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Math in Nature

Discovering math patterns in the natural world

There is beauty in mathematics, and nowhere is this more evident than in the patterns of nature we see all around us. Nature is a harmony of math, as demonstrated in acorns, honeycombs, starfish, spirals in seashells, the arcs of ocean waves, and the patterns of our Milky Way Galaxy. Snowflakes each have a uniquely beautiful crystalline structure and no two are ever alike. But what all snowflakes do have in common is that everyone is a six-pointed hexagon.

As summer adventures continue to unfold, students may find opportunities to discover math patterns in nature on woodland hikes, in community gardens, or even in their own backyards.

For example, look at the seeds of a sunflower. They form beautiful and complex spiral patterns. Math biologists love studying sunflowers because they follow a precision formula called the Fibonacci math sequence. In fact, this same mathematical pattern is observed in pineapples, pinecones, and even broccoli. Researchers have called the Fibonacci sequence “nature’s secret code.”

The National Museum of Mathematics can tell you how to count sunflower spirals!

Spider webs are another familiar phenomenon. But did you know that an estimated 5,000 types of “orb-web spiders” spin circular webs with a “radial symmetry” that is almost geometrically perfect? The spider extends lines of thread out from a circle at the center of her web. The angles of those threads create perfect triangles. She then weaves more threads in parallel lines down each triangle. The result is a strong web that evenly distributes force and doesn’t break easily. It is a natural feat of spectacular engineering that mathematicians marvel at.

Here’s an article with a more detailed look at some examples of math in nature, from land to shoreline and out into the galaxy. And though we’re a long way from winter, here are more cool math facts about snowflakes!