Ways to think about DWEG problems.

There are two or three useful points of view when thinking about DWEG problems.

• The Worms-Eye view of an inhabitant of the DWEG plane is the same as the view we normally take of the Euclidean plane.  What we can do depends on the tools we have and the theorems we know. DWEG lines look like straight lines and the go off to infinity without ever meeting.
• The Olympian Euclidean view of the model looks down from the perch of the gods and sees to infinity in a Euclidean plane, where the point at infinity looks like an ordinary point O. The view has the limitation that some ordinary DWEG point is so far off it looks like infinity, so some DWEG lines look like circles and some look like lines, but all go through O. 
• The Olympian Inversive view of the model looks down from the perch of the gods and sees all, including infinity, which looks like an I-point O. So all DWEG lines look like I-circles that pass through O.

Olympian Euclidean is the view we must take when we construct figures with Sketchpad, but we can use the other views to figure out what to do.