Understanding Inspheres in Geometry and Topology

Insphere is a term used in geometry and topology to describe a set of points that are contained within a larger set. The term "insphere" is derived from the words "in" and "sphere".

An insphere of a set of points is a smaller set of points that is completely contained within the larger set. In other words, every point in the insphere is also a point in the larger set. The insphere of a set of points is also sometimes called the "interior" or "innermost" sphere of the set.

For example, if we have a set of points in two-dimensional space, the insphere of those points would be the smallest circle that contains all of the points. The insphere is useful in various mathematical and computational contexts, such as in the study of convex hulls, Voronoi diagrams, and other geometric concepts.