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Articles

Vol. 9 No. 1 (2021)

Angle Trisection, Bhaskara?s Proof, and Pythagorean Theorem

DOI:
https://doi.org/10.32871/rmrj2109.01.01
Submitted
January 23, 2021
Published
May 28, 2021
pdf

Keywords

  • right angle
  • angle trisection
  • Bhaskara’s first proof
  • 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.

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