This problem outlines one of the shortest proofs of the
Chapter 1, Problem 32(choose chapter or problem)
This problem outlines one of the shortest proofs of the Pythagorean theorem. The proof was discovered by the Hindu mathematician Bhaskara (1114 ca. 1185). (For other proofs, see the next exercise and also Exercise 100 on page 83.) In the figure we are given a right triangle ACB with the right angle at C, and we want to prove that a2 b2 c2 . In the figure, is drawn perpendicular to (a) Check that and that ^BCD and ^BAC are similar. (b) Use the result in part (a) to obtain the equation a/y c/a, and conclude that a2 cy. (c) Show that ^ACD is similar to ^ABC, and use this to deduce that b2 c2 cy. CAD (d) Combine the two equations deduced in parts (b) and (c) to arrive at a2 b2 c2
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