Mathematics is discovered by looking at examples, noticing patterns, making conjectures, and testing those conjectures. Once discovered, the final results get organized and put in textbooks. The details and the excitement of the discovery are lost. This book introduces the reader to the excitement of the original discovery. By means of a wide variety of tasks, readers are led to find interesting examples, notice patterns, devise rules to explain the patterns, and discover mathematics for themselves. The subject studied here is the mathematics behind the idea of symmetry, but the methods and ideas apply to all of mathematics. The only prerequisites are enthusiasm and a knowledge of basic high-school math. The book is only a guide. It will start you off in the right direction and bring you back if you stray too far. The excitement and the discovery are left to you.A Guide to Discovering Mathematics David W. Farmer. 3.4 INVERSES 35 Here is the multiplication table of the symmetries of the triangle: Each row and each column of the table is labeled with a symmetry written in ... But rm is not in our standard form, so instead we use mr2, because rm a mr2, and mr2 is in standard form.
|Title||:||Groups and Symmetry|
|Author||:||David W. Farmer|
|Publisher||:||American Mathematical Soc. -|