What do you see when you look around yourself in nature? While the answer can be many things, here we are talking math. Yes, nature, in its own way, represents mathematics, especially geometry.

One of the most repetitive elements in nature is geometrical shapes and patterns. If you look closely, everything in nature, from the gigantic mountains to the microscopic insects, is governed by some shape. The shapes and patterns are not necessarily defined; for example, there are round fruits like oranges and grapes, as well as undefined shaped microorganisms like amoebae. But more common than others, or rather the most common shape that is found ingrained in nature, is the hexagon.

A hexagon is a six-sided polygon. Also called the “6-gon,” it is a 2D shape with six edges, six vertices, and six angles. There are four main types of hexagons, namely regular, irregular, concave, and convex. Each internal angle of the shape is 120 degrees, and the total of all the internal angles of any regular hexagon is 720 degrees. Now that we know the geometrical facts about hexagons, let’s dive into why and in what ways nature adopts this shape.

Examples of Hexagons in nature

The hexagon is a common, naturally occurring shape that many believe to be sacred to nature. But keeping all beliefs aside, here are a few examples of hexagons that will truly make you question nature’s wonder.

1. Honeycomb

The most common and widely noticed natural hexagon is the beehive or honeycomb. It is so apparent that anyone not familiar with hexagons is also bound to notice the pattern in which bees create their homes. A beehive is simply a well-constructed cluster of numerous hexagons, and the way bees create it is nothing less than beautiful.

Scientists worldwide have spent ample time figuring out why bees use hexagons and not other shapes to construct the honeycomb. On discovering the answer, bees were reflected as natural architects. It is said that honeycombs are made in hexagons to effectively pack space with the least amount of material. Unlike other shapes like circles or squares, hexagons leave no empty space in between, allowing bees to have maximum cells in the smallest space.

1. Snow Flakes

As beautiful as they are, snowflakes are also naturally hexagonal in shape. These tiny droplets of water frozen in mid-air come in varied shapes and sizes, and one among them is the hexagonal snowflake. Snowflakes in the shape of hexagons are formed when two water molecules join together when water changes from a liquid state to a solid at low temperatures. The orientation of the water molecules is such that it can change with temperature, giving rise to cold white snowflakes.

1. Dragonfly

No, the shape of a dragonfly is not a hexagon, but its eyes are. The eye of a dragonfly is a collection of tiny lenses, and interestingly, each lens is in the shape of a hexagon. So what we see as a tiny insect with an even tinier eye packs more than 30,000 hexagonal lenses. This incredible number of lenses can fit inside the eyes of a dragonfly thanks to the effective packaging principle of the hexagonal shape.

Dragonflies also have far superior color discrimination abilities than human beings. They have a vision that scientists refer to as ultra-multicolor. Simply put, the compound eyes of dragonflies are divided into two regions⏤upper and lower. While the upper region detects prey against bright color backgrounds, the lower region has photoreceptors that cover a spectral range from UV to red.

1. Turtle Shell

The shells that protect tortoises from harm also exhibit the six-sided polygon design. Compared to the other three examples, this is a less popular example, but true. When turtles are looked at closely, one can observe that the entire shell is made from individual subunits and that its patterns resemble the shape of a hexagon. Turtle shells are formed in this shape because hexagons can effectively cover closed surfaces with minimal material waste.

1. Carbon

What might surprise many but not the chemistry students is⏤carbon atoms bond in a hexagonal shape. The six bonded carbon atoms in the benzene ring form a perfect hexagon with each angle measuring 120 degrees. About  12 percent of our body is made of carbon atoms like this. By having a series of carbon hexagon chains nicely packed together, the atomic structure of organic materials like human skin is formed. This is why the element is present throughout our body, called carbon-based life forms.

1. Cooled Lava

When cooled, lava erupting from volcanoes creates some surprising hexagonal shapes in nature. While some of those formations are perfect hexagons, others are irregularly hexagonal in design. When it starts cooling, the contraction of lava creates immense pressure, resulting in different physiographic formations. It is proved that the tension angle is equal to the internal angle of a hexagon⏤120°. That’s probably the reason behind rock formations like the Giant’s Causeway and the Devil’s Postpile in California.

The Giant’s Causeway is a tourist spot in Ireland that is said to have been formed due to the fractured horizontal contractions of solidified lava. The place is a pillar-like structure with columns made of rocks in the shape of almost perfect hexagons.

1. North Pole of Saturn

The discussion on natural hexagons cannot end with addressing the out-of-the-world example⏤Saturn’s the North Pole. The cloud surrounding or covering the north pole of Saturn is in the shape of a hexagon. There are various hypotheses about this natural hexagon, but its exact reasons are unknown. One fact that might blow your mind is that each side of the hexagon cloud is bigger than the Earth’s diameter.

The examples provided most prominently showcase how nature adopted geometrical shapes even before humans discovered them. And after observing and learning from nature for hundreds of years, humans also utilize the hexagon shape in their artificially created structures. A few examples of man-made hexagonal structures are footballs, nuts-bolts, pencils, cookies, etc.

Hexagonal structures are extremely useful in effectively managing a large number of materials in small spaces; thus, they remained through the past and will continue to live through the future. It also points out that math is present everywhere without noticing its application.

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