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The Yff contact circle is the circumcircle of the Yff contact triangle. Its center has triangle center function alpha=((b-c)(3a^3+b^3+c^3-2a^2b-2a^2c-abc))/a, (1) which does ...

If a function f(x) is continuous on a closed interval [a,b], then f(x) has both a maximum and a minimum on [a,b]. If f(x) has an extremum on an open interval (a,b), then the ...

The point of illumination for a caustic.

The second Brocard circle is the circle having center at the circumcenter O of the reference triangle and radius R_B = sqrt(1-4sin^2omega)R (1) = (2) where R is the ...

The point S^' which makes the perimeters of the triangles DeltaBS^'C, DeltaCS^'A, and DeltaAS^'B equal. The isoperimetric point exists iff a+b+c>4R+r, (1) where a, b, and c ...

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 ...

Bürmann's theorem deals with the expansion of functions in powers of another function. Let phi(z) be a function of z which is analytic in a closed region S, of which a is an ...

The first Brocard point Omega is the interior point Omega (also denoted tau_1 or Z_1) of a triangle DeltaABC with points labeled in counterclockwise order for which the ...

The nine-point center N (sometimes instead denoted F) is the center of the nine-point circle. It has equivalent triangle center functions alpha_5 = cos(B-C) (1) alpha_5 = ...

Given a unit circle, pick two points at random on its circumference, forming a chord. Without loss of generality, the first point can be taken as (1,0), and the second by ...