MTH 232
Section 10.3
The Pythagorean Theorem
Pythagoras
• Born approximately 570 B.C. on the Greek island of
Samos
• Founded his academy approximately 518 B.C. in
southern Italy. He and his followers held five basic
beliefs:
(1) that at its deepest level, reality is mathematical in
nature,
(2) that philosophy can be used for spiritual purification,
(3) that the soul can rise to union with the divine,
(4) that certain symbols have a mystical significance, and
(5) that all brothers of the order should observe strict
loyalty and secrecy.
The Theorem
• Because of the communal nature of the
Society, it is likely that someone else
“discovered” the Theorem but Pythagoras
received credit for the discovery.
• There is evidence that the Theorem was used
previously by the Babylonians,
Mesopotamians, Indians, and Chinese.
• Pythagoras, however, is credited with
providing the first mathematical proof.
a2 + b2 = c2
• In a right triangle, the square of the length of
the hypotenuse (the longest side of a right
triangle, located directly across from the right
angle) is equal to the sum of the squares of
the lengths of the legs (the two sides adjacent
to the right angle).
• The converse is also true (if the sides of a
triangle satisfy the conditions of a right
triangle, then the triangle is a right triangle).
Pythagorean Triples
• Pythagorean Triples are integers that, used as
the lengths of a right triangle, satisfy the
Pythagorean Theorem:
• 3, 4, 5
• 5, 12, 13
• 7, 24, 25
• 8, 15, 17
• 9, 40, 41