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The slope-intercept form of a line in the Cartesian plane is given by y=mx+b, where b is the y-intercept and m is the slope.

The power of a fixed point A with respect to a circle of radius r and center O is defined by the product p=AP×AQ, (1) where P and Q are the intersections of a line through A ...

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, ...

Let a circle C_1 lie inside another circle C_2. From any point on C_2, draw a tangent to C_1 and extend it to C_2. From the point, draw another tangent, etc. For n tangents, ...

Given three mutually tangent circles, there exist exactly two nonintersecting circles which are tangent circles to all three original circles. These are called the inner and ...

The intersection Ev of the Gergonne line and the Euler line. It has triangle center function alpha=(b(a-b+c)cosB+c(a+b-c)cosC-2a^2cosA)/(2a) and is Kimberling center X_(1375).

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 ...

The rotation vector of the trihedron of a curve with curvature kappa!=0 when a point moves along a curve with unit speed. It is given by D=tauT+kappaB, (1) where tau is the ...

Consider Kimberling centers X_(20) (de Longchamps point Z; intersection L_S intersection L_E of the Soddy line and Euler line), X_(468) (intersection L_E intersection L_O of ...

On a Riemannian manifold M, tangent vectors can be moved along a path by parallel transport, which preserves vector addition and scalar multiplication. So a closed loop at a ...