Bringing the beauty of mathematics into fashion design
Every year my neighbourhood group of the Australian Sewing Guild sets its members a challenge. In 2015 it was “I feel good in blue”, and therein lay my problem. Though I do make clothes in blue that was some time ago. More recently I have found more excitement in oranges and greens. So, I spent months wondering desultorily what blues I had in my fabric stash and could I get excited enough to make something with any of them.
Then came 9 August, 2015 and University open day. One of the students had made a hyperbolic scarf. There are many examples of making on this – see link I was fascinated by the idea of making something very mathematical. And I could hardly sleep the next few nights, while I kept wondering what I could make. Making a scarf would be easy, but evening wear was what I wished to create.
Let me explain what I mean.
Making a hyperbolic plane requires one to join many tiles, such as pentagonal tiles – almost like quilting. This means that there are many, many, many raw edges. Thus people usually make hyperbolic scarves out of polar fleece. This takes out the requirement of finishing these edges. However polar fleece is not what you would call fabric suitable for evening wear.
Then I hit on the idea – I would use some blue satin backed shantung that a friend had given me. She had given me about 2.5mtrs and I thought, “That should be enough.” Little did I know how much more I would need! I cut out some pentagons and realised that I needed much, much more fabric.
Then a friend reminded me that she had some navy jacquard fabric that I had given her some years ago, and that since she had not found a use for it, she was returning it to me. And that fabric seemed to be the very thing – it lifted the skirt from being just blue to extraordinary!
There is some history behind this navy jacquard fabric. It was given to me by a B&B owner in Ireland in 2009, when she found out that I was interested in fabric and sewing. I then gave this to the friend as she was more into blues than I was. And here it was, come full circle, just when I needed it.
Once I had made the skirt (and the slip, and a cross-over top), I decided I needed a jacket to finish the outfit, and I wanted a jacket that was more fitting – I felt that a bolero jacket would really set off the outfit. And in keeping with the mathematical theme, I decided that a Penrose-tiled Jacket would be just the thing.
The hyperbolic Skirt with the cross-over Top, and slip showing.
Here is a closeup of the skirt showing the pentagons at the waist.
Read on for the details of the constructions – I will start with the skirt first.
Constructing the Hyperbolic Plane skirt
Tiling the plane
You may have noticed that a plane, that is, a flat surface, for example the floor, is usually tiled with square or rectangular tiles – four sided figures. It is also possible to tile a plane with hexagons (6-sided) or octagons (8-sided). In fact a plane can be tiled with any even-sided figure. This may bring to mind rolling plains, but that is a different matter.
Here is a picture of rectangular tiling:
So, what happens if one tries to tile a plain with odd sided figures, say as a triangle or a pentagon? Well, it is not possible. When we start tiling with an odd sided figure, we get a hyperbolic plane. The tiling requires only that four of these odd-sided figures meet at each corner.
Here’s how pentagonal tiles would need to fit together.
As you can see there is not enough space for the fourth tile to go in – hence the resultant unevenness of the surface created, unlike the surface created using rectangles. You can read more about hyperbolic planes here (link) and about hyperbolic tiling here (link).
This skirt is constructed using a regular pentagon – a five-sided figure that has equal sides. There are plenty of pentagon templates available online – I enlarged one on the photocopier to the size I needed.
I started with the first row made up of 5 pentagons. Each pentagon had a side equal to 1/5 of my waist measurement plus seam allowances. A zip was centred on one of the pentagons. This row of pentagons was made from satin-backed shantung.
The next row of pentagons was made of the navy jacquard fabric. This row needed 21 pentagons.
The
hyperbolic plane tends to grow very fast and the third row has over 49
pentagons – over 49 because I lost count! This is when I realised I needed much more of the blue satin-backed shantung fabric. Luckily my friend still had the rest of the roll, which she very generously gave to me.
As you can see the skirt is very full. The hem of the skirt is very uneven.
1 cm width seams were used with overlocking/zigzag done on many of the seams to prevent fraying.
A rolled hem was used, and took a total of 4 hours – 2 hours to roll each piece of the hem, and then another couple of hours to tuck in the ends (tails) of the rolled hem.
Here are some pictures showing the fullness of the skirt.
The Penrose tiled bolero jacket
In keeping with the mathematical theme of the ensemble, I constructed a Penrose tiled bolero.
Penrose tiling is an example of non-periodic tiling (link) – simply put this means that the pattern is never repeated.
The jacket uses two tiles – a kite and a dart (link) to tile the plane, in this case, the material that would be sewn into the jacket.
The non-periodic tiling means it was very hard to get a square piece of material requiring much ingenuity to create enough fabric to cut the pieces of the jacket. Hence the sleeves were made from plain fabric.
The jacket is lined with the satin side of the satin-backed shantung.
