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For a subgroup H of a group G, the index of H, denoted (G:H), is the cardinal number of the set of left cosets of H in G (which is equal to the cardinal number of the set of ...

An ordered finite configuration with certain pairs of points, called cables, which are constrained not to get further apart and certain other pairs of points, called struts, ...

Also known as the total curvature. The linear element of the indicatrix ds_P=sqrt(ds_T^2+ds_B^2).

The third Morley adjunct triangle has trilinear vertex matrix [2 sec[1/3(C-4pi)] sec[1/3(B-4pi)]; sec[1/3(C-4pi)] 2 sec[1/3(A-4pi)]; sec[1/3(B-4pi)] sec[1/3(A-4pi)] 2]. The ...

A topological groupoid over B is a groupoid G such that B and G are topological spaces and alpha,beta, and multiplication are continuous maps. Here, alpha and beta are maps ...

An extension field of a field F that is not algebraic over F, i.e., an extension field that has at least one element that is transcendental over F. For example, the field of ...

Let CD be the altitude of a triangle DeltaABC and let E be its midpoint. Then area(DeltaABC)=1/2AB·CD=AB·DE, and ABFG can be squared by rectangle squaring. The general ...

Every real number is negative, 0, or positive. The law is sometimes stated as "For arbitrary real numbers a and b, exactly one of the relations a<b, a=b, a>b holds" (Apostol ...

Not decidable as a result of being neither formally provable nor unprovable.

An ungula is a portion of a solid of revolution obtained by cutting via a plane oblique to its base. The term derives from the Latin word ungula for the hoof of a horse. ...