Sweeps and Orbits Hub

For many years truangle geometry has focused on the properties of individual or small groups of objects. We have now discovered so many objects that large quantities can have definable properties. I call several of these properties "orbits" and "sweeps."

A sweep is a pattern of triangle centers I noticed in triangle geometry. It is derived from the orbit phenomenon, a pattern of points fomed from a single point under the repeated action of the projective transformation it defines. Fancy words for a fairly simple idea.

 

	Orbits This picture is the orbit of the incenter, simultaneously a pattern of triangle centes and an invariant curve of a projective transformation.
	The Non-Euclidean Geometry of Euclidean Points This article explains the principles behind orbits and sweeps.
	The distribution of triangle centers Here the points in The Encyclopedia of Triangle Centers are plotted.
	Sweeps of Points An organizational structure of triangle points
	Sweeps of Lines The corresponding structure in triangle lines.
	Picture of a projective transformation The sweeps and orbits follow an invariant curve for a projective transformation.