Reflecting triangles with a dense set of vertex points in the plane
Date of Publication
1999
Document Type
Master's Thesis
Degree Name
Master of Science in Mathematics
Subject Categories
Algebraic Geometry
College
College of Science
Department/Unit
Mathematics and Statistics
Thesis Adviser
Dr. Jose Tristan Reyes
Defense Panel Chair
Dr. Yolando B. Beronque
Defense Panel Member
Dr. Blessilda P. Raposa
Dr. Leonor A. Ruivivar
Abstract/Summary
This thesis is an expository work based on the main part of the paper Reflecting a Triangle in the Plane by Peter Frankl, Imre Barany, and Hiroshi Maechara published in Graphs and Combinatories (1993) 9: 97-104. The article states that if the three angles of a triangle (delta) in the plane are different from (60 degrees, 60 degrees, 60 degrees), (30 degrees, 30 degrees, 120 degrees), 45 degrees, 45 degrees, 90 degrees), (30 degrees, 60 degrees, 90 degrees), then the set of vertices of those triangles which are obtained from (triangle) by repeating edge-reflection (denoted by Omega ABC) is dense in the plane. This thesis will prove the following main results: Theorem 0.0.1 Let delta ABC be a rational triangle with angles alpha less than or equal to beta less than or equal to y. If (alpha, beta, y) is not equal to (60 degrees, 60 degrees, 60 degrees), (30 degrees, 30 degrees, 120 degrees),(45 degrees, 45 degrees, 90 degrees), (30 degrees, 60 degrees, 90 degrees),then Omega ABC is dense in the plane. Theorem 0.0.2 Let ABC be an irrational triangle, then Omega ABC is dense in the plane.
Abstract Format
html
Language
English
Format
Accession Number
TG02866
Shelf Location
Archives, The Learning Commons, 12F Henry Sy Sr. Hall
Physical Description
52 numb. leaves
Keywords
Triangle; Geometry; Plane; Vertex operator algebras
Recommended Citation
Daval Santos, P. A. (1999). Reflecting triangles with a dense set of vertex points in the plane. Retrieved from https://animorepository.dlsu.edu.ph/etd_masteral/1971
