The Probability that a Random Triangle in a Cube is Obtuse
Dominik Beck
TL;DR
This paper calculates the exact probability that three randomly chosen points inside a unit cube form an obtuse triangle, providing precise mathematical insights into geometric probability.
Contribution
It derives the exact formula for the probability of obtuse triangles formed by random points in a cube, a novel result in geometric probability.
Findings
Exact probability formula for obtuse triangles in a cube
Mathematical characterization of triangle angles in 3D space
Enhanced understanding of geometric probabilities in three dimensions
Abstract
In this paper, we derive the exact formula for the probability that three randomly and uniformly selected points from the interior of the unit cube form vertices of an obtuse triangle.
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Taxonomy
TopicsMathematics and Applications