Angle Trisection, Bhaskara’s Proof, and Pythagorean Theorem

Abstract

This paper deals with 1) angle trisection, 2) Bhaskara’s first proof, and 3) Pythagorean theorem. The purpose of this paper is threefold. First, to show a new, direct method of trisecting the 90⁰ angle using unmarked straight edge and compass; secondly, to show Bhaskara’s first proof of the Pythagorean theorem (c² = a² + b²) as embedded in this new, direct trisection of the 90⁰ angle; lastly, to show the derivation of the Pythagorean theorem from this trisection of the 90⁰ angle. This paper employs the direct dissection method. It concludes by presenting four points: a) the concept of trisectability as distinct from concept of constructability; b) the trisection of the 90⁰ angle as really a new, different method; c) Bhaskara’s first proof of the Pythagorean theorem as truly embedded in this trisection of the 90⁰ angle and; d) another way of deriving Pythagorean theorem from this trisection of the 90⁰ angle.