These 3D Printed Porcelain Coffee Mugs & Donuts are Clever Topology-Related Joke

Share this Article

Henry Segerman’s jokes aren’t meant to be obscure but can be hopelessly perplexing if you don’t know anything about topology. His latest 3D-printed, topology-related project–a coffee mug transforming into a donut, which in turn transforms into a coffee mug, and so on–won’t make much sense to you unless you’re a topology insider and, doubtless, that’s probably a pretty small segment of the population. Here’s the joke: Topologists can’t tell the difference between a coffee mug and a doughnut.

Fortunately, mercifully, Henry explains this in a video that’s provided in a Shapeways article about Segerman’s most recent topology-inspired effort. Segerman, who is a mathematical artist and Shapeways community member, is collaborating with postdoctoral fellow at Columbia University, Keenan Crane, who is most certainly a member of that elite group of topology insiders. Crane explains that his research “draws on insights from differential geometry and computer science to develop fundamental algorithms for working with real-world geometric data. In short, he and Segerman speak the same arcane language of coffee mugs and donuts that are indistinguishable from one another.

But, wait a minute! What’s topology anyway? In mathematics, topology is the study of the properties of space that are preserved under continuous deformations like bending and stretching. As a field of study, topology developed out of geometry and set theory. Topologists analyze concepts of space, dimension, and transformation and two important properties in topology are compactness and connectedness. Think of the mobius strip, for instance. It’s what happens when you connect the ends of a rectangle to one another but, rather than doing so directly and creating a cylinder, you twist the center of the rectangle and connect the ends that way (see the image if this makes no sense). You aren’t lengthening the rectangle but you are changing the way its edges are identified. The mobius strip ends up with one edge whereas the cylinder (and its precursor, the rectangle) has two. Imagine! People make a living thinking about concepts and constructions like this!

mobius band

One such person is Henry Segerman, whose 3D-printed and utterly captivating sculptures are based on his study of topology and can be seen on his Shapeways shop. In addition to collaborating with Crane, Segerman also works with mathematician, Saul Schleimer, of the University of Warwick in the UK, another topology and geometry insider, and kinetic sculptor, Marco Mahler, with whom he shares a second Shapeways shop.

Segerman’s work is egghead heart, reminding one of the two-dimensional work of MC Escher, whose imagery seems to confound spatial logic. The coffee mugs and donuts are 3D printed in porcelain material as part of Shapeways’ porcelain pilot program, which is still in an experimental phase. The objects are life size, as you can see when watching the video, and are 3D printed in a pretty, robin’s egg blue porcelain.

For the most part, Segerman’s topological sculptures are white, with the exception of a few, including his fascinating “Twisted Earth.” While many of the objects are visually compelling, inviting one to pick them up and turn them around and around, some are puzzles, which should satisfy even the most confirmed brainiacs on your gift-shopping list. The pieces are also generally quite modestly priced. Our personal favorites are the stereographic projections, the knots (we define you to look upon one without becoming frustrated), and the lattices. While you don’t have to understand them to appreciate them, Segerman’s sculptures certainly invite further study.

"Twisted Earth" is 3D printed in full color sandstone and costs $14.00 through Segerman's Shapeways store.

“Twisted Earth” is 3D printed in full color sandstone and costs $14.00 through Segerman’s Shapeways store.

 

Share this Article


Recent News

Why Automated Post Processing Makes Manufacturing With 3D Printers Possible

Interview with Malika Khodja on Women in 3D Printing



Categories

3D Design

3D Printed Art

3D Printed Food

3D Printed Guns


You May Also Like

3D Printing News Briefs: September 6, 2019

In 3D Printing News Briefs today, we’ve got some business and materials news to share. ASTM International has announced five female board nominees, and cycling brand fizik is working with...

Interview with Emma Molobi on Additive Manufacturing for Railway Infrastructure

Emma Molobi 3D printing and additive manufacturing are becoming important tools in the engineering sector. One nascent development is occurring in the railway sector which is trying to utilise the...

3D Printing News Briefs: August 29, 2019

For this edition of 3D Printing News Briefs, we’re telling you about award nominations, a 3D printing workshop, and a Kickstarter campaign. Johnson & Johnson is now taking nominations for...

Kenyan and Zimbabwean Researchers Study 3D Printed Polymer/PLA on Fabric

Researchers from Kenya and Zimbabwe are tackling more complex 3D printing adhesion and material topics in their recently published, ‘Use of regression to study the effect of fabric parameters on...


Shop

View our broad assortment of in house and third party products.


Print Services

Subscribe To Our Newsletter

Subscribe To Our Newsletter

Join our mailing list to receive the latest news and updates from our 3DPrint.com.

You have Successfully Subscribed!