March 30, 2011
Leonardo da Vinci's Mathematical Slip-Up
Dirk Huylebrouk in Scientific American:
Artist, inventor and philosopher Leonardo da Vinci (1452–1519) was without a doubt a genius. Yet, there is some criticism. In his book 1434: The Year a Magnificent Chinese Fleet Sailed to Italy and Ignited the Renaissance (William Morrow, 2008) British author and retired submarine commander Gavin Menzies claims that da Vinci swiped most of his ideas from the Chinese. Menzies's theory was poorly received by the world of science. Besides, isn't da Vinci's brilliance beyond question? Definitely, but the Dutch mathematician and artist Rinus Roelofs did find an error in one of the Renaissance man's drawings (at right).
A clue can be found in a portrait (below) of Luca Pacioli, a mathematician who, like his contemporary da Vinci, worked at the court of the Duke of Milan. The polyhedron in the left upper corner, hanging from a string, is called a rhombicuboctahedron: a polyhedron with an equilateral triangle that is always surrounded by squares. Leonardo illustrated it separately in Pacioli's book.
The rhombicuboctahedron can also be found in the star-shaped figures, at least if we put a pointed protrusion on each side surface—that is, a pyramid with a triangular or quadrangular base.
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