Geometry, Volume 1, Issue 1

It is well known that the four ancient Greek triangle centers and others have homogeneous barycentric coordinates that are polynomials in the sidelengths a,b, and c of a triangle ABC. For example, the circumcenter is represented by the polynomial a(b...

In this article, we provide elementary proofs of two projective generalizations of Hagge’s theorems. We describe Steiner’s correspondence as a projective generalization of inversion.

We describe a series of parallel lenses with constant proportions packed in a circle. To construct n lenses, a regular 2(n + 1)-gon is drawn with a central diagonal of 2r length, followed by an array of n parallel diagonals perpendicular to the forme...

Suppose that X is a triangle center with homogeneous coordinates (barycentric or trilinear) x:y:z. Eight unary operations discussed in this paper include u1(X)=(y−z)/x:(z−x)/y:(x−y)/z. For each ui, there exist, formally, two points,...

In the ancient realm of geometry, we have witnessed the ultimate display of mathematical abstract thought [...]