Suggested models

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).-1

    • 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.250px-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:clebsch


  • A pseudosphere illustrating some of the principles of non-Euclidean geometry.pseudosphere
  • Some minimal surfaces, including the helicoid and catenoid:Helicatenoid
  • Prof. Pollack suggests printing some models of lattices in R^3 which have interesting connections to algebra.
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3D Printing of Mathematical Models — An Invitation

On Thursday, Sept 26th, Professors Adeboye and Constantine will give a talk introducing the project in the Undergraduate Math Club meeting.  Here’s the blurb:

Undergrad Math Club Meeting: Thursday, September 26 at noon in the Woodhead Lounge.

From Platonic solids in a geometry to graphs of surfaces in Calc 3 to knots and Klein bottles in topology, being able to visualize the sometimes complicated geometric objects which appear throughout mathematics is key to understanding and working with them. And these objects are not only important to geometers and topologists. Geometric models and intuition help us understand topics in analysis and algebra as well.

3D printing provides a new and very versatile way to produce models of various geometrical objects (at least the ones that can be modeled in 3-dimensional space!). In this talk we will announce a project you can be involved in to conceive, design, and print 3D models of mathematical objects.  Participants in the project will learn about these objects, about the 3D printing process itself, and will learn to design objects which we will print on Wesleyan’s new 3D printers.

Students of all levels are welcome to join the project!  We’ll show you some possible objects to design, at least one printed example, and we’ll tell you about the how the project will run and what joining entails.

Be sure to come by and hear about the project. Pizza will be served!

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This post collects some resources about 3D printing in general and 3D math models specifically.

  • This paper, by Henry Segerman, is a great place to start learning about 3D printing math models.
  • This paper, by Schleimer and Segerman has some more ideas and and explanation of a way to model in R^3 objects which are not naturally 3-dimensional.
  • This nice post from the Simons Foundation provides more general ideas.
  • This paper, by George Hart, has a fair amount of detail on ways one can use Mathematica’s programming abilities to generate some interesting models.
  • This paper, by Knill and Slavkovsky, contains many possible models and a lot of info on ways to produce them in Mathematica.

Related to 3D printing in general:

  • Wesleyan’s 3D printers are from Makerbot.  Thingiverse has a lot of online resources and ideas about printing with these machines in general.
  • and more to come…
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hyperdodecahedronWelcome to the group blog for the 3D Printing of Mathematical Models project.  Here you will find basic information about the project, how to get involved, resources, and ideas.  The blog is also a place to share questions and ideas, and to discuss our progress.

See the About page for more info about the project, and follow the links at right for ideas, resources, etc.

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