A Conformal Projection: Stereographic Mapping
A Conformal Type: The Stereographic Projection
A type of conformal projection is the Stereographic map, which maps most of the points of a sphere onto a plane. See an example of the stereographic map of earth below. Try play with the applet below to learn some new facts.
Question: "Stereographic"-Definedness
Play with the applet by dragging the points around. We said "most" points of the sphere get mapped. Which ones aren't defined on the plane?

Question: Lost Properties (Stereographic)
Which of three (distance, area, angles) would get distorted here?
Question: Retained Properties (Stereographic)
Which of the three would get preserved?
Question: Mercator vs. Stereographic Maps
What are some advantages of the Stereographic Projection to the Mercator? What are disadvantages?