Pythagorean Theorem By Jane Doe. Pythagoras The Man Who Made the Theory.

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Presentation transcript:

Pythagorean Theorem By Jane Doe

Pythagoras The Man Who Made the Theory

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

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

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

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

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

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

Pythagoras: Death Pythagoras is said to have been involved in a dispute between Croton and Sybaris. Pythagoras is said to have been involved in a dispute between Croton and Sybaris. Pythagoras’ school got attacked by a Croton noble 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. 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.

The Pythagorean Theorem The Famous Theory for a Right Triangle

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

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

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 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

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: 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 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 a wire going from the ground to a telephone pole or house Measuring the height of a building indirectly (without actually measuring it) 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. Knowing the hypotenuse of a drill, to decide how big of a hole to make.

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) 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 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) Measuring TV’s and computer moniters (they are measured in diagonals)