The number of faces in a minimal foam
- 8 December 1992
- journal article
- Published by The Royal Society in Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
- Vol. 439 (1907) , 683-686
- https://doi.org/10.1098/rspa.1992.0177
Abstract
We derive a formula for the average number of faces per cell in a foam of minimal surfaces. In case of periodic minimal foam in R$^{3}$ this formula implies that the fundamental cell has at least 14 faces, a lower bound achieved by Kelvin's example from the last century.Keywords
This publication has 8 references indexed in Scilit:
- Geometric Measure Theory and the Calculus of VariationsProceedings of Symposia in Pure Mathematics, 1986
- Minimal surface formsThe Mathematical Intelligencer, 1982
- The Geometry of Soap Films and Soap BubblesScientific American, 1976
- The Structure of Singularities in Soap-Bubble-Like and Soap-Film-Like Minimal SurfacesAnnals of Mathematics, 1976
- Existence and regularity almost everywhere of solutions to elliptic variational problems with constraintsMemoirs of the American Mathematical Society, 1976
- An upper bound for the number of equal nonoverlapping spheres that can touch another of the same sizeProceedings of Symposia in Pure Mathematics, 1963
- A Geometrical Approach to the Structure Of LiquidsNature, 1959
- LXIII. On the division of space with minimum partitional areaJournal of Computers in Education, 1887