Math of Sunflowers
Sunflowers are beautiful, and iconic for the way their giant yellow heads stand off against a bold blue sky. And of course most of us love to munch on the seeds they produce. However, have you ever stopped to look at the pattern of seeds held within the center of these special flowers? Sunflowers are more than just beautiful food -- they're also a mathematical marvel.
The pattern of seeds within a sunflower follows the Fibonacci sequence, or 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144... If you remember back to math class, each number in the sequence is the sum of the previous two numbers. In sunflowers, the spirals you see in the center are generated from this sequence -- there are two series of curves winding in opposite directions, starting at the center and stretching out to the petals, with each seed sitting at a certain angle from the neighboring seeds to create the spiral.
According to PopMath: In order to optimize the filling [of the seeds in the flower's center], it is necessary to choose the most irrational number there is, that is to say, the one the least well approximated by a fraction. This number is exactly the golden mean. The corresponding angle, the golden angle, is 137.5 degrees...This angle has to be chosen very precisely: variations of 1/10 of a degree destroy completely the optimization. When the angle is exactly the golden mean, and only this one, two families of spirals (one in each direction) are then visible: their numbers correspond to the numerator and denominator of one of the fractions which approximates the golden mean : 2/3, 3/5, 5/8, 8/13, 13/21, etc."
Here is a little more about sunflowers, the Fibonacci sequence and the Golden Ratio that you can review with kids from Math Is Fun.
Sunflower seeds and amazing math. When you stop to think about this, it reminds you that nature is truly mind-blowing!
Do you have any photos of the patterns found in sunflower centers? Or what about patterns found in other flower petals, pinecones or branching plants? Add your images to our TreeHugger Flickr group or post to Instagram and tag us. We're @TreeHuggerDotCom on Instagram.
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