Number Theory and Modern Algebra: A Personal Approach

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.