Search Results for ""

The lines joining the vertices of a tetrahedron to the centroids of the opposite faces are called medians. Commandino's theorem states that the four medians of a tetrahedron ...

A vertex is a special point of a mathematical object, and is usually a location where two or more lines or edges meet. Vertices are most commonly encountered in angles, ...

The envelope of the plane lx+my+nz=c, (1) where c is the speed of propagation of a wave in the direction (l,m,n) (i.e., l, m, and n are the direction cosines) is known as the ...

An important theorem in plane geometry, also known as Hero's formula. Given the lengths of the sides a, b, and c and the semiperimeter s=1/2(a+b+c) (1) of a triangle, Heron's ...

The Hilbert curve is a Lindenmayer system invented by Hilbert (1891) whose limit is a plane-filling function which fills a square. Traversing the polyhedron vertices of an ...

Let the characteristic polynomial of an n×n complex matrix A be written in the form P(lambda) = |lambdaI-A| (1) = ...

Let four lines in a plane represent four roads in general position, and let one traveler T_i be walking along each road at a constant (but not necessarily equal to any other ...

Half of a sphere cut by a plane passing through its center. A hemisphere of radius r can be given by the usual spherical coordinates x = rcosthetasinphi (1) y = ...

The tangent indicatrix of a curve of constant precession is a spherical helix. The equation of a spherical helix on a sphere with radius r making an angle theta with the ...

A solution zeta_k=e^(2piik/d) to the cyclotomic equation x^d=1. The de Moivre numbers give the coordinates in the complex plane of the polygon vertices of a regular polygon ...