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A pandiagonal perfect magic cube is a perfect magic cube that remains perfect when any single orthogonal section is "restacked" cyclically so that the ordering of any set of ...

A pandiagonal semiperfect magic cube is a semiperfect magic cube that remains semiperfect when any single orthogonal section is "restacked" cyclically so that the ordering of ...

The arc length of the parabolic segment y=h(1-(x^2)/(a^2)) (1) illustrated above is given by s = int_(-a)^asqrt(1+y^('2))dx (2) = 2int_0^asqrt(1+y^('2))dx (3) = ...

The surface of revolution of the parabola which is the shape used in the reflectors of automobile headlights (Steinhaus 1999, p. 242; Hilbert and Cohn-Vossen 1999). It is a ...

The parallelogram law gives the rule for vector addition of vectors A and B. The sum A+B of the vectors is obtained by placing them head to tail and drawing the vector from ...

A rational function P(x)/Q(x) can be rewritten using what is known as partial fraction decomposition. This procedure often allows integration to be performed on each term ...

In a normal n×n Latin square, the entries in each row and column are chosen from a "global" set of n objects. Like a Latin square, a partial Latin square has no two rows or ...

The party problem, also known as the maximum clique problem, asks to find the minimum number of guests that must be invited so that at least m will know each other or at ...

Two knots are pass equivalent if there exists a sequence of pass moves taking one to the other. Every knot is either pass equivalent to the unknot or trefoil knot. These two ...

The pedal circle with respect to a pedal point P of a triangle DeltaA_1A_2A_3 is the circumcircle of the pedal triangle DeltaP_1P_2P_3 with respect to P. Amazingly, the ...