内容

目次

"A number is a multitude composed of units" (Euclid); "...there are noirrational numbers at all" (Kronecker); rationality, elliptic curves andFermat's last theorem; algebraic or transcendential?; complex numbers;complex arithmetic; stereographic projection; proof of the fundamentaltheorem of algebra; symmetries of regular polygons; discrete subgroups ofIso(R2); moebius geometry; complex linear fractional transformations; "out ofnothing I created a new universe" (Bolyai); Fuchsian groups; Riemannsurfaces; general surfaces; the five platonic solids; detour in topology -Euler Poincare characteristic; detour in graph theory - Eulerian, Hamiltonand the four colour theorem; the dimension leap; quaternions; back to R3; thefourth dimension; hints for selected problems.