A line-and-conic theorem having a visual correlate

Abstract

This article describes a new and general line-and-conic property, leading to a consideration of a ‘six-point’ circle and the related geometry of an interesting visual illusion.

A conic theorem generalised: directed angles and applications

“…A new and general proof of theorem [1] is presented, which accommodates directed angles and covers all possible configurations of line and conic. A sign convention for the use of directed angles in this setting is developed, and examples are given showing how this fundamental theorem can be used to establish, much more directly and succinctly, the many tangent/focus properties of conics.…”

“…Since this theorem highlights a fundamental conic relationship between lines, tangents and foci, it can be used to prove the various tangent/focus properties more efficiently and succinctly than the standard textbook methods, as shown in the following examples (see [1] also).…”