A Conformal Projection: Stereographic Mapping

A Conformal Type: The Stereographic Projection
A type of [b]conformal projection[/b] is the [b]Stereographic map[/b], 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?
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Information: A Conformal Projection: Stereographic Mapping