Proof Of Pythagoras Theorem Using Vedic Mathematics

  • May 2020
  • PDF

This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA


Overview

Download & View Proof Of Pythagoras Theorem Using Vedic Mathematics as PDF for free.

More details

  • Words: 187
  • Pages: 2
PROOF OF PYTHAGORAS THEOREM USING VEDIC MATHEMATICS Let's start by looking at a square whose side length is (a+b). We can mark a point on the side that divides it into segments of length a and b. Here are three examples, using different lengths for legs a and b:

Inside the blue square let's construct a yellow square of side length c. Its corners must touch the sides of the blue square. The remainder of the space will consist of four blue congruent abc triangles. Here it is for our example squares:

In each case, the area of the larger blue square is equal to the sum of the areas of the blue triangles and the area of the yellow square. Since the area of a square is (side length)2 and the area of a triangle is 1/2(base)(height), we can write the equation: (a+ b)2 = c2 + 4[(1/2)a b]  (a+b)(a+b) = c2 + 2ab  a2 + 2ab + b2 = c2 + 2ab Now subtract the 2ab from both sides of the equation, and we have the Pythagorean theorem:

a2 + b2 = c2

Related Documents