Proving the Euler line and nine-point-line theorems through the three concurrence theorems

Date of Publication

2002

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Abstract/Summary

This thesis is an exposition of the article by Frank M. Eccles entitled " The Euler Line and Nine-Point-Circle Theorems", which appeared in the Mathematics Magazine (1999). It presents two extraordinary theorems seldom used in geometry classes, the Euler Line and Nine-Point Circle Theorems. Both theorems concern three important points, the circumcenter, the centroid, and the orthocenter of a triangle, whose collinearity is proven by the Euler Line Theorem. The Nine Point Circle Theorem reveals a remarkable conclusion that other nine well-defined points all lie in a circle centered at the midpoint of the segment joining the circumcenter and the orthocenter.

The researcher provided the necessary background information such as the definition of geometric terms, theorems in similarity, and important notations so that these related information will give a more detailed explanation of how the theorems are derived.

Abstract Format

html

Language

English

Format

Print

Accession Number

TU11102

Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

Physical Description

48 numb. leaves

This document is currently not available here.

Share

COinS