TY - JOUR
AU - De Catalina, Emiliano C.
PY - 2021/05/28
Y2 - 2022/12/08
TI - Angle Trisection, Bhaskaraâ€™s Proof, and Pythagorean Theorem
JF - Recoletos Multidisciplinary Research Journal
JA - RMRJ
VL - 9
IS - 1
SE - Articles
DO - 10.32871/rmrj2109.01.01
UR - https://rmrj.usjr.edu.ph/rmrj/index.php/RMRJ/article/view/987
SP - 1-11
AB - <p>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 90<sup>0</sup> angle using unmarked straight edge and compass; secondly, to show Bhaskaraâ€™s first proof of the Pythagorean theorem (c<sup>2</sup> = a<sup>2</sup> + b<sup>2</sup>) as embedded in this new, direct trisection of the 90<sup>0</sup> angle; lastly, to show the derivation of the Pythagorean theorem from this trisection of the 90<sup>0</sup> 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 90<sup>0</sup> angle as really a new, different method; c) Bhaskaraâ€™s first proof of the Pythagorean theorem as truly embedded in this trisection of the 90<sup>0</sup> angle and; d) another way of deriving Pythagorean theorem from this trisection of the 90<sup>0</sup> angle.</p>
ER -