Getting A Better Angle

This month's column deals with one of my favorite problems. I originally found it in Heinrich Dorrie's 100 Great Problems in Elementary Mathematics [1], a wonderful book now out in paperback that I highly recommend. The problem is often referred to as the Problem of Regiomontanus and is reputed to be the first max-min problem of the modern age.

"At what point on the ground does a perpendicularly suspended rod appear largest [i.e., subtends the greatest visual angle]? It has been claimed that this was the first extreme problem in the history of mathematics since antiquity."