Have you ever stopped to look around and notice all the amazing shapes and patterns we see in the world around us? Mathematics forms the building blocks of the natural world and can be seen in stunning ways. Here are a few of **my favorite examples of math in nature**, but there are many other examples as well.

**The Fibonacci Sequence:**

Named for the famous mathematician, Leonardo Fibonacci, this number sequence is a simple, yet profound pattern.

Based on Fibonacci’s ‘rabbit problem,’ this sequence begins with the numbers 1 and 1, and then each subsequent number is found by adding the two previous numbers. Therefore, after 1 and 1, the next number is 2 (1+1). The next number is 3 (1+2) and then 5 (2+3) and so on.

What’s remarkable is that **the numbers in the sequence are often seen in nature**.

A few examples include the number of spirals in a pine cone, pineapple or seeds in a sunflower, or the number of petals on a flower.

The numbers in this sequence also form a a unique shape known as a Fibonacci spiral, which again, we see in nature in the form of shells and the shape of hurricanes.

**Fractals in Nature:**

Fractals are another intriguing mathematical shape that we seen in nature. A fractal is a self-similar, repeating shape, meaning the same basic shape is seen again and again in the shape itself.

In other words, if you were to zoom way in or zoom way out, the same shape is seen throughout.

Fractals make up many aspects of our world, included the leaves of ferns, tree branches, the branching of neurons in our brain, and coastlines.

Learn more about fractals and how we see and apply them in our world today at the Fractal Foundation.

**Hexagons in Nature:**

Another of nature’s geometric wonders is the hexagon. A regular hexagon has 6 sides of equal length, and this shape is seen again and again in the world around us.

The most common example of nature using hexagons is in a bee hive.

Bees build their hive using a tessellation of hexagons. But did you know that every snowflake is also in the shape of a hexagon?

We also see hexagons in the bubbles that make up a raft bubble. Although we usually think of bubbles as round, when many bubbles get pushed together on the surface of water, they take the shape of hexagons.

**Concentric Circles in Nature:**

Another common shape in nature is a set of concentric circles. Concentric means the circles all share the same center, but have different radii. This means the circles are all different sizes, one inside the other.

A common example is in the ripples of a pond when something hits the surface of the water. But we also see concentric circles in the layers of an onion and the rings of trees that form as it grows and ages.

If you live near woods, you might go looking for a fallen tree to count the rings, or look for an orb spider web, which is built with nearly perfect concentric circles.

**Math in Outer Space:**

Moving away from planet earth, we can also see many of these same mathematical features in outer space.

For instance, the shape of our galaxy is a Fibonacci spiral. The planets orbit the sun on paths that are concentric. We also see concentric circles in the rings of Saturn.

But we also see a unique symmetry in outer space that is unique (as far as scientists can tell) and that is the symmetry between the earth, moon and sun that makes a solar eclipse possible.

Every two years, the moon passes between the sun and the earth in such a way that it appears to completely cover the sun. But how is this possible when the moon is so much smaller than the sun?

*Because of math. *

You see, the moon is approximately 400 times smaller than the sun, but it is also approximately 400 times further away.

This symmetry allows for a total solar eclipse that doesn’t seem to happen on any other planet.

*Isn’t nature amazing??*

**Want to know even more about these topics and explore them more deeply with your kids?** Try my math enrichment curriculum: Math in Nature.

See what your kids will explore in this short video:

This curriculum, designed for **grades 3-6**, provides hands on lessons to look at math in the real world and also practice important math skills.

It includes **picture book lists** for each topic, a detailed **teacher manual**, **student handouts** for the lessons, **‘fun fact’ summary pages** and a list of **math art projects** to go along with each theme.

I also encourage you to grab the **FREE set of math in nature posters** to show your kids math in the real world. Use these to decorate your math space and invite discussions and excitement about the beauty of math.

Simply **enter your email below** to receive these posters. You will also receive ** a special offer for my Math in Nature curriculum**, as well as math teaching tips and other freebies and offers.

I hope this gives you some fun new math ideas to learn and explore along with your kids!

[…] Celebrating Earth Day on April 22 always provides teachers with a chance to incorporate fun environmental lessons into their curriculum. But the fun isn’t reserved for science teachers alone. In fact, it is possible to incorporate Earth Day lessons in any classroom. For example, history teachers can teach about Earth’s 4.5 billion year history or the history of Earth Day itself. Math teachers can show students all the ways math appears in nature. […]