‘Quick, Alan. We’ve got to go NOW or we’ll lose them. They’re only a tenner each.’
I didn’t question Sheila further. We jumped into the car and sped off in the direction of our local second-hand furniture shop. What she had spotted was a collection of ammunition boxes – leftovers from World War II that probably originated from the US army. But of course, what Sheila was after was wooden boards for her paintings.
Normally Sheila paints on commercial canvases. She was delighted to have the opportunity to paint on wood but also to be free to make this wooden ‘canvas’ to any size and shape she fancied. Now, as I am a big fan of a particular rectangular shape – the so-called ‘golden’ rectangle’ – and also because, I was the one wielding the saw, I suggested that we should cut up the box lid to create a board of this ‘golden’ shape.
A week later, this little ‘Apple Blossom’ beauty was hanging on our kitchen wall.
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| Apple Blossom |
This isn’t the only art object that Sheila has produced that was inspired by this particular 'golden' proportion. Here is her Golden Window, painted from a wrought-iron window frame in a crumbling fromagerie in Normandy.
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| Golden Window |
So what exactly is a golden rectangle and why is it considered to be special? Have a look at this 3-minute video to get a quick overview.
Golden Rectangle
Maori drawings
A few years ago, we spent a wonderful two months travelling around New Zealand. I had arranged a deal with a number of NZ mathematics advisors that I would provide a series of ‘inspiring’ talks/workshops in return for a night’s board and lodging in each location. That way we had a great time meeting and chatting to many teachers and their families in their own homes. But there was also plenty of time for sight-seeing. We particularly enjoyed having the opportunity to explore Maori culture and art.
On our return to England, we decided to mark the trip by commissioning, from my friend Roger the glass artist, a pair of small stained glass windows that celebrated the fusion of mathematics (upper) and Maori art (lower).
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| The Golden Spiral |
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| A Symbol from Maori Art |
The mathematical one shows a logarithmic spiral (sometimes referred to as the ‘golden’ spiral) inscribed inside a golden rectangle. Here's a detail to clarify the mathematical part of the picture.
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| A Detail of the Golden Spiral |
Starting out from the bottom left corner, the spiral takes a path between opposite corners of each square in turn. In order to construct it, Roger used compasses to form an arc inside each square which he drew as a quarter circle, centred at one of the other corners of its square.
Golden rectangles have been known about and celebrated since the time of Euclid. He didn't use the term 'golden' but referred to this special ratio as the "extreme and mean ratio". It's sometimes said that shapes formed from 'golden' proportions have a particular aesthetic appeal. I'm not totally convinced by this claim but it would be lovely if it were true!.
Anyway, this 'special' ratio is all very well, but it's not getting these lightbulbs sorted out ... .
Postscript
This post looked at the idea of a golden rectangle, which has proportions of approximately 1.618 to 1. The number, 1.618… is often referred to with the Greek letter Φ (phi). If you're interested in finding out where this number comes from and indeed other matters 'golden', have a look in my website, MathinPictures.co.uk
