Regiomontanus' Angle Maximization Problem/Historical Note

Historical Note on Regiomontanus' Angle Maximization Problem

Regiomontanus first posed this problem in $1471$ to Christian Roder.

He posed it in the context of choosing the optimum place to stand to view a statue positioned above eye level.

Too close and it will appear heavily foreshortened, too far away and it will just appear small.

It is notable as the first extremal problem since Heron's Principle of Reflection.

The problem has been reinvented several times, and has a contemporary application: it gives the best place to take a conversion kick in the game of rugby.

Sources

• 1991: David Wells: Curious and Interesting Geometry ... (previous) ... (next): angle in the same segment
• 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): The Best View of a Statue: $93$