Patterns of Beauty in Nature and Art
THE GOLDEN RATIO AND THE FIBONACCI SEQUENCE
“If there is a God, he’s a great mathematician.” —Paul Dirac
What do the Mona Lisa, the Parthenon, and a common pinecone have in common? They all conform to a specific mathematical ratio, called the “Golden Ratio,” that has fascinated the world’s great thinkers for millennia. It may surprise you, but there is an intimate and longstanding relationship between beauty, art, and math.
One of the easiest ways to define the Golden Ratio is through the famous sequence of numbers named after the mathematician Fibonacci. See if you can identify the pattern in the following set of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34... Each number is the sum of the previous two numbers. When you divide any of the numbers (after the first few) by the one before it, you get roughly the same number (about 1.6, or ), and the value becomes increasingly refined as the numbers get larger.
This “golden” proportion, when applied visually, creates specific kinds of rectangles and spirals whose precise shapes we find all over the place in nature. Cones, shells, and flowers, for example, typically illustrate the pattern in the elegant arrangement of their features. The uncanny recurrence of the ratio in nature, and its mysterious connection with beauty, has inspired many artists, from Dalí to the architects of the Great Pyramids, to employ it in their own compositions. —CKG
QUESTIONS TO PONDER
• Why is this pattern found so often in nature?
• What would make one set of proportions more beautiful than another?