We consider the three natural centers of mass associated with a general quadrilateral together with the Fermat-Torricelli center and explore the degree of regularity implied by the coincidence of two or more of these four centers. We then extend this investigation to include cyclic quadrilaterals, where we add the circumcenter to the list, and circumscriptible quadrilaterals, where we add the incenter.

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A collection of matrices for testing computational algorithms, Wiley-Interscience, New York (1969). 4. I. R. Savage and E. Lukacs, Tables of inverses of finite segments of the Hilbert matrix. In O. Taussky (ed.) Contributions to the solution of systems of linear equations and the determination of eigenvalues.

A theorem of Pompeiu states that the distances from the vertices of an equilateral triangle to an arbitrary point in its plane can serve as the side lengths of a triangle. A similar theorem holds for the medians of any triangle. Generalizations to higher dimensions of Pompeiu's theorem are established by M. Fiedler in 1977 and by Gh. Al-Afifi et al in a forthcoming paper. This paper is concerned with similar possible higher dimensional theorems for the medians. (2010): 51M04, 51M16, 51M15, 51M25, 51M20. Mathematics subject classification

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