# An Exploration of Spherical Geometry

## University

Shawnee State University

## Major

Integrated Mathematics 7-12

## 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

## Recommended Citation

McKinney, Abigail, "An Exploration of Spherical Geometry" (2024). *Celebration of Scholarship*. 6.

https://digitalcommons.shawnee.edu/cos/2024/monday/6

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.