Sphere packings from Kepler until today. An introduction for pupils, students and teachers. With a foreword by Jörg M. Wills (Q2785512)

Sphere packings have a long history tracing back to the 17th century. In 1611, Kepler posed the problem of determining the densest packing of congruent spheres in ordinary space. This is still an open problem today (although there are claims for a proof, which however is seriously questioned by most experts). Kepler's Problem has had an enormous impact on the development of geometry and has led to deep connections with other fields including number theory, algebra, group theory, coding theory and crystallography.NEWLINENEWLINENEWLINEThe book by Max Leppmeier is a well-written introduction to the geometry of sphere packings aiming at an audience consisting primarily of college students, high school teachers and upper grade high school students. The author has mastered the courageous task of leading the mathematically inclined, but not research oriented, reader to the front of current research in some areas of the subject, while at the same time elaborating on historical aspects and the relations to other fields. Among the topics discussed are the classical theory of lattice sphere packings, as well as the more recent developments on finite arrangements of spheres in space. The reader will find it very instructive to work through the detailed examples, which are also well-illustrated by figures and complemented by numerous exercises. This is an enjoyable text which will be a valuable source for the reader.