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The Gergonne line is Oldknow's (1996) term for the perspectrix of a contact triangle DeltaDEF and its reference triangle DeltaABC. It is determined by the Nobbs points D^', ...

Given a unit line segment [0,1], pick two points at random on it. Call the first point x_1 and the second point x_2. Find the distribution of distances d between points. The ...

A line in the complex plane with slope +/-i. An isotropic line passes through either of the circular points at infinity. Isotropic lines are perpendicular to themselves.

A "line" having imaginary coefficients in its equations which can arise in algebraic geometry.

Mark a point P on a side of a triangle and draw the perpendiculars from the point to the two other sides. The line between the feet of these two perpendiculars is called the ...

A line that simultaneously bisects a triangle's perimeter and area.

A number of points on a line segment. The term was first used by Desargues (Cremona 1960, p. x). If the points A, B, C, ... lie on a line segment with the coordinates of the ...

Given two intersecting lines OA and OB forming an angle with vertex at O and a point X inside the angle ∠AOB, the Philo line (or Philon line) is the shortest line segment AB ...

The three planes determined by the edges of a trihedron and the internal bisectors of the respectively opposite faces are coaxal, and the common line of these planes is ...

The orthopoles of a line l with respect to the four triangles formed by three out of four vertices of any quadrilateral ABCD lie on a straight line L known as the orthopolar ...