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A proof that is only based on visual elements, without any comments. An arithmetic identity can be demonstrated by a picture showing a self-evident equality between numerical ...

In predicate calculus, an existential formula is a prenex normal form formula (i.e., a formula written as a string of quantifiers and bound variables followed by a ...

In predicate calculus, a universal formula is a prenex normal form formula (i.e., a formula written as a string of quantifiers and bound variables followed by a ...

The Woodbury formula (A+UV^(T))^(-1)=A^(-1)-[A^(-1)U(I+V^(T)A^(-1)U)^(-1)V^(T)A^(-1)] is a formula that allows a perturbed matrix to be computed for a change to a given ...

An interpretation of first-order logic consists of a non-empty domain D and mappings for function and predicate symbols. Every n-place function symbol is mapped to a function ...

A rotation through 180 degrees (pi radians).

The function giving the volume of the spherical quadrectangular tetrahedron: V=(pi^2)/8f(pi/p,pi/q,pi/r), (1) where (2) and D=sqrt(cos^2xcos^2z-cos^2y). (3)

An occurrence of a variable in a logic formula which is not inside the scope of a quantifier.

A formula which counts the number of fixed points for a topological transformation.

Values of the trigonometric functions can be expressed exactly for integer multiples of pi/20. For cosx, cos(pi/(20)) = 1/4sqrt(8+2sqrt(10+2sqrt(5))) (1) cos((3pi)/(20)) = ...