A decade long experience of teaching the course ‘Fundamental of Geometry’, many notes for exercises, and endless extra reading are the bases for this bulky work.
The online manuscript already includes many topics with many exercises including solutions and hundreds a elaborate computer generated drawings.
The first volume begins with Hilbert’s axioms from the Foundations of Geometry, and goes on to projective, neutral and basic Euclidean geometry.
The present second volume deals with many more advanced topics form Euclidean geometry and contains a long treatise about hyperbolic geometry.
Here the disk models of Poincar/’e and Klein are used to do a lot of constructions, using straightedge and compass from the background Euclidean geometry. Too, Hilbert’s axiomatic approach based on the asymptotic rays, is explained from the beginning up to the reconstruction of the Poincar/’e disk model. The last section gives a short course on Gauss’ differential geometry and the pseudo sphere.
Про автора
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 Z’urich, a doctorate in T’ubingen. He got his Habilitation and venia legendi from the university at T/’ubingen (1984) and the Ludwig Maximilian university of Munich (1988). He has published about 40 articles, and meanwhile three books about mathematics.Since 1990 a professorship at the University of North Carolina at Charlotte, USA. His is now retired because of health problems.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.Some recent information about activity during the years 2017-2021, in all fields, is gathered on the websitewww.franzrothe.com
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