Excenterslip

Excenterslip is a term used in geometry to describe a specific type of transformation that combines the properties of an excenter and a glide reflection. An excenter is a center of a triangle that is equidistant from all three sides of the triangle, but not necessarily from the vertices. A glide reflection is a transformation that combines a reflection across a line with a translation parallel to that line.

In an excenterslip, the triangle is first reflected across one of its excenters, and then a glide reflection is applied. This results in a new triangle that is similar to the original, but with its sides parallel to the original's sides. The excenterslip can be used to generate a series of similar triangles, each with its sides parallel to the previous one.

The excenterslip is a useful tool in geometric constructions and proofs, as it allows for the creation of similar triangles with specific properties. It is also a useful concept in understanding the relationships between different types of transformations in geometry.