A Divine Error

Dirk Huylebrouck
Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture (2015)
Pages 93–98


In the ‘De Divina Proportione’, illustrated by Leonardo da Vinci, author Luca Pacioli formulated a brash statement about a theorem claiming six summits of pyramids of the elevated icosidodecahedron lay in one plane. Pacioli provided no proof while Leonardo's illustration for this statement contains errors. Thus, Jos Janssen (The Netherlands) suspected Pacioli's theorem was not true, and Rinus Roelofs (The Netherlands) confirmed his doubts using geometric computer software. Here, we confirm their rejection using arithmetical techniques Pacioli could have employed in his time. And yet, the abundant literature about ‘De Divina Proportione’ never revealed this error in the past 500 years.