The probability that a random triangle in a cube is obtuse

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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Publication Details

Journal
Journal of Applied Probability
Published
2026-03-09
DOI
https://doi.org/10.1017/jpr.2026.10075
Primary Topic
Point processes and geometric inequalities
Type
article
Field-Weighted Citation Impact
0.00

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article

The probability that a random triangle in a cube is obtuse

Dominik Beck
Journal of Applied Probability
Point processes and geometric inequalities
article

The probability that a random triangle in a cube is obtuse

Dominik Beck
article en

Abstract

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.

Journal of Applied Probability
Charles University (CZ)
Univerzita Karlova v Praze, Grantová Agentura, Univerzita Karlova
Reduced inequalities
Openalex Percentile: Top 26%
Point processes and geometric inequalities
DOIOpen Access PDFOpenAlex
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The probability that a random triangle in a cube is obtuse — Dominik Beck · Journal of Applied Probability (2026) | TGRS Research Map | TGRS