On regular packing of equal circles touching each other on the surface of a sphere
✍ Scribed by Viggo Brun
- Publisher
- John Wiley and Sons
- Year
- 1976
- Tongue
- English
- Weight
- 342 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0010-3640
No coin nor oath required. For personal study only.
✦ Synopsis
D r ~b a k , Noway
Some literature on this subject already exists. In a paper by H. S. M. Coxeter, A n upper bound of equal nonoverlapping spheres that can touch another of the same size in Proceedings of Symposia in Pure Mathematics, Vol. 7, 1963, we find a list of references which contains 30 entries. I shall also mention a newly published paper by J. Molnar, O n a generalisation of the Tammes problem, Publ. Mathem. Debrecen, 22, 1975. But I believe that this interesting subject deserves additional consideration. I hope that younger mathematicians will take it up.
Among the easiest solutions of the problem are those based on the Platonic regular surface-nets and the Archimedean half-regular nets. If one lets the corresponding polyhedral corners be the centers of equal circles drawn on the sphere, one usually obtains interesting results.
I shall restrict myself here to two different possibilities which I believe to be novel, at least the first one.