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Any geometric correlation which transforms one range into a projectively related pencil (or vice versa).

The number of operations needed to effect a geometric construction as determined in geometrography. If the number of operations of the five geometrographic types are denoted ...

Squaring is the geometric construction, using only compass and straightedge, of a square which has the same area as a given geometric figure. Squaring is also called ...

It is always possible to "fairly" divide a cake among n people using only vertical cuts. Furthermore, it is possible to cut and divide a cake such that each person believes ...

Maximize the distance a Jeep can penetrate into the desert using a given quantity of fuel. The Jeep is allowed to go forward, unload some fuel, and then return to its base ...

A set in R^d is concave if it does not contain all the line segments connecting any pair of its points. If the set does contain all the line segments, it is called convex.

Let A be a matrix and x and b vectors. Then the system Ax=b, x>=0 has no solution iff the system A^(T)y>=0, b^(T)y<0 has a solution, where y is a vector (Fang and Puthenpura ...

The Kuhn-Tucker theorem is a theorem in nonlinear programming which states that if a regularity condition holds and f and the functions h_j are convex, then a solution ...

A subset S subset R^n is said to be pseudo-convex at a point x in S if the associated pseudo-tangent cone P_S(x) to S at x contains S-{x}, i.e., if S-{x} subset P_S(x). Any ...

The pseudo-tangent cone P_S(x) of a subset S subset R^n at a point x in S is the set P_S(x)=convK_S^_, where K_S is the contingent cone of S and where conv(A) is the smallest ...