Section 1
Mathematics, Geometry and Art

C. A. Folio 307 verso
Transformation of a Circle into Stellar Structures

traces of black chalk and visible incisions and compass points,
circa 1517-18
©Veneranda Biblioteca Ambrosiana/Mondadori Portfolio

Folio 307 verso
This sheet dates from Leonardo’s late years when he was in France and is also the last in a series dedicated to a geometric exercise or game called ludo geometrico. The “ludo” was a mathematical problem that Leonardo was trying to solve. Put simply, it involved transforming a curvilinear surface area into a rectilinear one of exactly the same surface area, and vice versa and is in fact an unsolvable problem. This final drawing in the series produced the most spectacular and complex decorative image of the entire Codex. The rose-window-like pattern is generated by the fragmentation of a large circle into its component star or lunar sections (called biangular surfaces), based on proportional relationships of multiples of the number 6. Above the circular form, Leonardo has worked out the first 50 multiples of the number 6, though he makes a simple arithmetic mistake which throws the series off.