The beauty of Hexagons
Accessible for all HS grades
Based on CGP Grey— https://www.cgpgrey.com/
Hexagons are essentially the best polygon. Why? Efficiency.
To prove this, look no further than the fabled honeybees. Honeybees store their honey in honeycombs made of wax. Honeybee wax is made from their own honey and it is costly to form. This raises an issue, in what shape should the honeycombs be made in order to ensure the maximum of honey able to be stored per unit of wax? Lucky for us, millions of years of evolution gave us the answer: Hexagons.
Tiling is a way of arranging identical plane shapes so that they completely cover an area without overlapping. You theoretically tile with any shape however that does not mean that they are all of the same efficiency. Complicated tiling like below is extremely inefficient.
The ideal tiling would be wherein the all shapes are uniform and no gaps are made between them. This rule would make Polygons, Heptagons, Octagons, and everything after to be unfit. This leaves us with just 3 options: Squares, Triangles, and Hexagons.
Now, another question is raised, what makes the Hexagon better than the square and triangle? Well, although Hexagons don’t lose or win in efficiency with squares, they are more geometrically interesting as they don’t form an infinite series of parallel lines. Although the same could be argued for triangles, there is another reason why Hexagons are superior to triangles. Triangles tile in 6s in which they actually form a hexagon thus just causing an inefficiency due to their interior vertices as shown below:
Additionally, what about irregular shapes that you may have never thought of such as rhombuses, triakis, kisrombilles, and etc. Proving the geometric beauty of a hexagon, all these irregular shapes form a Hexagon with the same inefficient internal vertices as shown below:
In conclusion, hexagons are the most geometrically beautiful shape. Evident as almost every other shape tries to imitate the Hexagon due how naturally efficient it is. So much so that it appears in nature, not only in bee honeycombs but even our eyes’ light receptors are hexagons. You could even say that you can only admire the beauty of our world with the hexagon.
