell, on pages 535, 540, and 557

  14. Pythagorean Theorem: Real Life Uses • There are many real-life uses for the Pythagorean Theorem. Most of them have to do with construction. They are: • Building a harp; use the theorem to find the ratio of each string from the first • Measuring a wire going from the ground to a telephone pole or house • Measuring the height of a building indirectly (without actually measuring it) • Knowing the hypotenuse of a drill, to decide how big of a hole to make.

  15. Pythagorean Theorem: Real Life Uses(continued) • Knowing the maximum height of a bunk-bed to be able to stand up straight (they are built on the side, and then stood up straight) • Digging a foundation for a house; measure the floor and sides and hypotenuse, and if it fulfills The Pythagorean Theorem, it is a 90° angle • Measuring TV’s and computer moniters (they are measured in diagonals)

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