What It Shows
As shown in the drawing, the Mercator projection is a cylindrical map projection of the spherical globe. The meridians and parallels of latitude on the globe end up appearing as lines crossing at right angles in the projection. Areas on the globe far from the equator appear to be much larger on the projection. It's not trivial to visualize this projection and the intention of this demonstration is to shed some light on it (literally).
How It Works
The continents of the Earth are drawn on a 15-inch diameter glass globe (ceiling light enclosure). A bright point source of light1 is positioned in the center of the globe and the outlines of the continents cast shadows on a translucent cylindrical screen2 wrapped around the globe.
One can see that the land masses near the equator are true to scale whereas the higher latitudes are greatly expanded. Greenland, for example, appears as large as Africa, even though the area of Africa is 14 times greater. Another way of showing the distortion inherent in this projection is to use a watchglass with the arctic circle drawn on it.
The meridians converging at the north pole appear quite distorted when shadow projected onto the cylindrical screen. However, when the watchglass is placed at the north pole (where it's supposed to be), the meridians appear as parallel vertical lines!
Setting it up:
Globe, cylindrical screen, and power transformer can all reside on a small cart.
Wikepedia is great on this subject and includes the mathematics of the Mercator projection.
1. OSRAM HLX 64640 FCS 24 V 150 W bulb powered by a 24 VAC transformer.
2. Vellum translucent film sheet