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The Regiomontanus Problem

Summary The Regiomontanus problem is that of determining the optimal place to stand to view a painting. The problem, which predates calculus by some 200 years, appears in most modern calculus books, though isn’t known by that name. The original solution was purely geometric, the optimality following from the well-known intersecting secants theorem. Modern treatments are analytic, using calculus, but none of the underlying geometry (or its original solution) is apparent. In this paper, we generalize the problem and unite the two solutions using parametric curves and results from differential geometry.