Simplexes in spaces of constant curvature |
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| Authors: | B V Dekster J B Wilker |
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| Institution: | (1) Department of Mathematics, Mount Allison University, E0A 3C0 Sackville, New Brunswick, Canada;(2) Physical Sciences Division, Scarborough College, University of Toronto, M1C 1A4 West Hill, Ontario, Canada |
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| Abstract: | In hyperbolic, Euclidean and spherical n-space, we determine, for each positive number l, the largest interval of the form 
n
(l) l
ijl which guarantees the existence of an n-simplex p
1
p
2 ... p
n+1 with edge-lengths p
ipj=l
ij. (In spherical geometry of curvature 1 the interval is empty unless l2 arcsin
) The assertion that these intervals are as large as possible is justified because each of them allows certain degenerate simplexes. We determine explicitly all of these critical configurations.This work was supported by Canadian NSERC grants. |
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