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

1 plus 1 equal 2 — sounds like a simple calculation for humans but a tricky one for fish. And guess what? Fish can do math too! A new study at the University of Bonn in Germany revealed that fish species including cichlids and stingrays can perform basic addition and subtraction of the number 1, ranging up to 5.

Surprisingly, yet this is not the first time we discover how mother nature proves that mathematics exists everywhere and explains even the most complex phenomenon happening around us.

Today, advanced techniques like computer simulations and maths equations help us study the evolution of collective behavior and coordinated animal groups. We hear about poetic comparisons, the application of science and technology, or art that is 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 astonishes with its architecture, beauty, and concealed charms. From how the Earth rotates and how rivers bend to recurring series of petals and even the spots on a leopard.

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

From vegetation on land to the spiraling of galaxies, mathematical models are used by theoretical biologists and mathematicians to study patterns.

On World Environment Day, let us look at some interestingly unusual fundaments of mathematics found in nature:


We watch days turn to nights and witness seasons as they come and go. Pi is used in many interpretations of these changes that happen on our planet, in our solar system, and in galaxies.

It appears in circles and spheres like raindrops, bubbles, pupils of eyes, and tree rings.

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


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

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 pinecones.


Whales, like humans, use a hierarchical structure of communication. Whale songs contain repeating interval patterns which structurally resemble human rhyming.

There are mathematical procedures that can turn sound waveforms to wave patterns through software.

Maths is used to analyze a whale’s aqua sonic acoustics which is then used as raw data to translate into pictorial forms to study these sounds.


What if the wings of a bird were not approximately equal in size, would they be able to fly straight? Similarly, there are many symmetries we see in nature. Bodies of animals, cutting fruits through exactly the centre, rotating elements to get a circle or cutting planes to find radical symmetricity.

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

Fractal symmetries are also present in intangible elements like wavelengths and frequency patterns of sound and light.


Beehive is the first one that comes to mind, right? An interesting thing about bees building in hexagon is that hexagons use the least amount of separating wall, so it makes sense that bees would prefer them, because it needs less beeswax.

This is instinct behaviour. But there are many more elements than we can think of that are shaped hexagonally in nature.

Volcanic eruptions leading to hexagon formations, corals, snowflakes, and crystals also inhibit this perfect shape.

As Galileo once said, “Nature’s great book is written in mathematics.” It hides mathematical proportions, models, patterns, and equations.

It is truly 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 Chairman, Cuemath


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