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According to G. Pólya, the method of finding geometric objects by intersection. 1. For example, the centers of all circles tangent to a straight line s at a given point P lie ...

A permutation matrix is a matrix obtained by permuting the rows of an n×n identity matrix according to some permutation of the numbers 1 to n. Every row and column therefore ...

An algorithm is said to be solvable in polynomial time if the number of steps required to complete the algorithm for a given input is O(n^k) for some nonnegative integer k, ...

All Euclidean geometric constructions can be carried out with a straightedge alone if, in addition, one is given the radius of a single circle and its center. The theorem was ...

Consider the expression 3×7+2^2. This expression has value (3×7)+(2^2)=25 due to what is called operator precedence (or "order of operations"). Precedence of common operators ...

A presheaf C of categories consists of the following data: 1. For every local homeomorphism f:Y->X of topological spaces X, Y, a category C(f:Y->X); 2. For every diagram f ...

The term "product" refers to the result of one or more multiplications. For example, the mathematical statement a×b=c would be read "a times b equals c," where a is called ...

For a cyclic quadrilateral, the sum of the products of the two pairs of opposite sides equals the product of the diagonals AB×CD+BC×DA=AC×BD (1) (Kimberling 1998, p. 223). ...

A radical integer is a number obtained by closing the integers under addition, multiplication, subtraction, and root extraction. An example of such a number is RadicalBox[7, ...

Let the two-dimensional cylinder function be defined by f(x,y)={1 for r<R; 0 for r>R. (1) Then the Radon transform is given by ...