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Angle sums of random simplices in dimensions 3 and 4.
- Source :
-
Proceedings of the American Mathematical Society . Jul2020, Vol. 148 Issue 7, p3079-3086. 8p. - Publication Year :
- 2020
-
Abstract
- Consider a random d-dimensional simplex whose vertices are d + 1 random points sampled independently and uniformly from the unit sphere in Rd. We show that the expected sum of solid angles at the vertices of this random simplex equals 1/8 if d = 3 and 539/288π2 − 1/6 if d = 4. The angles are measured as proportions of the full solid angle which is normalized to be 1. Similar formulae are obtained if the vertices of the simplex are uniformly distributed in the unit ball. These results are special cases of general formulae for the expected angle sums of random beta simplices in dimensions 3 and 4. [ABSTRACT FROM AUTHOR]
- Subjects :
- *UNIT ball (Mathematics)
*ANGLES
*BETA distribution
*STATISTICAL sampling
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 148
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 143306107
- Full Text :
- https://doi.org/10.1090/proc/14934