This applet demonstrates distortion characteristics of a couple simple projections.

To use it, select a projection from the drop down list. On the graticule, the red vertical line is the prime meridian; the red horizontal line is the equator.

You can change the longitude, latitude, and radius of the drawn circle by changing the values in the appropriate fields and hitting the Enter key. Right now the app does very little range checking so it's pretty breakable. Click your browser's reload button if things get too weird.

A note on the formula for plotting the circle: this comes from formulas 7.45 and 7.46 on p. 225 of Bugayevskiy and Snyder, "Map Projections: A Reference Manual," Taylor and Francis, 1995. This is a wonderful book for figuring out how to do all kinds of projections as well as solving a variety of problems based on spherical and polar coordinates.