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If (1+xsin^2alpha)sinbeta=(1+x)sinalpha, then (1+x)int_0^alpha(dphi)/(sqrt(1-x^2sin^2phi))=int_0^beta(dphi)/(sqrt(1-(4x)/((1+x)^2)sin^2phi)).

A birotunda in which the bases are in opposite orientations.

A cupolarotunda in which the bases are in opposite orientations.

An estimator of the actual values of population.

The point with respect to which a radial curve is computed.

The tensor defined by T^l_(jk)=-(Gamma^l_(jk)-Gamma^l_(kj)), where Gamma^l_(jk) are Christoffel symbols of the first kind.

A number of attractive tetrahedron 5-compounds can be constructed. The first (left figures) is one of the icosahedron stellations in which the 5×4 vertices of the tetrahedra ...

A grid usually refers to two or more infinite sets of evenly-spaced parallel lines at particular angles to each other in a plane, or the intersections of such lines. The two ...

A number which is simultaneously octagonal and triangular. Let O_n denote the nth octagonal number and T_m the mth triangular number, then a number which is both octagonal ...

A circle packing is called rigid (or "stable") if every circle is fixed by its neighbors, i.e., no circle can be translated without disturbing other circles of the packing ...