Raphael\u27s School of Athens: A Theorem in a Painting?

Raphael\u27s famous painting The School of Athens includes a geometer, presumably Euclid himself, demonstrating a construction to his fascinated students. But what theorem are they all studying? This article first introduces the painting, and describes Raphael\u27s lifelong friendship with the eminent mathematician Paulus of Middelburg. It then presents several conjectured explanations, notably a theorem about a hexagram (Fichtner), or alternatively that the construction may be architecturally symbolic (Valtieri). The author finally offers his own null hypothesis : that the scene does not show any actual mathematics, but simply the fascination, excitement, and joy of mathematicians at their work