Titlebook: Symmetry; A Mathematical Explo Kristopher Tapp Textbook 2021Latest edition Springer Nature Switzerland AG 2021 Cayley table.Euclidean space

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Symmetries of 3D Objects,a classification of the ways in which bounded 3D objects can be symmetric. No matter what object I print on my 3D printer or sculpt from clay, you soon will be able to determine how it fits into the classification scheme.

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What Is a Number?,s chapter precisely answers this question and relates the answer back to our study of symmetry. It ends with an optional “Elements of Mathematics” section that uses equivalence relations to define . and . even more rigorously.

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Excursions in Numbers,e set of prime numbers (Euclid’s Theorem) and the size of the set of real numbers (Cantor’s Theorem). This chapter is optional because it is not directly related to symmetry, but is included in order to showcase some of the most beautiful proofs in the history of mathematics.

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Rigid Motions as Functions,hapter). This new viewpoint is the right starting point, not only for finally going back and proving some of the important theorems in this book, but also for exploring whole new vistas in higher mathematics. Along the way, you’ll encounter a visual proof of the Pythagorean Theorem.