Geometry: ancient and modern (Q2715722)

This is an excellent book about geometry which covers most aspects of planar geometry. In order to be able to enjoy all the details, the reader should have quite a large and working knowledge of several branches of mathematics.NEWLINENEWLINENEWLINEThe book starts with geometry ``by hand'', featuring and fostering geometric constructions and thereby the geometric intuition. To present proofs, the author switches over into an appropriate analytical language, using vector spaces, linear mappings or the complex numbers. A part of trigonometry is treated within calculus, starting with the sine- and cosine-series.NEWLINENEWLINENEWLINEA central part of the book is dedicated to the ideas of Klein's Erlanger program: Isometries, many groups of symmetries and similarities are investigated and classified in the planar geometry as well as in higher dimensions with the powerful help of group theory. Many of these ideas are also applied to study the conics and lead us also into affine and projective geometry. In order to present some algebraic geometry and to handle cubics, we finally enter the world of the complex projective geometry.NEWLINENEWLINENEWLINEMany exercises go along with the text, whose answers are also provided.