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65537 is the largest known Fermat prime, and the 65537-gon is therefore a constructible polygon using compass and straightedge, as proved by Gauss. The 65537-gon has so many ...

The idea of a velocity vector comes from classical physics. By representing the position and motion of a single particle using vectors, the equations for motion are simpler ...

The Ricci curvature tensor, also simply known as the Ricci tensor (Parker and Christensen 1994), is defined by R_(mukappa)=R^lambda_(mulambdakappa), where ...

The Laplace transform is an integral transform perhaps second only to the Fourier transform in its utility in solving physical problems. The Laplace transform is particularly ...

A one-person game played on a rectangular lattice of lamps which can be turned on and off. A move consists of flipping a "switch" inside one of the squares, thereby toggling ...

The j-function is the modular function defined by j(tau)=1728J(tau), (1) where tau is the half-period ratio, I[tau]>0, ...

For a right triangle with legs a and b and hypotenuse c, a^2+b^2=c^2. (1) Many different proofs exist for this most fundamental of all geometric theorems. The theorem can ...

A quaternion Kähler manifold is a Riemannian manifold of dimension 4n, n>=2, whose holonomy is, up to conjugacy, a subgroup of Sp(n)Sp(1)=Sp(n)×Sp(1)/Z_2, but is not a ...

A general quadratic Diophantine equation in two variables x and y is given by ax^2+cy^2=k, (1) where a, c, and k are specified (positive or negative) integers and x and y are ...

A Gröbner basis G for a system of polynomials A is an equivalence system that possesses useful properties, for example, that another polynomial f is a combination of those in ...