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 The triangle of reflections.

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Type of Resource: text

Genre: Electronic Thesis or Dissertation

Issuance: single unit

Date Created: Spring 2014

Date Issued: 2014

Publisher: Florida Atlantic University

Physical Form: Online Resource

Extent: 89 p.

Language(s): English

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

Identifier: FA00004167 (IID)

Note(s): Includes bibliography.Thesis (M.S.)--Florida Atlantic University, 2014.

Subject(s): Geometer's SketchpadGeometry -- Study and teachingGeometry, HyperbolicMathematics -- Computer network resourcesProblem solving

Held by: Florida Atlantic University Digital Library

Sublocation: Boca Raton, Fla.

Persistent Link to This Record:

Restrictions on Access: All rights reserved by the source institution

Owner Institution: FAU

Autor: Torres, Jesus, author Yiu, Paul Dr., Thesis advisor Charles E. Schmidt College of Science, Degree grantor



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