One of the things that I really enjoy about nature is that it produces proofs that it obeys natural laws in the most unusual — and beautiful — ways. This spring and early summer I ran across three examples of math in plants.

Scorpianweed, like most plants in the hydrophyllaceae family, has a flower stalk that is tightly coiled. It reminds me of the shell of a nautilus seashell that gets bigger as the animal grows. The coil of each grows according the Fibonacci sequence: 1+1=2; 1+2=3; 2+3=5; 3+5=8.

Coiled scorpionweed flowers follow the Fibonacci sequence.

For scorpionweed, though, at the top of the curl is an open flower. As the flower fades, the stem uncurls to allow another flower to come to the top and open.

When you look at the face of a sunflower, you are really looking at many many flowers that grow on a central disk. These flowers follow the Fibonacci sequence as well, but here it shows up as ever expanding spirals on the disk face.

Disk of the sunflower is made up of spirals of flowers that follow the Fibonacci sequence.

Finally, I was astounded by this picture.

The flowers of miner’s candle march up the stalk in spirals.

What I thought I was taking a picture of was the really cool butterfly on the miner’s candle, in the borage family. It was only when I was sprucing the picture up that I realized that the white flowers were arranged in several spirals, or helixes. The geometry here is a bit more complicated, but the flowers do indeed appear on the stalk with mathematical precision.

There is order in the universe, and you can see it in the math of plants.

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Very Cool!

This is awesome Amy! I’m going to share with my daughter that loves math and the outdoors. She’ll love to see how her favorite things go together. Thank you!