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The geometric construction of the regular 17, 257 and even the 65 537-gon are given in complete details, including programming codes. The theory of geometrical constructions and its connection to Galois theory is treated in detail. Later parts deal with totally positive real numbers as sums of squares, cyclotomic polynomials,
Chebychev polynomials, Gaussian periods, Galois theory, and more related topics. The solvability of equations is treated as far as it is related to geometric constructions, and tailored to prove the steps needed is that context, as simple as possible. Much less known is the relation between the lunes of Hippocrates and transcendental numbers to which the final section is dedicated.
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.
