Théodore Olivier’s string models of descriptive geometry – DIY version

This past summer, I visited the Musée des Arts et Métiers in Paris for the first (but oh my god not the last) time. It was incredible from top to bottom, I spent hours there and could have easily spent many more, and I can’t wait to go back.

The collection is a repository of industrial inventions and scientific instruments. Lavoisier’s actual lab equipment, Pascal’s actual calculators, and Foucault’s actual pendulum are just right there hanging out. How have I not heard of this place until now?!

The top floor is a collection of antique scientific instruments – completely breathtaking and worth the price of admission all by itself. One of the exhibits that particularly captivated me was a collection of models made by Théodore Olivier. In the mid-1800’s he made a series of models using string to illustrate various geometric concepts in 3D. There are a bunch of them and they are gorgeous:



I was so inspired by them – I was dying to get behind the glass and turn the knobs and play with them. And open that wooden box and see what’s inside! I knew intellectually that each of those red strings was a perfectly straight line running from the upper circle to the lower one, but seeing the beautiful curves that they made in aggregate made me want to make a model myself so I could really really believe it.  I didn’t have the time, tools, or skills to duplicate this with the brass fittings, but the dovetail construction on the box gave me an idea for cutting out something similar with a laser cutter and make my own mini-version.

Step one, design the parts and cut them out with with the laser (at TechShop – one of the best places in the city – go check it out!).


Having very little box-making experience, my first attempt was diagonally challenged:


But after two more tries, I came up with a simple design that would support itself at right angles:



The shape was solid, but the burnt edges from the laser were distracting. So I spray painted the whole thing. Gold, because I had some.

Finally time for some string! Now I could really see each string going in as a perfectly straight line. It was great to see the curves forming as I made my way around the circle.


Once I had gone all the way around, I had a passable version of Olivier’s model:


There were 24 holes around the circle. I’m not sure why I picked 24 except that I had a vague notion that the 12 hours on a clock face wouldn’t be enough to really describe the shape, and 30 was too many for the small-scale model I was building.

I played a bit with the number of holes to offset the string as I went from top to bottom. If I had run the string vertically, I would have ended up with a simple cylinder (see Olivier’s original model above) and going directly across (12 steps) from the originating hole would cross directly over the center of the model and would have given the silhouette more of an “X” shape than the cool curved “waist” I was after. I ended up offsetting each string 9 holes from top to bottom.

Seen from the top, there’s a perfect circle in the middle:


I was really happy with the result and it made me want to make more of them. Olivier made tons and they are so beautiful – check out some images here. I’d like to try some more at a larger scale and maybe even add some moving parts so you can change some of the parameters of the shapes as you’re looking at it.

Okay everyone – go make something!




For I have seen the shadow of the earth upon the moon


“Evidence” was inspired by a quote from the explorer Ferdinand Magellan. About to set sail around the world at a time when the medieval Christian church officially believed that the earth was flat, he knew that he was in no danger of sailing off the edge. He had the empirical evidence of his own eyes – he had seen the actual shadow of the actual earth upon the moon, and the shadow was round, and so therefore the earth must also be round. And off he went, and of course he was right.

I loved this from the moment I heard it, and had it filed away somewhere in my inspirational quotes file, and I thought it would make a nice painting,

The trouble is, he never said that. Magellan was born in 1480, and there’s no mention of any such quote in any record of his voyages until the 1800s when someone made it up and attributed it to Magellan. A lot of people must have loved it as much as I did, because they kept repeating it, and then we invented the internet, and now it’s pretty much an Internet True Fact. Except it isn’t true. Dammit.

Also, it turns out that the medieval Christian church, while it was definitely AWFUL, did not believe that the earth was flat. The ancient Greeks figured out that the earth was round in Hellenistic times, and we’ve all pretty much known that since then. Dammit again.

After discovering all of that, I painted it anyway, because I love what the quote represented to me originally and now it also serves as a kind of meta-reminder to make sure you have evidence before you go believing what you hear just because you want it to be true.

Hyperbolic Crochet – Mini Coral Reef Installation

This project hit a lot of my happy points: fiber arts, math geekery, and nature worship.

So there’s a branch of mathematics called hyperbolic geometry.

I’m no mathematician, but I’ll try to summarize: if you took “regular” geometry in school, it was probably Euclidian geometry. For a long time, no one called it that because it was the only geometry, so it was just “geometry.”  Anything that happens on a plane in Euclidian geometry is assumed to happen on a flat 2 dimensional plane, like a piece of paper.

And you might remember one of the fundamental axioms of geometry, that if you have a straight line A and a point B that is not on that line:A line and a single point not on that line

then there is only one possible line that is both parallel to line A and runs through point B:
parallel lines

That’s pretty easy to understand when you hear it, because you can see it and touch it and draw it yourself.

So then back to hyperbolic (NON-Euclidian) geometry. It turns out that if your plane is NOT 2-D like a piece of paper, but curved in a way that makes the plane expand or contract as you go backward and forward (Huh? I know, stick with me…), then you *can* have two lines that cross each other at point B, but neither one will ever cross line A:

parallel lines on a hyperbolic plane

No way, right? It makes no sense, because I’m trying to show it on a 2D plane. For a long time, even super-brainy math majors were forced to just sort of bend the paper and “try and imagine it,” and wrap their brains around it the best they could. sometimes people tried to make models of it with paper in 3D, but it didn’t work very well.

Until one day a math professor, Daina Taimina, thought up the idea of building a model of a hyperbolic plane in crochet. It looked something like this:

crocheted hyperbolic plane

You start out with a simple straight line of say 20 crochet stitches, and then you add some stitches to the next row, and then add more stitches to each row until there are so many stitches in each row that it can’t lie flat and starts to fold over on itself. Voila! A touchable, foldable, hyperbolic plane.

And when you temporarily flatten out the plane to show where a “straight” line would go on this plane, and then “draw” a straight line on the plane using a string:





And then repeat the process with two more lines that cross each other:





You can now clearly see that on a hyperbolic plane the two crossing lines will never touch the third line even though all of them are straight lines!

Hyperbolic geometry is all wrapped up in a lot of complicated ideas like Einstein’s general theory of relativity and other things that are officially way over my head – but as usual, the internet will tell you all about it if you’re curious.

Nature is the best designer. It’s usually really hard for humans to make things that are anywhere near as beautiful as the flowing, irregular, organic shapes found in nature.

Well, it turns out that nature uses hyperbolic geometry to make a lot beautiful things:

Butter lettuce
Flickr image: Dwight Sipler
Flickr image: Liz West
Flickr image: Liz West
Lettuce slug
Flickr image: Laslo Ilyes – This one is an animal, not a plant – crazy!

Suddenly, thanks to Daina Taimina, people realized they could easily emulate the amazing forms found in shells and coral and seaweed in crochet. And crochet is easy, even for beginners.

People got very excited about this idea and started crocheting their own coral reefs:

Flickr image: Stitchlily
Flickr image: Stitchlily

The one pictured above is a small one – some of them fill entire rooms. Large-scale museum exhibits have been mounted, and they are incredible. A Google image search for “hyperbolic crochet” will provide you with more examples than I have room for here.

I was so inspired by the whole thing that I created my own miniature reef installation, shown in the first photo of this post.

And it really is SO easy to try. It takes about 5 minutes to learn the basic crochet stitch.

The supplies are cheap – grab yourself a basic crochet hook and some yarn, and you’re ready to go. If you decide to get more in depth, there are books you can get to show you how to do specific things, but really between YouTube and the many awesome web sites out there, you can (as usual) probably find what you need online.

Watching videos is not a substitute for making things, though – give it a try! And if you do, please send photos.

Go make something!