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If a function f(x) is continuous on a closed interval [a,b], then f(x) has both a maximum and a minimum on [a,b]. If f(x) has an extremum on an open interval (a,b), then the ...

A fiber bundle (also called simply a bundle) with fiber F is a map f:E->B where E is called the total space of the fiber bundle and B the base space of the fiber bundle. The ...

The first Brocard Cevian triangle is the Cevian triangle of the first Brocard point. It has area Delta_1=(2a^2b^2c^2)/((a^2+b^2)(b^2+c^2)(c^2+a^2))Delta, where Delta is the ...

The first Morley triangle DeltaA^'B^'C^', also simply known as "Morley's triangle", is the triangle constructed from pairwise intersections of the angle trisectors of a given ...

A G-space is a special type of T1-Space. Consider a point x and a homeomorphism of an open neighborhood V of x onto an open set of R^n. Then a space is a G-space if, for any ...

A ruled surface is called a generalized cone if it can be parameterized by x(u,v)=p+vy(u), where p is a fixed point which can be regarded as the vertex of the cone. A ...

A ruled surface is called a generalized cylinder if it can be parameterized by x(u,v)=vp+y(u), where p is a fixed point. A generalized cylinder is a regular surface wherever ...

There are no fewer than two closely related but somewhat different notions of gerbe in mathematics. For a fixed topological space X, a gerbe on X can refer to a stack of ...

The harmonic parameter of a polyhedron is the weighted mean of the distances d_i from a fixed interior point to the faces, where the weights are the areas A_i of the faces, ...

A device consisting of two coupled pendula, usually oscillating at right angles to each other, which are attached to a pen. The resulting motion can produce beautiful, ...