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The curve which is the envelope of reflected (catacaustic) or refracted (diacaustic) rays of a given curve for a light source at a given point (known as the radiant point).

Given a circle expressed in trilinear coordinates by a central circle is a circle such that l:m:n is a triangle center and k is a homogeneous function that is symmetric in ...

A chamfered octahedron, which could also know known as a tritruncated rhombic dodecahedron, is a polyhedron obtained by chamfering a regular octahedron. The illustration ...

A chamfered tertrahedron, also known as the alternate truncated cube, is a polyhedron obtained by chamfering a regular tetrahedron. The illustration above shows increasing ...

There are at least two theorems known as Chebyshev's theorem. The first is Bertrand's postulate, proposed by Bertrand in 1845 and proved by Chebyshev using elementary methods ...

Let the probabilities of various classes in a distribution be p_1, p_2, ..., p_k, with observed frequencies m_1, m_2, ..., m_k. The quantity ...

Consider a unit circle and a radiant point located at (mu,0). There are four different regimes of caustics, illustrated above. For radiant point at mu=infty, the catacaustic ...

A triangle ABC formed by three circular arcs. By extending the arcs into complete circles, the points of intersection A^', B^', and C^' are obtained. This gives the three ...

The circumsphere of given set of points, commonly the vertices of a solid, is a sphere that passes through all the points. A circumsphere does not always exist, but when it ...

The circumtangential triangle is an equilateral triangle formed by the three points X on the circumcircle of a reference triangle DeltaABC at which the line XX^(-1), where ...