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A general space based on the line element ds=F(x^1,...,x^n;dx^1,...,dx^n), with F(x,y)>0 for y!=0 a function on the tangent bundle T(M), and homogeneous of degree 1 in y. ...

Let M be a regular surface with v_(p),w_(p) points in the tangent space M_(p) of M. Then the first fundamental form is the inner product of tangent vectors, ...

In general, a frieze consists of repeated copies of a single motif. b ; a d; c Conway and Guy (1996) define a frieze pattern as an arrangement of numbers at the intersection ...

Gauss's theorema egregium states that the Gaussian curvature of a surface embedded in three-space may be understood intrinsically to that surface. "Residents" of the surface ...

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 ...

The internal (external) bisecting plane of a dihedral angle of a tetrahedron divides the opposite edge in the ratio of the areas of the adjacent faces.

The gnomonic projection is a nonconformal map projection obtained by projecting points P_1 (or P_2) on the surface of sphere from a sphere's center O to point P in a plane ...

There does not exist an everywhere nonzero tangent vector field on the 2-sphere S^2. This implies that somewhere on the surface of the Earth, there is a point with zero ...

A tiling consisting of a rhombus such that 17 rhombuses fit around a point and a second tile in the shape of six rhombuses stuck together. These two tiles can fill the plane ...

The construction of polyhedra using identical building blocks. The illustrations above show such constructions for the cuboctahedron, octahedron rhombic dodecahedron, and ...