We will use this post to collect ideas and suggestions of things to print. See also the Project List page to see which projects already have people working on them.
- Prof. Rasmussen:
Given any knot, one can find a polynomial parametrization of said knot, and as a result, it can be represented as the vanishing set of some ideal of polynomials in R^3. As a result, each individual polynomial in the ideal describes a surface in R^3 that contains the knot. This gives a beautiful visualization that I think 3-d printing could provide.
I would love to have any of the following:
(a) a surface in R^3, with a highlighted copy of the knot embedded in it, (or even the same for several different surfaces),
(b) two different colored surfaces in R^3, (whose intersection would be the knot in question).
- Prof. Emeritus Linton suggests the Steinmetz surface as a nice, symmetrical surface.
- Prof. Ramyaa has some ideas about 3D printing a demonstration of how a 3D model can be reconstructed from several 2D images.
- Prof Constantine would like models illustrating the Hopf fibration.
I would also like to print models of the Sierpinski pyramid and the Menger sponge.
- Prof. Scowcroft suggests we look into the series of models Felix Klein popularized at the Chicago World’s Fair.
- We should certainly print some cubic surfaces with their 27 lines:
- It is possible to cut a Klein bottle apart into two Moebius strips. It would be nice to design a model demonstrating this.
- We could print some Seifert surfaces for various knots and links.
- A pseudosphere illustrating some of the principles of non-Euclidean geometry.
- Some minimal surfaces, including the helicoid and catenoid:
- Prof. Pollack suggests printing some models of lattices in R^3 which have interesting connections to algebra.
