Search Results for ""

The adjective "affine" indicates everything that is related to the geometry of affine spaces. A coordinate system for the n-dimensional affine space R^n is determined by any ...

The Grassmannian Gr(n,k) is the set of k-dimensional subspaces in an n-dimensional vector space. For example, the set of lines Gr(n+1,1) is projective space. The real ...

Cut a sphere by a plane in such a way that the volumes of the spherical segments have a given ratio.

A tensor t is said to satisfy the double contraction relation when t_(ij)^m^_t_(ij)^n=delta_(mn). (1) This equation is satisfied by t^^^0 = (2z^^z^^-x^^x^^-y^^y^^)/(sqrt(6)) ...

The genesa is a mystical figure that correspond to a spherical cuboctahedron.

A shell bounded by two similar ellipsoids having a constant ratio of axes. Given a chord passing through a homeoid, the distance between inner and outer intersections is ...

A hosohedron is a regular tiling or map on a sphere composed of p digons or spherical lunes, all with the same two vertices and the same vertex angles, 2pi/p. Its Schläfli ...

A geodesic triangle with oriented boundary yields a curve which is piecewise differentiable. Furthermore, the tangent vector varies continuously at all but the three corner ...

The formulas j_n(z) = z^n(-1/zd/(dz))^n(sinz)/z (1) y_n(z) = -z^n(-1/zd/(dz))^n(cosz)/z (2) for n=0, 1, 2, ..., where j_n(z) is a spherical Bessel function of the first kind ...

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. ...