| 释义 |
Magic Geometric ConstantsN.B. A detailed on-line essay by S. Finchwas the starting point for this entry.
Let  be a compact connected subset of  -dimensional Euclidean Space. Gross (1964) and Stadje (1981) proved that there is a unique Real Number  such that for all  ,  , ...,  , there exists  with
 | (1) |
 of is defined by
 | (2) |
 | (3) |
 | (4) |
 is a subinterval of the Line and  is a circular Disk in the Plane, then
 | (5) |
 is a Circle, then
 | (6) |
 | (7) |
 -D space by  . Thenwhere  is the Gamma Function (Nikolas and Yost 1988).
An unrelated quantity characteristic of a given Magic Square is also known as a Magic Constant.
References
Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/magic/magic.htmlCleary, J.; Morris, S. A.; and Yost, D. ``Numerical Geometry--Numbers for Shapes.'' Amer. Math. Monthly 95, 260-275, 1986. Croft, H. T.; Falconer, K. J.; and Guy, R. K. Unsolved Problems in Geometry. New York: Springer-Verlag, 1994. Gross, O. The Rendezvous Value of Metric Space. Princeton, NJ: Princeton University Press, pp. 49-53, 1964. Nikolas, P. and Yost, D. ``The Average Distance Property for Subsets of Euclidean Space.'' Arch. Math. (Basel) 50, 380-384, 1988. Stadje, W. ``A Property of Compact Connected Spaces.'' Arch. Math. (Basel) 36, 275-280, 1981.
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