# Symmetry

## A Mathematical Exploration

• Kristopher Tapp
Textbook

1. Front Matter
Pages i-xiv
2. Kristopher Tapp
Pages 1-16
3. Kristopher Tapp
Pages 17-33
4. Kristopher Tapp
Pages 35-50
5. Kristopher Tapp
Pages 51-62
6. Kristopher Tapp
Pages 63-74
7. Kristopher Tapp
Pages 75-86
8. Kristopher Tapp
Pages 87-114
9. Kristopher Tapp
Pages 115-137
10. Kristopher Tapp
Pages 139-148
11. Kristopher Tapp
Pages 149-165
12. Kristopher Tapp
Pages 167-178
13. Kristopher Tapp
Pages 179-197
14. Kristopher Tapp
Pages 199-211
15. Back Matter
Pages 213-215

### Introduction

This textbook is perfect for a math course for non-math majors, with the goal of encouraging effective analytical thinking and exposing students to elegant mathematical ideas.  It includes many topics commonly found in sampler courses, like Platonic solids, Euler’s formula, irrational numbers, countable sets, permutations, and a proof of the Pythagorean Theorem.  All of these topics serve a single compelling goal: understanding the mathematical patterns underlying the symmetry that we observe in the physical world around us.

The exposition is engaging, precise and rigorous.  The theorems are visually motivated with intuitive proofs appropriate for the intended audience.  Students from all majors will enjoy the many beautiful topics herein, and will come to better appreciate the powerful cumulative nature of mathematics as these topics are woven together into a single fascinating story about the ways in which objects can be symmetric.

Kristopher Tapp is currently a mathematics professor at Saint Joseph's University.  He is the author of 17 research papers and one well-reviewed undergraduate textbook, Matrix Groups for Undergraduates.  He has been awarded two National Science Foundation research grants and several teaching awards.

### Keywords

Cantor’s theorem Cayley table Euclidean space Euler characteristic Platonic solid Pythagorean Theorem Symmetry alternating group chirality group theory irrational number isomorphism isoperimetric linear algebra orthogonal matrix permutation planar graph prime number real number reflection rotation symmetry group transformational geometry uncountable wallpaper pattern

#### Authors and affiliations

• Kristopher Tapp
• 1
1. 1., Department of MathematicsSaint Joseph's UniversityPhiladelphiaUSA