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Geometry is the study of figures in a space of a given number of dimensions and of a given type. The most common types of geometry are plane geometry (dealing with objects ...

A roulette is a curve traced by a fixed point on a closed convex curve as that curve rolls without slipping along a second curve. The roulettes described by the foci of ...

Each point in the convex hull of a set S in R^n is in the convex combination of n+1 or fewer points of S.

The Roman surface, also called the Steiner surface (not to be confused with the class of Steiner surfaces of which the Roman surface is a particular case), is a quartic ...

The central point (r=0) in polar coordinates, or the point with all zero coordinates (0, ..., 0) in Cartesian coordinates. In three dimensions, the x-axis, y-axis, and z-axis ...

On an algebraic curve, the sum of the number of coincidences at a noncuspidal point C is the sum of the orders of the infinitesimal distances from a nearby point P to the ...

A branch point of an analytic function is a point in the complex plane whose complex argument can be mapped from a single point in the domain to multiple points in the range. ...

C=tauT+kappaB, where tau is the torsion, kappa is the curvature, T is the tangent vector, and B is the binormal vector.

A symmetric bilinear form on a vector space V is a bilinear function Q:V×V->R (1) which satisfies Q(v,w)=Q(w,v). For example, if A is a n×n symmetric matrix, then ...

The point Ko of concurrence in Kosnita theorem, i.e., the point of concurrence of the lines connecting the vertices A, B, and C of a triangle DeltaABC with the circumcenters ...