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A set of n magic circles is a numbering of the intersections of the n circles such that the sum over all intersections is the same constant for all circles. The above sets of ...

A set of n distinct numbers taken from the interval [1,n^2] form a magic series if their sum is the nth magic constant M_n=1/2n(n^2+1) (Kraitchik 1942, p. 143). The numbers ...

The Maltese cross is a symbol identified with the Christian warrior whose outward points form an octagon (left figure). Another class of cross sometimes (incorrectly) known ...

The mean triangle area A^_ is the average area of a triangle in triangle picking within some given shape. As summarized in the following table, it is possible to compute the ...

The metabiaugmented hexagonal prism is a convex equilateral solid that is Johnson solid J_(56). The metabiaugmented hexagonal prism has volume V=1/6(2sqrt(2)+9sqrt(3)) (1) ...

Let a module M in an integral domain D_1 for R(sqrt(D)) be expressed using a two-element basis as M=[xi_1,xi_2], where xi_1 and xi_2 are in D_1. Then the different of the ...

The Möbius-Kantor graph is the unique cubic symmetric graph on 16 nodes, illustrated above in several embeddings. Its unique canonical LCF notation is [5,-5]^8. The ...

Given an m×n matrix B, the Moore-Penrose generalized matrix inverse is a unique n×m matrix pseudoinverse B^+. This matrix was independently defined by Moore in 1920 and ...

An n-fold multimagic cube is a magic cube that remains magic when each element is squared, cubed, etc., up to nth power. (Of course, when the elements of a cube are taken to ...

A multivalued function, also known as a multiple-valued function (Knopp 1996, part 1 p. 103), is a "function" that assumes two or more distinct values in its range for at ...