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Every point which can be constructed with a straightedge and compass, and no other points, can be constructed using identical matchsticks (i.e., identical movable line ...

A partial derivative of second or greater order with respect to two or more different variables, for example f_(xy)=(partial^2f)/(partialxpartialy). If the mixed partial ...

If lim_(z->z_0)(f(z)-f(z_0))/(z-z_0) is the same for all paths in the complex plane, then f(z) is said to be monogenic at z_0. Monogenic therefore essentially means having a ...

A nonuniform rational B-spline curve defined by C(t)=(sum_(i=0)^(n)N_(i,p)(t)w_iP_i)/(sum_(i=0)^(n)N_(i,p)(t)w_i), where p is the order, N_(i,p) are the B-spline basis ...

If each of two nonparallel transversals with nonminimal directions meets a given curve in finite points only, then the ratio of products of the distances from the two sets of ...

The centroid of the four points constituting an orthocentric system is the center of the common nine-point circle (Johnson 1929, p. 249). This fact automatically guarantees ...

Consider a reference triangle DeltaABC and any given point P. The perpendiculars to AP, BP and CP respectively meet BC, AC and AB in three collinear points defining line l. ...

Let gamma be a path given parametrically by sigma(t). Let s denote arc length from the initial point. Then int_gammaf(s)ds = int_a^bf(sigma(t))|sigma^'(t)|dt (1) = ...

The word "place" has a special meaning in complex variables, where it roughly corresponds to a point in the complex plane (except that it reflects the Riemann sheet structure ...

Suppose for every point x in a manifold M, an inner product <·,·>_x is defined on a tangent space T_xM of M at x. Then the collection of all these inner products is called ...