Math Photo: Pyramid Projection

Naturally, the geometry of this simple piece of playground equipment caught my eye, but the shadows really sparked my interest.

The shadows are the projections of the edges of this pyramid, and they form a set of angles on the ground.  Notice immediately that the largest angle (the shadow formed by the “back” face) is the sum of the other three angles.

There are many other interesting questions to ask, and relationships to explore.  What I was most curious about, however, is how accurately we could locate the sun in the sky based only on this information.