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The term Mandelbrot set is used to refer both to a general class of fractal sets and to a particular instance of such a set. In general, a Mandelbrot set marks the set of ...

Minimal surfaces are defined as surfaces with zero mean curvature. A minimal surface parametrized as x=(u,v,h(u,v)) therefore satisfies Lagrange's equation, ...

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 ...

Spherical coordinates, also called spherical polar coordinates (Walton 1967, Arfken 1985), are a system of curvilinear coordinates that are natural for describing positions ...

A unit-distance graph is a distance graph having an embedding in the Euclidean plane (unit-distance embedding) in which vertices are distinct points and all edges are of ...

Fermat's last theorem is a theorem first proposed by Fermat in the form of a note scribbled in the margin of his copy of the ancient Greek text Arithmetica by Diophantus. The ...

By the duality principle, for every polyhedron, there exists another polyhedron in which faces and polyhedron vertices occupy complementary locations. This polyhedron is ...

The M_(22) graph, also known as the 77-graph, is a strongly regular graph on 77 nodes related to the Mathieu group M_(22) and to the Witt design. It is illustrated above in ...

The pathological function f_a(x)=sum_(k=1)^infty(sin(pik^ax))/(pik^a) (originally defined for a=2) that is continuous but differentiable only on a set of points of measure ...

The regular tetrahedron, often simply called "the" tetrahedron, is the Platonic solid with four polyhedron vertices, six polyhedron edges, and four equivalent equilateral ...