Some Polynomial Conditions of Cyclic Quadrilaterals, Tilted Kites and Other Quadrilaterals

TL;DR

This paper explores polynomial conditions in Euclidean geometry related to various quadrilaterals, including cyclic and tilted kites, using algebraic methods like Groebner bases to establish geometric properties.

Contribution

It introduces new polynomial conditions characterizing specific quadrilaterals, combining geometric analysis with algebraic techniques such as Groebner bases.

Findings

Polynomial conditions for cyclic quadrilaterals derived

Conditions for tilted kites with equal angles established

Use of Groebner bases to prove geometric properties

Abstract

In this paper, we investigate some polynomial conditions that arise from Euclidean geometry. First we study polynomials related to quadrilaterals with supplementary angles, this includes convex cyclic quadrilaterals, as well as certain concave quadrilaterals. Then we consider polynomials associated with quadrilaterals with some equal angles, which include convex and concave tilted kites. Some of the results are proved using Groebner bases computations.