World Environment Day: From fractals to Fibonacci, 5 things to show that mathematics is an integral part of nature

1 plus 1 equals 2 – sounds like a simple calculation to humans but tricky to fish. And guess what? Fish also know how to do math! A new study at the University of Bonn in Germany revealed that fish species, including cichlids and stingrays, can perform basic additions and subtractions from the number 1, up to 5.

Surprising, however, this is not the first time that we discover how mother nature proves that mathematics exists everywhere and explains even the most complex phenomena that occur around us.

Today, advanced techniques like computer simulations and mathematical equations help us study the evolution of collective behavior and coordinated groups of animals. We hear about poetic comparisons, the application of science and technology, or art inspired by nature.

But there is so much more to mathematics that explains the hidden secrets of the environment we observe in our daily lives.

Nature is a powerful force. A force that amazes with its architecture, its beauty and its hidden charms. From the rotation of the Earth and the curvature of rivers to the recurring series of petals and even the spots on a leopard.

Stemming from human fascination, for years we have discovered mathematical expressions that help us learn more about our surroundings. The physical world can be viewed as a structural component with underlying fundamental laws of mathematics that provides the tool for precision and perception.

From terrestrial vegetation to the spiral of galaxies, mathematical models are used by theoretical biologists and mathematicians to study patterns.

On World Environment Day, let’s take a look at some interesting and unusual mathematical principles found in nature:


We watch the days turn into nights and witness the seasons come and go. Pi is used in many interpretations of these changes occurring on our planet, in our solar system and in the galaxies.

It appears in circles and spheres like raindrops, bubbles, pupils and dark circles.

Even where there is no circular connection, Pi is used in electromagnetic waves, the structure of DNA, and in calculating the wind of a river using a meander ratio.


The concentric circles and spirals we see in nature seem unpredictable, but most of them can be mapped to the Fibonacci sequence of the numerical model.

When we use Fibonacci’s golden ratio and apply it as a growth factor, we get a golden spiral. We can find examples of golden spirals in seashells, ocean waves, spider webs, ferns, buds, broccoli, sunflower seeds, and pine cones.


Whales, like humans, use a hierarchical communication structure. Whale songs contain repeating interval patterns that structurally resemble human rhymes.

There are mathematical procedures that can transform sound waveforms into wave patterns via software.

Mathematics is used to analyze the aqua sonic acoustics of a whale which is then used as raw data to be translated into pictorial forms to study these sounds.


What if a bird’s wings weren’t roughly the same size, would they be able to fly straight? Likewise, there are many symmetries that we see in nature. Bodies of animals, cutting fruit exactly through the center, rotating elements to obtain a circle or cutting planes to find radical symmetry.

In marine animals like jellyfish, we see symmetrically opposite sides with each side different from the adjacent side as in a rectangle.

Fractal symmetries are also present in intangibles like the wavelengths and frequency patterns of sound and light.


Beehive is the first that comes to mind, isn’t it? One cool thing about building bees in the hex is that hexes use the least amount of dividing wall, so it makes sense that bees prefer them because they require less beeswax.

It is an instinctive behavior. But there are many more elements than we can think of that are hexagonal in nature.

Volcanic eruptions leading to hexagonal formations, corals, snowflakes and crystals also inhibit this perfect form.

As Galileo once said, “the great book of nature is written in mathematics”. It hides mathematical proportions, patterns, patterns, and equations.

It’s really inspiring to unravel these hidden mysteries and a great opportunity for children to learn a little something every day!

– Article by Manan Khurma, Founder and President, Cuemath

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