MATH-UA 120 Lecture Notes - Lecture 1: Hypotenuse
Document Summary
After euclid came another mathematician with a way to solve the pythagorean theorem is a way never before conceived. This mathematician was the indian astronomer bh skara ii(1114-1185). He actually created two proofs to the theorem. His first proof shows four congruent right triangles surrounding a small square. The hypotenuses of the triangles surround the entire figure with a larger square. Let"s call the side length of the small square x, the hypotenuse c, the small leg a, and the large leg b. It can be seen in the first part of the figure that b is equal to a+x, which means that x is b-a, as shown in the second part. In the second part, the triangles were separated to make it easier to see. The area of the larger square is equal to the sum of the areas of the four right triangles and the area of the small square.
