*N.B. A detailed on-line essay by S. Finch
was 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) |

(2) |

(3) |

(4) |

(5) |

(6) |

(7) |

where 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.html

Cleary, 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.

© 1996-9

1999-05-26