Philippine E-Journals

Angle Trisection, Bhaskara’s Proof, and Pythagorean Theorem

Emiliano C. De Catalina

 

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.