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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.
About the author
Franz Rothe graduated from high school in Karlsruhe and studied mathematics, physics, and music there. Graduated with a diploma in mathematics from the E T H Zürich, and a doctorate in Tübingen. After some changes in life, a professorship at the University of North Carolina in Charlotte, USA.Rothe has published about 30 mathematical articles and three books about mathematics.In addition, Rothe and pianist Thomas Turner have developed a repertoire of classical music for flute and piano, and have recorded and released three CDs. This collection also contains several of their own transcriptions.
