Nienhuis USA_Summer2022

Fibonacci Sunflowers are beautiful and iconic. From the way their giant yellow heads brilliantly stand out against a bold blue sky; to the tasty seeds we love to munch on, the Sunflower, is exceptional! Have you ever peeked inside one of these marvels of nature… observed the magnificent pattern of seeds held within its center…? No? Then let’s discover together! Sunflowers are much more than just pleasing to look at and a beautiful food -- they are a mathematical wonder! The pattern of seeds within a sunflower follows the Fibonacci sequence, or 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. 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 its neighboring seed to create the spiral. According to Pop Math: “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... With this angle, one obtains the optimal filling, that is, the same space between all the seeds.” This angle has to be chosen very precisely: variations of 1/10th of a degree destroys 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.” “The scientific laboratory, the field of Nature where the teacher will be initiated into ‘the observation of the phenomena of the inner life,’ should be the school in which free children develop with the help of material designed to bring about development. ...she feels herself aflame with interest, ‘seeing’ the spiritual phenomena of the child, and experiences a serene joy and an insatiable eagerness in observing them...” Maria Montessori - The Advanced Montessori Method Volume I, p. 107

2