Widely Applied Mathematics Seminars

Chebyshev nets: geometries for design

Andrew O. Sageman-Furnas, Technical University of Berlin

Apr 23, 2021
12:00 pm to 1:00 pm | Zoom

What do fabrics with 1000s of interwoven yarns, kitchen strainers with 100s of plastically deforming wires, and architectural gridshells or medical stents with 10s of elastically deforming rods all have in common?

Their geometry: a shell-like grid of flexible but inextensible rods. In 1878, Russian mathematician P. Chebyshev showed how to encode the inextensibility of two families of flexible rods in the language of differential geometry.


In this talk, we see that Chebyshev net geometries apply across vastly different length scales and material properties. I will discuss a series of collaborative efforts in computational fabrication and inverse design. Theoretical obstructions expose the challenges in finding Chebyshev nets on surfaces with large amounts of curvature, suggesting a limited shape space. However, we show that a careful reformulation of the problem, combined with a discrete analog of Chebyshev nets, leads to computational tools that reveal a vibrant design space.

Speaker Bio

Andy studies curved shapes that are inherently discrete by developing analogs of differential geometry. Beyond providing an essential link between continuous formulations and computation, discrete differential geometry arises in applications ranging from large architectural structures down to molecular polymer networks and across to nonlinear superposition principles. After receiving his Ph.D. in 2017 from the Discrete Differential Geometry Lab at the University of Göttingen, Andy moved to the Technical University of Berlin as a postdoc. This summer he will start as an assistant professor in the NC State Math Department.


Changyeob Baek


Changyeob Baek

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