A couple weeks ago I gave a workshop to a pretty cool group of people at Brookhaven National Labs. We made what was, to my knowledge, the world's largest penny Sierpinki's Triangle, 8 feet to a side! I was invited by my friend Cindy Lawrence of The Museum of Mathematics, who also took a couple great photos:
It was pretty awesome.
— posted
Saturday, January 01, 2011 at 09:09PM EST
I was at my dad's place last night, and had a chance to check out his new makerbot. "What should we print?" he asked. Apollonian Gaskets were still on my mind due to my most recent video, and I thought doodling one out of plastic would be awesome! To take advantage of the 3d-ness of 3d printing technology, I decided each circle should be a hemispherical crater into a cylinder. George whipped up an .stl file for exactly that, and then we hit print!
This 3d printer is a robot that spits out plastic layer by layer. In the first photo it's about 3/4 of the way up. The second photo shows the finished piece. I think it's super awesome to be able to think of, design, and then print out a 3-dimensional mathematical sculpture during the course of dessert!
— posted
Saturday, December 04, 2010 at 11:54PM EST
I just finished the third and possibly final video in the Mathematical Doodling series:
The three videos are now on this webpage, which maybe someday I'll update with some more explanation and info, but for now just has helpful Wikipedia links.
— posted
Saturday, November 27, 2010 at 10:30PM EST
I did a bunch of sprucing up around the webpage today, mostly updating various pages, the menu, and the Everything Index. The art page got a major update, with all my drawings of hyperbolic planes consolidated into one Hyperbolic Figure Studies page, and also a new page with brand new content: digital doodles I've done for various reasons and that might not make any sense.
— posted
Monday, September 27, 2010 at 02:40AM EDT
Since drawing the hyperbolic ghost, the image has been haunting my mind. Tonight I managed to catch her on camera.
I wanted a light and airy hyperbolic plane that would float in the breeze. I decided to try making one out of plastic bags. I cut them into heptagons, ironed them together, and voila! The ironing was not easy, but it worked. I took some pictures of the process and plan on putting together a webpage soon.
To simulate the ghost drawing in a photo, I dressed all in black, wrapped the hyperbolic plane around my waist, and belted it into place. All I need now are proper lighting, camera, and a wind tunnel!
I've been continuing to sketch, visualize, and explore the hyperbolic plane in all its beauty. I've been playing with giving the hyperbolic plane forms that are a little less abstract, perhaps even representational. This one started in my head as the ghost of a lady in white, though it would be better if you too could see the dress flow and ripple as she floats along her favourite haunting grounds.
After my first two hyperbolic figure studies, I wanted to imagine more complex forms, forms that loop and fold in a sort of hyperbolic origami. In doing this, I accidentally re-discovered surfaces like Schwarz's P surface, which as it turns out can be made by rolling up a hyperbolic plane. While both those things are already known, I'm still going to give major points to mathematical art because they just as easily might not have been. Hopefully after a few more series of sketches I'll be entering new mathematical territory.
I wrote the music for this video by Erik and Martin Demaine, for their project Waves In Glass, which combines mathematics, paper folding, and blind-folded glassblowing.
When writing this music, I tried to capture the repetitive rotational feel in the process of both glassblowing and this particular instance of paper folding, as well as sneaking in elements of symmetry and mathematics. I see this video as a collaboration and communication between art, glass, music, math, paper, and people.
OK, this is officially the summer of the hyperbolic plane. I made the 3-heptagons-around-each-point model again, this time with big plastic beads and with colour!
I think the colour makes it much easier to see what's going on, though seeing is really no substitute for playing with it in your own hands, so I recommend you make your own.
I may have developed a thing for the hyperbolic plane. After making enough physical models, I got a better intuitive sense of the kind of shapes that sections of hyperbolic plane can curl into, and decided to draw some shapes out of my head using chalk pastels (mathematical accuracy not guaranteed):
One neat thing about this is that by drawing freehand I have no limitations except for my own ability to visualize hyperbolicness; it tests my visualization skills and allows for forms that might not be found by other methods. I hope to take the concept further once I develop my drawing skills and hyperbolic intuition a bit more.
The Hyperbottlic Plane and Bottlonic Solids
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After talking to Nick Sayers and seeing his wonderful mathematical art made with found objects, I realized I needed to find something that could function as a giant bead. I immediately thought of Mario Marin's method of putting soda bottles together. I varied the method to leave a hole through the bottles, used some ribbon to thread them together, and voila:
The first photo shows the three platonic solids that have triangular faces, and the second photo is of a hyperbolic tiling that has seven triangles around every vertex. I plan eventually to put a webpage together with more details and instructions. Mostly I'm glad that I had a stockpile of empty bottles lying around!
I meant to let this project sit for a bit, but this morning I found some better beads and couldn't help but make another hyperbolic plane, this time by tiling three heptagons around each vertex. It was so much easier than the one I made yesterday, and so fun to play with, that I decided instructions had to be put online immediately!
I put up a new webpage on hyperbolic beading so that you can make your own. So far the page only contains diagrams for the above model, but I hope in the future to try some other tilings and patterns.
To take a break from balloon hyperbolic planes, I made this one out of beads. Each bead represents the edge of a pentagon in the uniform tiling of four pentagons around each point. Beadwork hyperbolic planes have been made by others, though I couldn't find any existing examples of a close-knit uniform tiling like this. It's quite nice to play with. If anyone knows of any other examples of hyperbolic planes made out of beads, let me know!
I consider this a rough test for future mathematical beadwork, hopefully with nicer beads, colour patterns, and artistry. I was inspired to pursue mathematical beadwork by some of the very beautiful models I saw at BRIDGES this year, notably the works by Laura Shea and Bih-Yaw Jin. There are also some connections between computational balloon twisting and computational beadwork (if you wanted to minimize the length of the path the string takes).
The BRIDGES conference is always a lot of fun, but this year was especially so. Not only did I meet and hang out with lots of great people, give a talk, host music night as well as jam with lots of other mathematical musicians, and act in theater night, but I also got tessellated.
Yes, one of the many fun people I hung out with was Mike Naylor, the mastermind behind Naked Geometry. A group of us got together and tried doing some human geometry. Here is a cube we made with ourselves, and a lovely tessellation that Mike created out of me.
![[Vi Hart logo]](/images/butterfly_small.png)
![[video preview image]](/music/WavesInGlass.jpg)
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