Showing papers on "Regular polygon published in 1973"
TL;DR: In this article, the probability distributions of various aggregates of random convex polygons determined by the standard isotropic Poisson line process in the plane are investigated, defined in an ergodic sense.
66 citations
11 citations
TL;DR: In this paper, the dominant dependence of the N-particle cycle is given by the classical action of a rotation of a planar N-sided regular polygon through an angle 2n/N.
Abstract: Cyclic N-particl.e exchange terms for a hard sphere fluid are analysed m the limit that the thermal wavelength- is much shorter than the hard sphere diameter (a). This is a path integral analysis of cluster integrals in virial expansions in equilibrium statistical mechanics. In the results, the dominant dependence of the N-particle cycle is given by the classical action of a rotation of a planar N-sided regular polygon (side a) through an angle 2n/N. Extension of these results to general permutations of N particles and the relation of the results to theories of the Actransition in 4He are discussed.
5 citations
01 Jan 1973
3 citations
2 citations
01 Jan 1973
TL;DR: In this article, a technique of R. B. Frucht for constructing symmetrical graphs as Cayley diagrams for some interesting finite groups, such as the linear groups SL(2, 3) of order 24, and GL( 2, 3), was presented.
Abstract: Section 1 generalizes a technique of R. Frucht for constructing symmetrical graphs as Cayley diagrams for some interesting finite groups, such as the linear groups SL(2, 3) of order 24, and GL(2, 3) of order 48. Section 2 relates these graphs to certain configurations in the unitary plane. Such configurations are “regular polygons” p{q}r according to a natural generalization of the ordinary regular q-gon 2{q}2, and their symmetry groups p[q]r generalize the dihedral group Dq ≈ 2[q]2, which is the symmetry group of the q-gon. Section 3 indicates how the regular complex polygons can be represented in a real 4-space and orthogonally projected onto a real plane. The real figures so obtained provide an agreeably symmetrical way to draw the Cayley diagrams. I am grateful to Dr. B. B. Phadke for making these figures.
2 citations