An Exploration of Spherical Geometry

Abigail McKinneyFollow

University

Shawnee State University

Major

Integrated Mathematics 7-12

Student Type

Undergraduate Student

Presentation Types

Oral Presentation

Keywords:

Geometry, Sphere, Lenart

Abstract

In geometry, there are many branches of geometry that have specific rules and conditions. Spherical geometry is a branch of geometry that is relatively unexplored; Euclidean geometry is the main branch of geometry that is learned in school mathematics. The goal of my senior research project was to explore spherical geometry and then compare it to the common facts that are accepted in Euclidean geometry. Through the use of a Lenart’s sphere and written labs, the rules of spherical geometry are investigated and reported through a combination of written out explanations and pictures of the experiments completed as a part of the labs. As spherical geometry was explored, Euclidean geometry was used to reason about and analyze the results. To integrate the results of the research for this capstone project, an analysis of the similarities and the difference of spherical geometry and Euclidean geometry was completed.

Human Subjects

no

IRB Approval

no

Faculty Mentor Name

Chris O’Connor

Faculty Mentor Title

Associate Professor

Faculty Mentor Academic Department

Mathematical Sciences

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An Exploration of Spherical Geometry

In geometry, there are many branches of geometry that have specific rules and conditions. Spherical geometry is a branch of geometry that is relatively unexplored; Euclidean geometry is the main branch of geometry that is learned in school mathematics. The goal of my senior research project was to explore spherical geometry and then compare it to the common facts that are accepted in Euclidean geometry. Through the use of a Lenart’s sphere and written labs, the rules of spherical geometry are investigated and reported through a combination of written out explanations and pictures of the experiments completed as a part of the labs. As spherical geometry was explored, Euclidean geometry was used to reason about and analyze the results. To integrate the results of the research for this capstone project, an analysis of the similarities and the difference of spherical geometry and Euclidean geometry was completed.