Uniform Triangles with Equality Constraints
Abstract
The equality constraint a+b+c=1 for random triangle sides corresponds to breaking a stick in two places. An analog a2+b2+c2=1 has a remarkable feature: the bivariate density for angles coincides with that for 3D Gaussian triangles. Interesting complications also arise for a+b=1 and for a2+b2=1, with the understanding that the angle gamma opposite side c is Uniform[0,pi]. Closed-form expressions for several side moments remain open.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.