Search Results for ""

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 ...

Lovász (1970) conjectured that every connected vertex-transitive graph is traceable (Gould, p. 33). This conjecture was subsequently verified for several special orders and ...

A random matrix is a matrix of given type and size whose entries consist of random numbers from some specified distribution. Random matrix theory is cited as one of the ...

Thurston's conjecture proposed a complete characterization of geometric structures on three-dimensional manifolds. Before stating Thurston's geometrization conjecture in ...

There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The ...

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 ...