Stones along the beach in Charles Daley Park are always interesting and intriguing. It got me thinking about how we used to collect beach glas. There isn't nearly as much as there used to be, and I presume that has to do with pollution prevention and waste recycling. I found a fascinating article explaining this HERE. Below are two excerpts:
"The reasons so much glass has got into large bodies of water vary. For millennia, glass entered the water from shipwrecks whose cargo spilled across the ocean floor. Until the London Convention on the Prevention of Marine Pollution was implemented between 1972 and 1975, ocean dumping of municipal waste was essentially unregulated. Until well into the 20th century, many towns and cities maintained municipal dump sites on or near lakes or oceans: the famous Glass Beach near Fort Bragg, California, a favourite tourist destination for coastal visitors, received tons of glass from local landfills operating between 1906 and 1967."
"Toronto might seem an unlikely place to find beach glass. But much of the city’s contemporary shoreline consists of land filled in with construction rubble and waste; in addition, some 141 former dump sites dot the city, many along now-filled-in ravines. In the decades before public recycling programs began, glass was a significant component of the waste stream, and over the course of a century, quite a lot of it washed into Lake Ontario. Conditions in Lake Ontario near Toronto — including good “fetch” (wide stretches of open water sufficient for significant wind-generated waves) and strong longshore drift currents — are also conducive to producing good beach glass."
It is still possible to find beach glass, but not in the quantities of the past. If we head over to eBay, one can buy lots beach glass in single or mixed colours, just like you combed the beach yourself.
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.
I spotted these glass balls at the Royal Botanical Gardens. They are large gazing balls for the garden. They bring to mind pictures of galaxies of the universe.
They have beautiful, brilliant clear colours and colour combinations, along with curved, natural shapes inside - things to make us stop to ponder and consider the mysteries around us.
These water reflections were taken a few years go at the Missouri Botanical Garden. This is a vast botanical garden and research centre with many interesting gardens. This centre court water garden had Chihuly glass balls amongst the lily pads.
We were in Kingston Ontario this week and visited a glass gallery. The frosted glass was perfect for photography - no reflections to deal with and the colours and shapes of the glass were wonderful.