Do a search for the meaning of mathematics and you are certain to find a great many definitions. Mathematics is the study of such things as quantity, structure, space, change, numbers, measurement, combination, interrelation, shape, and arrangement. This book looks at mathematics as a search for patterns, patterns arising from arithmetic, geometry, number theory, and algebra. Some of the patterns are displayed as single pictures, but others are revealed step by step via video recordings. The creation of a pattern is often the most important part of a pattern. All of the examples presented in this book were developed using software written by the author. You can learn more about the software, and download free copies of it, by visiting Syzygy Shareware at https://tcbretl.weebly.com.