Intuitive Geometry: (v.63 Colloquia Mathematica Societatis Janos Bolyai S.)

This volume contains research papers presented at the International Conference on Intuitive Geometry held in Szeged, 1991 as well as contributions from many prominent geometers. As a result, a broad variety of topics are covered, such as the theory of packing and covering, tiling, rigidity, combinatorial and computational geometry, convexity, geometry of numbers and classical differential geometry.

Table of Contents:
A remark on the packing density in the 3-space, A. Bezdek; on the transversal-conjecture of Katchalski and Lewis, A. Bezdek; on the number of lattice hyperplanes which are needed to cover the lattice points of a convex body, K. Bezdek and T. Hausel; a characterization of 3-dimensional convex sets with an infinite X-ray number, K. Bezdek and T. Zamfirescu; kaleidoscopes and mechanisms, R. Connelly et al; Cakaudrove patterns, D.W. Crowe and D. Nagy; similar configurations and pseudo grids, G. Elekes and P. Erdos; for most convex discs thinnest covering is not lattice-like, G. Fejes Toth and T. Zamfirescu; representation of planar graphs by segments, H. de Fraysseix et al; Kepler hypersolids, G. Gevay; sphere-of-influence graphs in higher dimensions, L. Guibas et al; on special integral erdos point sets, H. Harborth and L. Piepmeyer; solidity of the hexagonal tiling, A. Heppes; there is no cancellation law for metric products, I. Herburt; on the number of the minima of N-lattices, A.G. Horvath; convex 3-polytopes with constant edge weight, S. Jendrol; rational triangles, A. Kemnitz; nine points on the hemisphere, G. Kertesz; Hamiltonian surfaces in polytopes, W. Kuhnel; translates of a starlike plane region with a common point, K. Kuperberg and W. Kuperberg; on the maximal number of appearances of the minimal distance among n points in the plane, Y.S. Kupitz; on five points in a plane convex body pairwise in at least unit relative distances, M. Lassak; lower bounds on the numbers of shadow-boundaries and illuminated regions of a convex body, E. Makai; cross-sectional measures, H. Martini; classification of solid transitive simplex tilings in simply connected 3-spaces - the combinatorial description by figures and tables, results in spaces of constant curvature, E. Molnar and I. Prok; the euclidean space has 298 fundamental tilings with marked cubes by 130 space groups, I. Prok; full and partial inflation of plane curves, S.A. Robertson and B. Wegner; the densest packing of ten congruent spheres in a cube, J. Schaer; equality in the Aleksandrov-Fenchel inequality - present state and new results, R. Schneider; some notes on Eggleston's result about affine diameters, V. Soltan; the HEUREKA-polyhedron, H. Stachel; covering planar sets with sets of four times smaller diameter, B. Stolorz; regular circle packings, L. Szabo; packing of regular pentagons on a sphere, T. Tarnai and Zs. Gaspar; two identities in geometry of numbers with applications, B. Uhrin; triangles and reuleaux triangles in banach-minkowski planes, B. Wernicke. (Part Contents).