Angle Trisection, Bhaskaraâ€™s Proof, and Pythagorean Theorem
Keywords:right angle, angle trisection, Bhaskaraâ€™s first proof, Pythagorean theorem
This paper deals with 1) angle trisection, 2) Bhaskaraâ€™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 Bhaskaraâ€™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) Bhaskaraâ€™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.
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