 Cover of Math and the Mona Lisa, by
Bülent Atalay, Smithsonian Books, Copyright 2006
|
Recently
Professor Bülent Atalay of Mary Washington University presented a
fascinating public Lecture at Warren Wilson College on Leonardo's
Universe featuring much of the mathematics that Leonardo da Vinci
incorporated in many of his studies, drawings, and paintings -
including the Mona Lisa.
Much of the mathematics that Leonardo da Vinci used was discovered about 3 centuries earlier by "The Other Leonardo": Leonardo Fibonacci di Pisa. Leonardo Fibonacci is most noted for the simple series that bears his name: 1, 1, 2, 3, 5, 8, 13, 21, ... in which each succeeding number is the sum of the previous two numbers. These numbers are found in many instances of nature - replication of animals, tree branches, and the spirals of pine cone segments, sunflower seed heads, and pineapples. The ratio of any Fibonacci number to the previous number in the sequence has a magnificent property. As the numbers become larger, this number approaches a limit: 1.618034.... For example, the ratio of the 19th Fibonacci number (4181) divided by the 18th (2584) equals 1.618034.... This number, φ = "phi", is also called "The Golden Ratio", "The Golden Mean", and "The Divine Proportion". In the book Math and the Mona Lisa, Dr. Atalay points out many features in art, architecture, nature, and especially the Mona Lisa painting many instances of the divine proportion. It seems that Leonardo mastered the use of this simple irrational number to make his art take on a universal appeal. |
Fibonacci
numbers.
In
the enlarged photo of the cone of a common pitch
pine
(found in one of my neighbor's yards) the spirals have been highlighted
for easy counting. There are 8 spirals bending to the left as
they open out indicated in red. Likewise there are 13 spirals
opening to the right indicated by blue traces. 8 and 13 are
consecutive Fibonacci numbers. Several pine cones of the same
species also exhibited the 8 and 13 spirals. Cones of other pine
species exhibit 5 and 8 spirals - two other consecutive
Fibonacci numbers.