One of the most aesthetically beautiful works entered in the Bits to Its Art Show for which Potomac Photonics is the official 3D printing service is actually a realization of a mathematical equation.
Round Mobius Strip was created by Henry Segerman, a research fellow at Melbourne University in Australia with a PhD in mathematics from Stanford University. He uses 3D printing to bring abstract concepts to the physical world. Perhaps his entry is the most literal interpretation of Bits to Its.
Dr. Segerman studies 3-dimensional geometry and topology, and finds 3D printing allows visualization of otherwise difficult to grasp concepts. He says, “3D printing lets you hold in your hands ideas that would be very difficult to physically realize otherwise.” And that is his prime motivation.
While Dr. Segerman’s art pieces are as beautiful as any sculpture ever created, his goal is “to create a piece in a way that is as faithful as possible to the mathematical idea. Part of that is to make as few arbitrary choices as possible in translating between the mathematics and the physical object. I guess that makes me a minimalist!”
Seeing the one true way to represent an idea through fundamental guiding principles is the goal for mathematical art in its purest form. But Dr. Segerman admits to an ulterior motive. “I want to take an underlying concept, and pull it out from the abstract into something that can be appreciated by anyone. Then I can start to tell you about the math behind it!”
For those of us in engineering and science, this work is at its best when the outcome is what is frequently referred to as elegant. Dr. Segerman concurs that with “elegance you don’t have to ask why something is there. It’s complete, with no extraneous bits.”
For Potomac, the main difference in making this piece was that most of their customers come from industrial applications. Mike Adelstein, President and CEO of Potomac Photonics comments that marrying art with technology was intriguing and a fun departure from their mainstream business in medical device, sensors, and electronics parts.
Round Mobius Strip grew out of joint work with Saul Schleimer, a mathematician at the University of Warwick, in Dr. Segerman’s native England. He admits, “There are not that many people using 3D printing in mathematics. More and more universities and colleges have 3D printers but mostly in the design or architecture departments. We are however seeing good uses creeping into all kinds of courses.”
Dr. Segerman imagines a “course about understanding surfaces, or the kinds of things you need to know to be able to use CAD programs to build objects beyond squares and right angles. Often the problem a student faces in understanding a mathematical idea is in needing to see what’s going on – for which you need a good visualization. Imagine a course where part of assessment would be in 3d printing that visualization.” He muses, “Of course, these skills will be more and more important as we move closer to Stephenson’s The Diamond Age.” He is, of course, referring to the post-cyberpunk novel with machines called “compilers” that put current 3D-printers to shame.
Education outreach is also important to Dr. Segerman. In work with Swinburne University of Technology in Australia, he has developed 3D-printed illustrations of examples of surfaces from multi-variable calculus, such as the Hyperbolic Paraboloid on the left. He expands that 3D printing offers a unique solution in that often the physical object could not have been created any other way. “The first reaction I get from people seeing a piece of mathematical art for the first time is – how did you make this?! And that is one of the beauties of 3D printing.”
It was the online virtual world Second Life that led Dr. Segerman to the world of 3D printing. The multi-user online platform gave him the opportunity to create objects and then write scripts to make them move or interact. Shown on the right is a building he helped create with the Philips Corporation that uses the Hyperbolic Paraboloid, based on their design from the 1958 Brussels World’s Fair.
“Now there are more people in art using 3D Printing, but,” Dr. Segerman remembers, “10 years ago there were only a few artists, including Bathsheba Grossman. I first met her in Second Life; she arrived after I had already grabbed all the low hanging mathematical art fruit!”
So what’s next for Henry Segerman?
“Moving stuff is cool, so I’m thinking about mobiles, gears and puzzles. 3D printing can also be useful in research – sometimes a physical model can lead to a new mathematical realization. Mostly though it goes the other way: we need to understand the abstraction very well before we can tell a computer what to 3D-print. In any case, it adds a different flavor to the problems that we run into in our usual work!”
One thing is clear, Henry Segerman’s next work is sure to be a minimalist, elegant representation of his mathematical world.
Technical Note for Round Mobius Strip:
Here is the parametric formula for the basic surface in the unit sphere in 4-dimensional space:
{(cos(θ)cos(φ), cos(θ)sin(φ), sin(θ)cos(2φ), sin(θ)sin(2φ)) where 0 ≤ θ < π, 0 ≤ φ < π}
The surface is then mapped from 4-dimensional space to 3-dimensional space by stereographic projection.
You can learn more about Dr. Henry Segerman’s work on his website:
www.segerman.org
With 3 decades of experience in microfabrication including laser micromachining, 3D Printing and CNC machining, Potomac Photonics can bring your ideas to life. We’ve worked with artists, designers, engineers, technologists and entrepreneurs in industries ranging from medical devices, biotechnology, electronics, sensors and consumer products. Go to www.potomac-laser.com for more details
