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The Cassini ovals are a family of quartic curves, also called Cassini ellipses, described by a point such that the product of its distances from two fixed points a distance ...

There are two theorems commonly known as Feuerbach's theorem. The first states that circle which passes through the feet of the perpendiculars dropped from the polygon ...

The volumes of any n n-dimensional solids can always be simultaneously bisected by a (n-1)-dimensional hyperplane. Proving the theorem for n=2 (where it is known as the ...

The adjective "affine" indicates everything that is related to the geometry of affine spaces. A coordinate system for the n-dimensional affine space R^n is determined by any ...

The lines connecting the vertices and corresponding circle-circle intersections in Malfatti's problem coincide in a point X_(179) called the first Ajima-Malfatti point ...

Given a point with trilinear coordinates P=alpha:beta:gamma, the anticevian triangle DeltaA^'B^'C^' of a triangle DeltaABC with respect to P is a triangle such that 1. B^'C^' ...

A problem sometimes known as Moser's circle problem asks to determine the number of pieces into which a circle is divided if n points on its circumference are joined by ...

The devil's curve was studied by G. Cramer in 1750 and Lacroix in 1810 (MacTutor Archive). It appeared in Nouvelles Annales in 1858. The Cartesian equation is ...

For an ellipse with parametric equations x = acost (1) y = bsint, (2) the negative pedal curve with respect to the origin has parametric equations x_n = ...

The locus of the centers of all circumconics that also pass through the orthocenter of a triangle (which, when not degenerate, are rectangular hyperbolas) is a circle through ...