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A normed vector space X=(X,||·||_X) is said to be uniformly convex if for sequences {x_n}={x_n}_(n=1)^infty, {y_n}={y_n}_(n=1)^infty, the assumptions ||x_n||_X<=1, ...

A function f(x) is completely convex in an open interval (a,b) if it has derivatives of all orders there and if (-1)^kf^((2k))(x)>=0 for k=0, 1, 2, ... in that interval ...

The convex hull of two or more functions is the largest function that is concave from above and does not exceed the given functions.

A derived polygon with side ratios chosen as r=1/2 so that inscribed polygons are constructed by connecting the midpoints of the base polygon. For a triangle P, the ...

A curvilinear polygon built up of circular arcs. The Reuleaux polygon is a generalization of the Reuleaux triangle and, for an odd number of sides, is a curve of constant ...

A closed geometric figure on the surface of a sphere which is formed by the arcs of great circles. The spherical polygon is a generalization of the spherical triangle. If ...

The positions of the geometric centroid of a planar non-self-intersecting polygon with vertices (x_1,y_1), ..., (x_n,y_n) are x^_ = ...

A skew polygon such that every two consecutive sides (but no three) belong to a face of a regular polyhedron. Every regular polyhedron can be orthogonally projected onto a ...

A cyclic polygon is a polygon with vertices upon which a circle can be circumscribed. Since every triangle has a circumcircle, every triangle is cyclic. It is conjectured ...

A star polygon {p/q}, with p,q positive integers, is a figure formed by connecting with straight lines every qth point out of p regularly spaced points lying on a ...