Bees, Pomegranates and Parallelohedra
Let's start our discussion with this box which I intend to fill in with as many cans as possible. Look, it is filled with 40 cans already (Fig. 13.1.1). But I'd still like to add one more can in here [1, 16]. It looks like fully packed already, but can I squeeze in one more can? What do you think?
KeywordsVoronoi Diagram Code Word Sphere Packing Regular Hexagon Pomegranate Seed
Unable to display preview. Download preview PDF.
- J. Akiyama and R. L. Graham, Introduction to Discrete Mathematics (Risan Suugaku Nyumon) (in Japanese), Asakura. (1993)Google Scholar
- E. S. Fedorov, A Primer of the Theory of Figures (in Russian), Notices of the Imperial Mineralogical Society Ser. 2, Vol. 21 (1885), 1-279Google Scholar
- R. L. Graham, Lecture at the 1986 AMS-IMS-SIAM Summer Research Conference on Discrete and Computational Geometry, Santa Cruz, 1986Google Scholar
- T. Hales and S. Ferguson, The Kepler conjecture. The Hales-Ferguson proof, Including papers reprinted from Discrete Comput. Geom. 36 (2006). No. 1. Edited by J.C. Lagarias, Springer (2011)Google Scholar
- J. Kepler, The Six-Cornered Snowflake, Oxford University. Press (1966)Google Scholar
- H. Minkowski, Theorie der Konvexen Körper, Ges. Abh. Bd. 2, (1911) Teubner, Leipzig-BerlinGoogle Scholar
- G. Nakamura, Introduction to Mathematical Puzzles (Suuri Puzzle Nyumon ) (in Japanese), Rippu Shobo Pub. Co. Ltd (1981)Google Scholar
- I. Peterson, Islands of Truth, W. H. Freeman and Company (1990)Google Scholar
- C. A. Pickover, The Mαth βook, Sterling (2009)Google Scholar
- C. W. Triggs, Mathematical Quickies, Dover Publications, New Edition (1985), McGraw-Hill (1967)Google Scholar