After arriving in Milan in 1496, Pacioli formed a very close connection with da Vinci in which he tutored da Vinci in mathematics. The two men had a deep friendship that transcended their mathematical endeavors; their notebooks include comments to one another like “Well Leonardo, you can do more of this on your own” and “learn the multiplication of roots from Maestro Luca." They also shared the task of providing entertainment to the Court of Milan; their entertainments included brainteasers, magic tricks, and riddles. Mathematically speaking, the duo shared a deep interest in geometric shapes. Pacioli successfully taught da Vinci the works of Euclid’s Elements and less successfully taught him arithmetic techniques like multiplying squares and square roots.  During this time, da Vinci created several sketches of polyhedra that would be featured in Pacioli’s publication De Divina Proportione. In 1499 the French invaded Milan and the pair was forced to flee the city, eventually settling in Florence (where they lived together).

Sources

“Leonardo Da Vinci.” Leonardo Da Vinci (1452-1519), School of Mathematics and Statistics, University of St. Andrews, Scotland, www-history.mcs.st-and.ac.uk/Biographies/Leonardo.html.

Isaacson, Walter. Leonardo Da Vinci. Simon & Schuster Paperbacks, 2018.

“Luca Pacioli.” Luca Pacioli (1445-1517), School of Mathematics and Statistics, University of St. Andrews, Scotland, www-history.mcs.st-and.ac.uk/Biographies/Pacioli.html.

The image source is Wikimedia Commons, and it is in the public domain in the United States because it was published (or registered with the U.S. Copyright Office) before January 1, 1924.