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The shoelace formula, also known as Gauss's area formula, the shoelace algorithm, shoelace method, or surveyor's formula, is a name sometimes given to the polygon area ...

A formula of first-order logic is said to be in Skolemized form (sometimes also called Skolem standard form or universal form) if it is of the form forall x_1... forall x_nM, ...

A universal sentence is a sentence (i.e., formula of the predicate calculus without free variables) whose variables are universally quantified.

Propositional calculus, first-order logic, and other theories in mathematical logic are defined by their axioms (or axiom schemata, plural: axiom schemata) and inference ...

The volume of a polyhedron composed of N triangular faces with vertices (a_i,b_i,c_i) can be computed using the curl theorem as V=1/6sum_(i=1)^Na_i·n_i, where the normal n_i ...

Quantifier elimination is the removal of all quantifiers (the universal quantifier forall and existential quantifier exists ) from a quantified system. A first-order theory ...

The semiperimeter on a figure is defined as s=1/2p, (1) where p is the perimeter. The semiperimeter of polygons appears in unexpected ways in the computation of their areas. ...

J. Tupper concocted the amazing formula 1/2<|_mod(|_y/(17)_|2^(-17|_x_|-mod(|_y_|,17)),2)_|, where |_x_| is the floor function and mod(b,m) is the mod function, which, when ...

A proof based on a dissection which shows the formula for the area of a plane figure or of the volume of a solid. Dozens of different dissection proofs are known for the ...

The length of a number n in base b is the number of digits in the base-b numeral for n, given by the formula L(n,b)=|_log_b(n)_|+1, where |_x_| is the floor function. The ...