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A tangent vector v_(p)=v_1x_u+v_2x_v is a principal vector iff det[v_2^2 -v_1v_2 v_1^2; E F G; e f g]=0, where e, f, and g are coefficients of the first fundamental form and ...

The circle H which touches the incircles I, I_A, I_B, and I_C of a circular triangle ABC and its associated triangles. It is either externally tangent to I and internally ...

A number t_x=tan^(-1)(1/x)=cot^(-1)x, where x is an integer or rational number, tan^(-1)x is the inverse tangent, and cot^(-1)x is the inverse cotangent. Gregory numbers ...

The series for the inverse tangent, tan^(-1)x=x-1/3x^3+1/5x^5+.... Plugging in x=1 gives Gregory's formula 1/4pi=1-1/3+1/5-1/7+1/9-.... This series is intimately connected ...

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 ...

A univariate function f(x) is said to be odd provided that f(-x)=-f(x). Geometrically, such functions are symmetric about the origin. Examples of odd functions include x, ...

Given three coins of possibly different sizes which are arranged so that each is tangent to the other two, find the coin which is tangent to the other three coins. The ...

The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular ...

C=tauT+kappaB, where tau is the torsion, kappa is the curvature, T is the tangent vector, and B is the binormal vector.

K=(dT)/(ds), where T is the tangent vector defined by T=((dx)/(ds))/(|(dx)/(ds)|).