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First stated in 1924, the Banach-Tarski paradox states that it is possible to decompose a ball into six pieces which can be reassembled by rigid motions to form two balls of ...

Define a Bouniakowsky polynomial as an irreducible polynomial f(x) with integer coefficients, degree >1, and GCD(f(1),f(2),...)=1. The Bouniakowsky conjecture states that ...

Although the rigidity theorem states that if the faces of a convex polyhedron are made of metal plates and the polyhedron edges are replaced by hinges, the polyhedron would ...

The constant e^pi that Gelfond's theorem established to be transcendental seems to lack a generally accepted name. As a result, in this work, it will be dubbed Gelfond's ...

For a real number x in (0,1), let m be the number of terms in the convergent to a regular continued fraction that are required to represent n decimal places of x. Then Lochs' ...

The outer Napoleon triangle is the triangle DeltaN_C^'N_B^'N_A^' formed by the centers of externally erected equilateral triangles DeltaABE_C^', DeltaACE_B^', and ...

In the early 1960s, B. Birch and H. P. F. Swinnerton-Dyer conjectured that if a given elliptic curve has an infinite number of solutions, then the associated L-series has ...

Likelihood is the hypothetical probability that an event that has already occurred would yield a specific outcome. The concept differs from that of a probability in that a ...

A right triangle is triangle with an angle of 90 degrees (pi/2 radians). The sides a, b, and c of such a triangle satisfy the Pythagorean theorem a^2+b^2=c^2, (1) where the ...

In his Meditationes algebraicae, Waring (1770, 1782) proposed a generalization of Lagrange's four-square theorem, stating that every rational integer is the sum of a fixed ...