The Kissing Problem in Three Dimensions

@article{Musin2006TheKP,
  title={The Kissing Problem in Three Dimensions},
  author={Oleg R. Musin},
  journal={Discrete & Computational Geometry},
  year={2006},
  volume={35},
  pages={375-384}
}
The kissing number k(3) is the maximal number of equal size nonoverlapping spheres in three dimensions that can touch another sphere of the same size. This number was the subject of a famous discussion between Isaac Newton and David Gregory in 1694. The first proof that k(3) = 12 was given by Schütte and van der Waerden only in 1953. In this paper we present a new solution of the Newton–Gregory problem that uses our extension of the Delsarte method. This proof relies on basic calculus and… CONTINUE READING
Highly Cited
This paper has 56 citations. REVIEW CITATIONS
Tweets
This paper has been referenced on Twitter 2 times. VIEW TWEETS

From This Paper

Figures, tables, and topics from this paper.

Explore Further: Topics Discussed in This Paper

Citations

Publications citing this paper.

56 Citations

0510'07'10'13'16'19
Citations per Year
Semantic Scholar estimates that this publication has 56 citations based on the available data.

See our FAQ for additional information.

References

Publications referenced by this paper.
Showing 1-10 of 21 references

Newton and the kissing problem, http://plus.maths.org/issue23/features/kissing/ Received November 18, 2004, and in revised form June

  • G. G. Szpiro
  • Online publication October
  • 2005
1 Excerpt

The difficulties of kissing in three dimensions

  • B. Casselman
  • Notices Amer. Math. Soc
  • 2004
1 Excerpt

The Newton–Gregory problem revisited

  • K. Böröczky
  • 2003
2 Excerpts

The problem of the twenty - five spheres , Russian Math

  • O. R. Musin, A. M. Odlyzko, N. J. A. Sloane
  • 2003

The problem of the twenty-five spheres

  • O. R. Musin
  • Russian Math. Surveys
  • 2003
2 Excerpts

Isoperimetric theorem for spherical polygons and the problem of 13 spheres

  • H. Maehara
  • Ryukyu Math. J
  • 2001
2 Excerpts