Are there squares in nature? Not very many. Salt crystals would be the recognizable with the human eye. Pyrite has amazing cubic crystal shapes that are very visible. It is an abundant crystal and was produced in Italy in Elba. The Greek called it "fire" or pry. Was it inspirational?
The Egyptians calculated square roots using an inverse proportion method as far back as 1650BC. Chinese mathematical writings from around 200BC show that square roots were being approximated using an excess and deficiency method. I assume they were figuring out the volume of a pyramid. They used a lot of mathematics for calculating distance as well, also for taxes and wages, things often paid in volumes of beer and wheat..
What was the interest in developing squares and square roots? It is thought that the knowledge of square roots originally came from dividing areas of land into equal parts so that the length of the side of a square became the square root of its area.
The Babylonians and Greeks have been credited with the discovery of Heron’s method, the precursor of Newton’s iterative method, although Indian mathematicians are thought to have used a similar system around 800BC.
In relation to nature, I wondered what the most common shape might be. The Hexagon! A hexagon is the shape that best fills a plane with equal size units and leaves no wasted space. Hexagonal packing also minimizes the perimeter for a given area because of its 120-degree angles. With this structure, the pull of surface tension in each direction is most mechanically stable, which is why even though bees make their honey combs with circular units, the end result when the wax hardens into place is hexagonal.
So it isn't that far off from a square. Can you imagine our neighbourhoods where we have hexagonal properties forming a community shaped in a hexagon? I found lots on google.
Here's a wonderful joke to conclude:
The guru was happily teaching math to the students at his home. He said "5 sides --> pentagon" "6 sides -->hexagon" "8 sides -->octagon"
...then suddenly, the guru got a sudden heart attack, he fell onto the ground making a loud "thud" sound and died on the spot. Hearing the sound, his wife came running from the other room and asked "what happened ?" and the students replied: "--> gurugon"
Today's image is a little fun with Flexifly, the Flaming Pear software that returns square things into naturally shaped things. The original image was a windshield that was smashed. If this was an object of nature, I wonder what it might be.
Simple shapes - square, circle, triangle - are with us everywhere. These are the most basic shapes on Earth.
The notable books that explored this were Italian artist Bruno Munari's series which started with The Discovery of the Circle. He writes: “The first thing a child draws looks like a circle. People spontaneously arrange themselves in a circle when they need to observe something close up, and this led to the origin of the arena, the circus, and the stock exchange trading posts.”
Munari wrote over 60 books and covered the each basic shape in its own book. For example in Square, he writes: "As tall and as broad as a man with his arms outstretched, the square has always been used, from the oldest writings and rock engravings made by early man, to signify the idea of an enclosure, a house, a village. Enigmatic in its simplicity, in the monotonous repetition of its four sides, its four identical corners, it can generate a whole series of interesting figures".
Kurt Vonnegut's rejected master's thesis was a visual presentation titled "The Shapes of Stories". The article is HERE. Below is Maya Eilam's version of his thesis:
