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Let a spherical triangle be drawn on the surface of a sphere of radius R, centered at a point O=(0,0,0), with vertices A, B, and C. The vectors from the center of the sphere ...

The symbol tau (the lower case Greek letter tau) has many common uses in mathematics, as summarized in the following table. 1. tau(n) is an alternate notation for the divisor ...

A function f is said to have a upper bound C if f(x)<=C for all x in its domain. The least upper bound is called the supremum. A set is said to be bounded from above if it ...

A formula relating the number of polyhedron vertices V, faces F, and polyhedron edges E of a simply connected (i.e., genus 0) polyhedron (or polygon). It was discovered ...

Barycentric coordinates are triples of numbers (t_1,t_2,t_3) corresponding to masses placed at the vertices of a reference triangle DeltaA_1A_2A_3. These masses then ...

The ding-dong surface is the cubic surface of revolution given by the equation x^2+y^2=(1-z)z^2 (1) (Hauser 2003) that is closely related to the kiss surface. The surface can ...

The "echidnahedron" is the term for the spiky fourth icosahedron stellation (in the enumeration of Maeder 1994) apparently first used in the Netlib polyhedron database. It is ...

The surface of revolution given by the parametric equations x(u,v) = cosusin(2v) (1) y(u,v) = sinusin(2v) (2) z(u,v) = sinv (3) for u in [0,2pi) and v in [-pi/2,pi/2]. It is ...

The elongated dodecahedron, also known as the extended rhombic dodecahedron and rhombo-hexagonal dodecahedron, is a space-filling polyhedron and primary parallelohedron ...

Informally, self-similar objects with parameters N and s are described by a power law such as N=s^d, where d=(lnN)/(lns) is the "dimension" of the scaling law, known as the ...