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Let x be a point in an n-dimensional compact manifold M, and attach at x a copy of R^n tangential to M. The resulting structure is called the tangent space of M at x and is ...

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, ...

If the vertices A, B, and C of triangle DeltaABC lie on sides QR, RP, and PQ of the triangle DeltaPQR, then the three circumcircles CBP, ACQ, and BAR have a common point X. ...

Suppose f(x) is continuous at a stationary point x_0. 1. If f^'(x)>0 on an open interval extending left from x_0 and f^'(x)<0 on an open interval extending right from x_0, ...

The outer Vecten circle is the circumcircle of the outer Vecten triangle. It has center at Kimberling center X_(641), which is the complement of the outer Vecten point ...

Consider the distribution of distances l between a point picked at random in the interior of a unit cube and on a face of the cube. The probability function, illustrated ...

The triangle T that is externally tangent to the excircles and forms their triangular hull is called the extangents triangle (Kimberling 1998, p. 162). It is homothetic to ...

A hypersphere S^n is parallelizable if there are n vector fields that are linearly independent at each point. There exist only three parallelizable spheres: S^1, S^3, and S^7 ...

An evolute is the locus of centers of curvature (the envelope) of a plane curve's normals. The original curve is then said to be the involute of its evolute. Given a plane ...

Analytic continuation (sometimes called simply "continuation") provides a way of extending the domain over which a complex function is defined. The most common application is ...