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A fast boat is overtaking a slower one when fog suddenly sets in. At this point, the boat being pursued changes course, but not speed, and proceeds straight in a new ...

The Feuerbach point X_(11) (center of the Feuerbach hyperbola) lies on the nine-point circle. The Feuerbach antipode is the antipode of this point on nine-point circle. It ...

Given a convex plane region with area A and perimeter p, then |N-A|<p, where N is the number of enclosed lattice points.

Let P=alpha:beta:gamma be a point not on a sideline of a reference triangle DeltaABC. Let A^' be the point of intersection AP intersection BC, B^'=BP intersection AC, and ...

De Grey (2018) found the first examples of unit-distance graphs with chromatic number 5, thus demonstrating that the solution to the Hadwiger-Nelson problem (i.e., the ...

The trilinear quotient of two points p:q:r and u:v:w is the point p/u:q/v:r/w.

The Simson line is the line containing the feet P_1, P_2, and P_3 of the perpendiculars from an arbitrary point P on the circumcircle of a triangle to the sides or their ...

A polygon whose vertices do not all lie in a plane.

The four-color theorem states that any map in a plane can be colored using four-colors in such a way that regions sharing a common boundary (other than a single point) do not ...

The circumcircle of the Cevian triangle DeltaA^'B^'C^' of a given triangle DeltaABC with respect to a point P. The following table summarizes a number of named Cevian circles ...