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A condition which, if true, guarantees that a result is also true. (However, the result may also be true if the condition is not met.) If a condition is both necessary and ...

Any linear combination of real spherical harmonics A_lP_l(costheta)+sum_(m=1)^l[A_l^mcos(mphi)+B_l^msin(mphi)]P_l^m(costheta) for l fixed whose sum is not premultiplied by a ...

An irregular icosagon, also called the gammadion or fylfot, which symbolized good luck in ancient Arabic and Indian cultures. The mirror image of the above, sometimes called ...

The study of the meaning and relationships of statements used to represent precise mathematical ideas. Symbolic logic is also called formal logic.

A mathematical object is said to be symmetric if it is invariant ("looks the same") under a symmetry transformation. A function, matrix, etc., is symmetric if it remains ...

An (n,k)-talisman hexagon is an arrangement of nested hexagons containing the integers 1, 2, ..., H_n=3n(n-1)+1, where H_n is the nth hex number, such that the difference ...

An n×n array of the integers from 1 to n^2 such that the difference between any one integer and its neighbor (horizontally, vertically, or diagonally, without wrapping ...

The partial differential equation u_(xx)=au_(tt)+bu_t+cu.

The second-order ordinary differential equation y^('')=y^(3/2)x^(-1/2).

Maximize the amount of floor space which can be covered with a fixed tile (Hoffman 1998, p. 173).