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The spherical distance between two points P and Q on a sphere is the distance of the shortest path along the surface of the sphere (paths that cut through the interior of the ...

The difference between the sum of the angles A, B, and C of a spherical triangle and pi radians (180 degrees), E=A+B+C-pi. The notation Delta is sometimes used for spherical ...

The study of figures on the surface of a sphere (such as the spherical triangle and spherical polygon), as opposed to the type of geometry studied in plane geometry or solid ...

A sphericon is the solid formed from a bicone with opening angle of 90 degrees (and therefore with a=r=h) obtained by slicing the solid with a plane containing the rotational ...

A symmetric function on n variables x_1, ..., x_n is a function that is unchanged by any permutation of its variables. In most contexts, the term "symmetric function" refers ...

A coordinate system (mu,nu,psi) given by the coordinate transformation x = (mucospsi)/(mu^2+nu^2) (1) y = (musinpsi)/(mu^2+nu^2) (2) z = nu/(mu^2+nu^2) (3) and defined for ...

Any nontrivial, closed, simple, smooth spherical curve dividing the surface of a sphere into two parts of equal areas has at least four inflection points.

A number of four-tetrahedron compounds can be constructed by rotating about the center-centroid lines of each face. Three such compounds are shown above for rotations by ...

The tetranacci numbers are a generalization of the Fibonacci numbers defined by T_0=0, T_1=1, T_2=1, T_3=2, and the recurrence relation T_n=T_(n-1)+T_(n-2)+T_(n-3)+T_(n-4) ...

A torispherical dome is the surface obtained from the intersection of a spherical cap with a tangent torus, as illustrated above. The radius of the sphere R is called the ...