Gems of Geometry

Abstract

This book demonstrates in lively and entertaining way that the geometry is in fact full of beauty and fascination. The following catchwords allow a deeper look at the facts and problems discussed: The Golden number (Fibonacci, pentagons, phyllotaxis,\dots); shapes and solids (Polygons, tiling, polyhedra, Archimedean figures, pentagonal tilings,\dots), the fourth dimension (honeycombs, the 4-simplex, hypercube and l6-cell,\dots); projective geometry (Pappus' and Desargues' theorem, duality, finite geometries,\dots); topology (colour problems, Möbius band, Klein bottle, projective plane,\dots); bubbles; harmony of the spheres (inversion, Steiner's porism, Soddy's hexlet,\dots); chaos and fractals (fractional dimensions, Cantor sets, Julia and Mandelbrot sets,\dots); relativity (Lorentz transformation, time and relativitv, mass and energy, Einstein's equations, consequences of general relativity,\dots); final a lot of interesting and remarkable supplements and appendices.