It’s a well established truth that math is all around us. It informs how we live our daily lives and can be found in practically everything we interact with, from video games and music, to nature and food. One such element of math that can be found in almost every aspect of our world, is geometry.

Whether it’s a man made construction or an organic lifeform, geometric shapes, symmetry, and the golden rectangle have helped to shape the world around us. With that in mind, let’s take a brief look at how geometry has impacted the world we live in.

Geometry in Nature

Within nature, symmetrical geometry can be found among many things. From the six fold symmetry of snowflakes and the splash of raindrops that cause radial symmetry, to the bilateral symmetry on the faces of tigers or the wings of a butterfly.

Above, you’ll see a beautifully crafted symmetrical shape, which has been lovingly created by a puffer fish. The reason for this is simple, it’s part of his courtship ritual. Much like many other courtships in the wild, symmetry plays a big part. Its aesthetically pleasing to look at and catches the eye of a potential partner (think of the flamboyant feathers of a peacock).

Beyond the wildlife themselves, you can see geometry in the construction of their habitats. For example, the honeycomb structures within the nests of honey bees are made up of visually stunning hexagonal prismatic wax cells.

In the above image, we can see the floral symmetry that exists within nature. The flower to the left is a streptocarpus flower, which has mirror symmetry (much like a human’s face). The flower to the right has radial symmetry, which means the symmetry is present around the central axis (much like a starfish).

Geometry in Sport

There are many sports that utilize geometric shapes to help mark out the specific areas of play. Take a look at the soccer pitch below, the field of play is made up of quadrilaterals, rectangles, 90 degree angles, and circles.

Furthermore, these soccer pitches, tennis courts, and basketball courts have mirror symmetry. Again, look at the soccer pitch, you’ll notice that one half of the playing area (home) is identical to the other side (away).

Beyond the examples of geometric shapes and symmetry within the playing fields, geometry is also used by the athletes themselves. The relative position of figures is a key part of geometry, and an understanding of position and spatial awareness within a competitive sport is integral to success. To know where you teammates are in relation to you and your opponent is to know geometry. It allows you to calculate the space available to you and make more informed decisions in the moment.

Geometry in Design

Geometry has influenced how civilizations have constructed buildings and stadiums. In Ancient Greece, the “golden rectangle” was used to build aesthetically pleasing buildings that look to be in perfect proportion.

The rectangles shown in the image above, all have exactly the same proportions. This is because the golden rectangle can mathematical replicate itself indefinitely. These golden proportions were not only used in their architecture, but also in their sculptures too.

It’s a design philosophy that would shape the world for centuries to follow.  Most notably, the Cathedral of Notre Dame (completed in 1345), is a tremendous example of French gothic architecture and draws inspiration from the ancient Greeks and their use of the golden rectangle. Renaissance painters across Europe were also fond of using the golden proportions in their work. A good example of this can be found in the famous painting “Mona Lisa” (1503) by Leonardo Da Vinci.

These are just a few examples of geometry in the world around us. If you look at things with a keen eye, you’ll find examples of geometry in almost everything you see. Studying geometry makes us more aware of the world around us, we learn how and why things are constructed, and that in turn, influences are own creations.

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