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# Of Sunflowers and Fibonacci

Christina Sng for Maths@Singapore

On days when I am fortunate enough to walk in nature, I often stop to admire the flora that grows in our region. That’s when I draw closer to see there is an astounding amount of math in flowers.

Research agrees, as indicated in recent crowdfunded studies by the Museum of Science and Industry in Manchester, U.K.

Of all flowers, mathematical biologists love sunflowers the most. They are beautiful and clearly demonstrate the hidden mathematical rule shaping the patterns of life: the Fibonacci sequence, a set in which each number is the sum of the previous two (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, …).

John Bohannon, in his article “Sunflowers show complex Fibonacci sequences”, states that the Fibonacci sequence is “found in everything from pineapples to pine cones. In this case, the telltale sign is the number of different seed spirals on the sunflower’s face. Count the clockwise and counterclockwise spirals that reach the outer edge, and you’ll usually find a pair of numbers from the sequence: 34 and 55, or 55 and 89, or—with very large sunflowers—89 and 144.”

The math is beautiful, but we still can’t explain how sunflower seed patterns arise. Plants don’t always show perfect Fibonacci numbers and data on real sunflower diversity is scarce.

So, the Museum of Science and Industry invited members of the public to grow their own sunflowers and submit photographs and counts of the spiral patterns for 4 years.

After they verified the counts from 657 flowers, they discovered that “nearly one in five of the flowers had either non-Fibonacci spiraling patterns or patterns more complicated than has ever been reported, including near-Fibonacci sequences and other mathematical patterns that compete and clash across the flower’s face.”

This is exciting news for everyone who loves math and flowers.

To read the article, visit https://www.science.org/content/article/sunflowers-show-complex-fibonacci-sequences

Thanks to Yair Mejía @20ymn17 for making this photo available freely on Unsplash