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The components of the gradient of the one-form dA are denoted A_(,k), or sometimes partial_kA, and are given by A_(,k)=(partialA)/(partialx^k) (Misner et al. 1973, p. 62). ...

A compact surface is a surface which is also a compact set. A compact surface has a triangulation with a finite number of triangles. The sphere and torus are compact.

Two angles alpha and beta are said to be complementary if alpha+beta=pi/2. In other words, alpha and beta are complementary angles if they produce a right angle when combined.

Complex infinity is an infinite number in the complex plane whose complex argument is unknown or undefined. Complex infinity may be returned by the Wolfram Language, where it ...

Let L be a link in R^3 and let there be a disk D in the link complement R^3-L. Then a surface F such that D intersects F exactly in its boundary and its boundary does not ...

Confocal parabolas are parabolas sharing a common focus.

A transformation of the form g=D^(T)etaD, where det(D)!=0 and det(D) is the determinant. Isometries are also called congruence transformations.

The discriminant of the general conic section ax_1^2+bx_2^2+cx_3^2+2fx_2x_3+2gx_1x_3+2hx_1x_2=0 is defined as Delta=|a h g; h b f; g f c|=abc+2fgh-af^2-bg^2-ch^2. If b=a and ...

The contact angle between a sphere and a tangent plane is the angle alpha between the normal to the sphere at the point of tangency and the basal plane with respect to which ...

f(x)=1/x-|_1/x_| for x in [0,1], where |_x_| is the floor function. The natural invariant of the map is rho(y)=1/((1+y)ln2).