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A formula of first-order logic is in prenex normal form if it is of the form Q_1x_1...Q_nx_nM, (1) where each Q_i is a quantifier forall ("for all") or exists ("exists") and ...

Proof theory, also called metamathematics, is the study of mathematics and mathematical reasoning (Hofstadter 1989) in a general and abstract sense itself. Instead of ...

Pythagoras's theorem states that the diagonal d of a square with sides of integral length s cannot be rational. Assume d/s is rational and equal to p/q where p and q are ...

A rhombus is a quadrilateral with both pairs of opposite sides parallel and all sides the same length, i.e., an equilateral parallelogram. The word rhomb is sometimes used ...

Rodrigues' rotation formula gives an efficient method for computing the rotation matrix R in SO(3) corresponding to a rotation by an angle theta about a fixed axis specified ...

A usually simple algorithm or identity. The term is frequently applied to specific orders of Newton-Cotes formulas. The designation "rule n" is also given to the nth ...

A root-finding algorithm which assumes a function to be approximately linear in the region of interest. Each improvement is taken as the point where the approximating line ...

A spatial point process is a point process which models data that is localized at a discrete set of locations in space or, more specifically, on a plane.

A map which uses a set of rules to transform elements of a sequence into a new sequence using a set of rules which "translate" from the original sequence to its ...

The tilde is the mark "~" placed on top of a symbol to indicate some special property. x^~ is voiced "x-tilde." The tilde symbol is commonly used to denote an operator. In ...