Beauty of Geometry

<p>Written by a distinguished mathematician the dozen absorbing essays in this versatile volume offer both supplementary classroom material and pleasurable reading for the mathematically inclined.<br>The essays promise to encourage readers in the further study of elementary geometry not just for its own sake but also for its broader applications which receive a full and engaging treatment. Beginning with an analytic approach the author reviews the functions of Schlafli and Lobatschefsky and discusses number theory in a dissertation on integral Cayley numbers. A detailed examination of group theory includes discussion of Wythoff's construction for uniform polytopes as well as a chapter on regular skew polyhedra in three and four dimensions and their topological analogues. A profile of self-dual configurations and regular graphs introduces elements of graph theory followed up with a chapter on twelve points in PG (5 3) with 95040 self-transformations. Discussion of an upper bound for the number of equal nonoverlapping spheres that can touch another same-sized sphere develops aspects of communication theory while relativity theory is explored in a chapter on reflected light signals.<br>Additional topics include the classification of zonohedra by means of projective diagrams arrangements of equal spheres in non-Euclidean spaces and regular honeycombs in hyperbolic space. Stimulating and thought-provoking this collection is sure to interest students mathematicians and any math buff with its lucid treatment of geometry and the crucial role geometry can play in a wide range of mathematical applications.</p><p></p>