Georges Louis Leclerc, Comte de Buffon, is best remembered as one of the founders of the science of natural history and the author of a massive 44 volume work on the subject. But the earlier in life, in his twenties, he had an interest in mathematics. In 1733 he set out to gain membership of the Royal Academy Of Sciences in Paris by proposing a solution to a fascinating mathematical problem.
Buffon began his paper with an exploration of a simple popular game by the name of franc-carreaux, where players would throw a coin on to the tiled floor, with wagers placed on whether the coin would touch one of the cracks between the tiles. He went on in the paper to deal with the more complex – and interesting – problem of what became known as Buffon’s Needle.
What is the probability of a needle thrown onto a floor made up of boards with cracks between them crossing one of the cracks? Well if the length of the needle is the same as the width of one of the boards, the answer is that the probability is 2/pi.
Actually Buffon missed an important wider observation that was staring him in the face and which was actually only proved 100 years later. But his finding is nevertheless fascinating, not least because – with a few matchsticks/needles, a piece of paper and a bit of patience – it can be used to obtain a reasonably accurate value for pi with no real calculation at all!
A fuller explanation can be found at http://ddxart.co.uk/pi-sticks/, after which you can always head over to https://ddxart.patternbyetsy.com/ and make the design your own.
For many years I found those curves that appeared on the old oscilloscopes a slippery thing. How were they ‘sine waves’ and what on earth did it mean when people said that two wave forms were ’90 degrees out of phase’.
It helped when it first dawned on me what simple concepts sines and cosines actually were. Bot still..’90 degrees out of phase’?
So I like this design for its liveliness, for the neatness of the concept embodied in the small icons and, not least, because when I look at it sets my mind at rest.
It’s not a stained glass window for a new church – though it could be. The principle is very simple and you can find the explainer here. In a nutshell, for any three points on a plane there is one, and only one, circle which touches those three points. The reaction to that statement is often one of incredulity – ‘Rubbish, give me that piece of paper and I’ll demonstrate how to draw more than one circle. Errr…’
But it’s a fact, one of those beautiful mathematical facts that reveal the sometimes simple building blocks underlying the universe. And just because it’s a fact, if we take any of the infinite number of triangles that can be drawn within a single circle and draw perpendicular lines through the middle of their sides, all those lines will meet at one point – the centre of the circle.
And if you are looking for a stained glass window, I happen know a wonderful stained glass artist, and I could have a word with her…
Serendipity is alive and well. Ordering two boxes of paper from a new supplier – or rather directly from the same supplier instead of via Amazon – I managed to confuse myself over the infinite varieties of Canson Infinity. Blinded by the 310 gsm weight, I ended up ordering the Aquarelle paper instead of my beloved Velin. Both are archival but I was horrified to see that the Aquarelle was more textured (and even more expensive). How would this paper cope with the clean lines that characterize the designs?
There seemed little point in trying to arrange replacement, with the cost of postage both ways, so I decided to sacrifice one of the boxes with a test print. The result was simply wonderful. The design lost none of the sharpness but viewed close up it seemed almost to float above the surface of the paper. We’ll see if there’s any reaction from buyers but my inclination is to stick with the Aquarelle.
It’s one of the many reminders that when you get into this game you start off thinking that it’s all about ideas and inspiration but you quickly learn that alongside those things you’re engaged in a manufacturing process, with all the pitfalls that that implies. Investing in a top line printer and keeping your software up to date is just the start of things, the other lessons usually come as the result of mistakes, and they can be painful. Crease a design by putting it down carelessly somewhere and that’s an expensive sheet and ink wasted. You spend time putting a design into a good-looking frame and then, on the way out of the house to an exhibition, the door swings to slightly, catching the corner of the frame. Your pride and joy now has either to be reframed or offered at a knock-down price. Worst of all is perspex. Many buyers don’t want glass, they prefer the safety of plastic but the damned stuff marks so easily. You can create scratches with even the wrong kind of soft cloth.
So after more than few disasters, you learn to take things slowly and carefully. Your babies are swathed in blankets before they are moved, and carried out to the car with all the attention and deliberation you would devote to moving a human newborn. Or maybe even more since, as every parent knows, human babies tend to recover from your mistakes. Framed pictures don’t.
Much cheered by a conversation with another member of the Malvern Arts and Crafts co-operative. A non-mathematician, she had been intrigued the Fibonacci Rectangles design and had gone off to find out more about the Fibonacci series. Now she finds herself seeing the sequence everywhere, especially in nature. She counts the petals of wildflowers (the numbers are usually Fibonacci numbers). Best of all, she recently restocked her fireplace with pine cones and was delighted to confirm for herself that the individual ‘petals’ fell into 8 spirals in one direction and 13 in the other. Chalk one up for ddx art, because at the heart of the whole idea is the conviction that making maths beautiful can open up new ways of looking at the world for people who’ve been sold the lie that they can’t ‘do’ maths.
Intriguing chat with a mum who brought her two sons with her when she wandered around our set-up in the exhibition room the Malvern Hills Gallery earlier in the year. One of her sons, who is apparently counted as very good at maths, walked round and shrugged. Disappointing, because most of the people who relate to the work are precisely people who like to think themselves as good at maths. But the really fascinating thing was the reaction of her other son, who ‘struggles’ with maths. Apparently he spent ages going round the display, reading the explanations and then staring at each design until he could see how it worked. For him at least, the designs did exactly what they’re supposed to do.
Someone should tell him that what he did was real mathematics – taking an idea and worrying it like a dog with a toy until it reveals its secrets – why it is as it is and why it must be that way.
This site is a work in progress – and I do mean work. Most of Sunday was spent rebuilding the catalogue page. It turned out that having a NextGen gallery for each design on the same page was waaaay too slow – it took a lifetime for the page to appear.
Instead I’ve built a little illustration for each design like the one below, with a larger thumbnail accompanied by some tiny representations of different colour variants. The page now loads quickly and, in any case, the catalogue is only meant to be a quick gateway to the fuller explanation pages.
New design over the weekend. For a long time I’ve been playing with the idea of a design to illustrate (a+b)(a+b), (a+b)(a-b) and (a-b)(a-b). I tried several variants but none of them really had the ‘aha!’ quality that I like to characterize every design. Then a few nights ago (it usually happens at night) when I was turning the idea over, the new version came into my head and I spent the whole of Saturday refining it in Illustrator. It’s not that it’s hugely different from previous versions, just that the negative quantities are properly incorporated into the shape and there’s a consistency of method between the three illustrations that somehow makes it easier to see what’s going on. As always, the explainer on ddxart.co.uk took almost as long to create as the design itself. So that was the weekend!
Finally got around to creating a shop. I could have gone for something nerdy on this site but experience suggests that unless you’re going to throw some decent money at the problem, it can be more trouble tha it’s worth.
So I decided to go, at least for the time being, with Etsy. Whether that’s a sensible choice, I suppose only time will tell. In any case it’s cheap and it’s not irrevocable.
Click here to visit >> d/dx art shop on Etsy
Comments from people not trying desperately to sell me things welcome. Sales even more welcome.