Angles as probabilities

American Mathematical Monthly

Volumn 116, Issue 8, 2009, Pages 732-735

  Feldman, David V ^a   Klain, Daniel A ^b  

^a University of New Hampshire   (United States)

^b University of Massachusetts Lowell   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 72149107830     PISSN: 00029890     EISSN: None     Source Type: Journal    
DOI: 10.4169/193009709X460868     Document Type: Article

References (9)

1. D. Barnette, The sum of the solid angles of a d-polytope, Geom. Dedicata 1 (1972) 100-102. doi: 10. 1007/BF00147383
2. J. W. Gaddum, The suras of the dihedral and trihedral angles in a tetrahedron, this MONTHLY 59 (1952) 370-371. doi:10.2307/2306805
3. Distance sums on a sphere and angle sums in a simplex, this MONTHLY 63 (1956) 91-96. doi: 10.2307/2306430
4. B. Grünbaum, Convex Polytopes, 2nd ed., Springer Verlag, New York, 2003.
5. P. McMullen, Non-linear angle-sum relations for polyhedral cones and polytopes, Math. Proc. Cambridge Philos. Soc. 78 (1975) 247-261. doi: 10.1017/S0305004100051665
6. Valuations and Euler-type relations on certain classes of convex polytopes, Proc. London Math. Soc. 35 (1977) 113-135. doi: 10.1112/plms/s3-35.1. 113
7. M. A. Perles and G. C. Shephard, Angle sums of convex polytopes, Math. Scand. 21 (1967) 199-218.
8. D. M. Y. Sommerville, An Introduction to the Geometry of n Dimensions, Dover, New York, 1983.
9. E. Welzl, Gram's equation-a probabilistic proof, in Results and Trends in Theoretical Computer Science-Graz, 1994, Lecture Notes in Comput. Sci., vol. 812, Springer, Berlin, 1994, 422-424.