Essays about Number Theory

For a regular 17-gon the formulas above give the x-coordinate of the firstvertex in the upper half plane. The first formula goes back to Gauss. Thesecond formula is obtained by a more elementary method see pages 39 to 47in this book. This method uses only the trigonometric addition theorem andsome clever guesses.It needed some optimism to create this book about number theory. The proofsare gapless and readable and there are given some exercises with solutions andalgorithms. Especially the geometric construction of the regular 17 257 andeven the 65 537-gon are treated in complete and purely constructive detailsincluding programming codes. Otherwise could be covered just an importantclassical selection.