Pascal's hexagon theorem reproved by elementary tools only

Insong Choe

doi:10.4134/CKMS.c210397

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Commun. Korean Math. Soc. 2022; 37(4): 989-993

Online first article September 20, 2022 Printed October 31, 2022

https://doi.org/10.4134/CKMS.c210397

Pascal's hexagon theorem reproved by elementary tools only

Insong Choe

Konkuk University

Abstract

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Abstract

In this paper, we prove Pascal's hexagon theorem by elementary tools only. We follow the well-known route to prove the theorem by Bez\'{o}ut's theorem, explaining all the details in elementary argument. In particular, we prove a toy version of Study's lemma.

Keywords: Pascal's hexagon theorem, Bez\'{o}ut's theorem, Study's lemma, resultant

MSC numbers: 51A05, 51N15, 00A09