Randomness and Geometric Probability
- Buffon's needle.
What is the probability that a dropped needle lands on a crack on a
From Kunkel's mathematics
- Geometric probability question.
What is the probability that the shortest paths between three random
points on a projective plane form a contractible loop?
probability constants. From MathSoft's favorite constants pages.
- Green-haired geometric pre-hominids.
- Points on
a sphere. Paul Bourke describes a simple random-start hill-climbing
heuristic for spreading points evenly on a sphere, with pretty pictures
and C source.
- Random domino tiling of an Aztec diamond
and other undergrad research on random tiling.
- Random spherical arc crossings.
Bill Taylor and Tal Kubo prove that if one takes two random geodesics
on the sphere, the probability that they cross is 1/8.
This seems closely related a famous problem on the probability
of choosing a convex quadrilateral from a planar distribution.
The minimum (over all possible distributions) of this probability
also turns out to solve a seemingly unrelated combinatorial
geometry problem, on the minimum
number of crossings possible in a drawing of the complete graph with
see also "The
rectilinear crossing number of a complete graph
and Sylvester's four point problem of geometric probability",
E. Scheinerman and H. Wilf, Amer. Math. Monthly 101 (1994) 939-943,
crossing constant, S. Finch, MathSoft, and
- Random polygons.
Tim Lambert summarizes responses to a request for
a good random distribution on the n-vertex simple polygons.
- Self-trapping random walks,
- Zonohedron generated by 30 vectors in a circle,
and another generated by 100 random vectors,
Paul Heckbert, CMU.
As a recent article in The Mathematica Journal explains,
the first kind of shape converges to a solid of revolution of a
sine curve. The second clearly converges to a sphere but Heckbert's example looks more like a
From the Geometry Junkyard,
and recreational geometry pointers.
Send email if you
know of an appropriate page not listed here.
from a common source file.