Author Type

Graduate Student

Date of Award

2014

Document Type

Thesis

Publication Status

Version of Record

Submission Date

October 2026

Thesis/Dissertation Advisor [Chair]

Yiu, Paul Y.

Abstract

This thesis presents some results in triangle geometry discovered using dynamic software, namely, Geometer’s Sketchpad, and confirmed with computations using Mathematica 9.0. Using barycentric coordinates, we study geometric problems associated with the triangle of reflections T of a given triangle T, yielding interesting triangle centers and simple loci such as circles and conics. These lead to some new triangle centers with reasonably simple coordinates, and also new properties of some known, classical centers. Particularly, we show that the Parry reflection point is the common point of two triads of circles, one associated with the tangential triangle, and another with the excentral triangle. More interestingly, we show that a certain rectangular hyperbola through the vertices of T appears as the locus of the perspector of a family of triangles perspective with T, and in a different context as the locus of the orthology center of T with another family of triangles.

Extent

89 p.

Comments

Includes bibliography.|Thesis (M.S.)--Florida Atlantic University, 2014.|FAU Electronic Theses and Dissertations Collection|Includes bibliography.

Identifier

FA00004167

Format

pdf

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