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The exterior angle bisectors (Johnson 1929, p. 149), also called the external angle bisectors (Kimberling 1998, pp. 18-19), of a triangle DeltaABC are the lines bisecting the ...

A circumconic hyperbola, which therefore passes through the orthocenter, is a rectangular hyperbola, and has center on the nine-point circle. Its circumconic parameters are ...

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 ...