Number Theory and Modern Algebra

For a regular 17-gon, the formulas above give the x-coordinate of the first vertex in the upper half plane.The first formula goes back to Gauss. The second formula is obtained by a more elementary method, see pages 175 to 180 in this book. This method uses only the trigonometric addition theorem and some clever guesses.

This book is a our through topics from number theory and modern algebra, including the Chinese remainder theorem, quadratic reciprocity and geometric construction of the regular 17, 257 and even the 65 537-gon, Galo is theory, and more. The book contains detailed proofs and many numerical examples with computer code.

Franz Rothe received his doctoral degree in mathematics from the university of Tübingen, Germany. He got Habilitation and venia legendi from the university at Tübingen (1984) and the Ludwig Maximilian university of Munich (1988). He has published about 40 articles and a monograph. At the university of Charlotte, he has been teaching for 28 years undergraduate and graduate courses in mathematics. Because of health reasons, Dr. Rothe is retired since two years, and is now emeritus professor.