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Weill's theorem states that, given the incircle and circumcircle of a bicentric polygon of n sides, the centroid of the tangent points on the incircle is a fixed point W, ...

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 first Fermat point X (or F_1) (sometimes simply called "the Fermat point," Torricelli point, or first isogonic center) is the point X which minimizes the sum of distances ...

A type of point at infinity in which parallel lines in the hyperbolic plane intersect at infinity in one direction, while diverging from one another in the other.

The point-slope form of a line through the point (x_1,y_1) with slope m in the Cartesian plane is given by y-y_1=m(x-x_1).

A branch point of an analytic function is a point in the complex plane whose complex argument can be mapped from a single point in the domain to multiple points in the range. ...

The triangulation point Y of a reference triangle DeltaABC for which triangles DeltaBYC, DeltaCYA, and DeltaAYB have congruent incircles. It is a special case of an Elkies ...

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 ...

Consider the excircles J_A, J_B, and J_C of a triangle, and the external Apollonius circle Gamma tangent externally to all three. Denote the contact point of Gamma and J_A by ...

A hyperbolic fixed point of a differential equation is a fixed point for which the stability matrix has eigenvalues lambda_1<0<lambda_2, also called a saddle point. A ...