Leonardo Fibonacci di Pisa
Leonardo Fibonnaci di Pisa was an Italian mathematician born around 1170 A.D. He learned his mathematical knowledge while traveling though North Africa with his father. He wrote the book Liber Abaci in 1202, which posed a question about the reproduction of rabbits. The answer to this question brought to pass the Fibonacci Sequence-- This sequence, where each number is the sum of the previous two numbers starting with 0 and 1, begins 0, 1, 1, 2, 3, 5, 8, 13, 21,34, 55, 89,233, . . .. It is interesting to note is that the higher up the sequence, the closer two consecutive numbers from the sequence, when divided by each other, will approach the "golden ratio" of phi, approximately 1.61803.

Leonardo da Vinci
Leonardo da Vinci was an Italian painter, sculptor, architect, mathematician, inventor, writer and much more. He was born April 15, 1452 and described as the ideal "Renaissance Man" and a man of "unquenchable curiosity." This sums up the notion of math, art, and Leonardo very well:

"The integration of science and art has many more strands than Fibonacci's mathematics and Leonardo's art: It also draws in elements of architecture, astronomy, biology, chemistry, geology, engineering, mathematics, philosophy, physics- encompassing the extraordinary range of Leonardo da Vinci's interests. For him these were branches of the same tree, part of a grand unified structure, the universe." (Bulent Atalay, Math and the Mona Lisa, p.14)

The Golden Ratio
Another way that mathematics and art have combined has been through the irrational number phi (approximately 1.61803), also known as the "golden ratio," the "golden mean," and "the divine proportion." This number is believed to be the equation for things perceived as being aesthetically pleasing. Artists and architects through the ages have constructed pieces that contain geometric constructions of phi, such as the "golden triangle," the "golden rectangle," the "golden pyramid," and the "logarithmic spiral," which can be seen below:

The Golden Triangle


The Golden Rectangle


The Golden Pyramid


The Logarithmic Spiral

From sculptures, paintings, sketches, buildings, monuments, to mathematics- everything can be connected to this magnificent ratio. Leonardo Di Vinci found importance in it, as seen evident in his paintings. You can find golden ratios in many of da Vinci's paintings, such as:


Mona Lisa


The Vitruvian Man


Last Supper

As an interactive activity, use the applet I created in the link below to find different "Golden Triangles" in the Mona Lisa Painting!

Mona Lisa & the Golden Ratio: An Interactive Applet

Leonardo da Vinci on Proportion and Painting
Another way the Leonardo da Vinci incorporated mathematics into his art was through proportions. He developed mathematical formulas to compute the relationship between the distance from the eye to the object and its size on the intersecting plane, or canvas, on which the picture will be painted:

"If you place the intersection one metre from the eye, the first object, being four metres from the eye, will diminish by three-quarters of its height on the intersection; and if it is eight metres from the eye it will diminish by seven-eighths and if it is sixteen metres away it will diminish by fifteen-sixteenths, and so on. As the distance doubles so the diminution will double."
-- Leonardo da Vinci
(Martin Kemp, Leonardo On Painting, p.57)