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Attach a string to a point on a curve. Extend the string so that it is tangent to the curve at the point of attachment. Then wind the string up, keeping it always taut. The ...

The trilinear pole of the orthotransversal of a point P is called its orthocorrespondent. The orthocorrespondent of a point P=p:q:r is given by where S_A, S_B, and S_C is ...

In the plane, the reflection property can be stated as three theorems (Ogilvy 1990, pp. 73-77): 1. The locus of the center of a variable circle, tangent to a fixed circle and ...

An open connected set is called a region (sometimes also called a domain).

An ambient isotopy from an embedding of a manifold M in N to another is a homotopy of self diffeomorphisms (or isomorphisms, or piecewise-linear transformations, etc.) of N, ...

Using a Tschirnhausen transformation, the principal quintic form can be transformed to the one-parameter form w^5-10cw^3+45c^2w-c^2=0 (1) named after Francesco Brioschi ...

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 ...

_0F_1(;a;z)=lim_(q->infty)_1F_1(q;a;z/q). (1) It has a series expansion _0F_1(;a;z)=sum_(n=0)^infty(z^n)/((a)_nn!) (2) and satisfies z(d^2y)/(dz^2)+a(dy)/(dz)-y=0. (3) It is ...

A nonplanar graph G is said to be critical nonplanar if the removal of a vertex results in a planar graph for every vertex of G. Critical nonplanar graphs differ from apex ...

A graph G with m edges is said to be elegant if the vertices of G can be labeled with distinct integers (0,1,2,...,m) in such a way that the set of values on the edges ...