74 citations · 190 across the 73 of their papers we have counts for
5 papers · 1 filter
Correlation between Angle and Side
Steven R. Finch
Let alpha be an arbitrary angle in a random spherical triangle Delta and a be the side opposite alpha. (The sphere has radius 1; vertices of Delta are independent and uniform.) If…
Random Spherical Triangles
Steven R. Finch, Antonia J. Jones
Let Delta be a random spherical triangle (meaning that vertices are independent and uniform on the unit sphere). A closed-form expression for the area density of Delta has been kno…
Perimeter Variance of Uniform Random Triangles
Steven Finch
Let T be a random triangle in a disk D of radius R (meaning that vertices are independent and uniform in D). We determine the bivariate density for two arbitrary sides a,b of T. In…
Two Sample Covariances from a Trivariate Normal Distribution
Steven Finch
The joint distribution of two off-diagonal Wishart matrix elements was useful in recent work on geometric probability [Finch 2010]. Not finding such formulas in the literature, we…
Random Gaussian Tetrahedra
Steven Finch
Given independent normally distributed points A,B,C,D in Euclidean 3-space, let Q denote the plane determined by A,B,C and D^ denote the orthogonal projection of D onto Q. The prob…