3D Printed Models for Multivariable Calculus

John Zweck


Still Life With Models

This web page is a repository for material I have developed to use 3D printed models of curves and surfaces to help Multivariable Calculus students develop their geometric imagination/visualization skills. The surfaces were designed with the aid of Mathematica. The Mathematica notebooks, which are available at the link below, generate STL files that can be printed using a 3D printer. Some of the models are simple enough that we were able to print them cheaply using a PrintrBot Simple printer. The remainder can be printed by Shapeways at a moderate cost. The STL files are also available at the link below. To view the models you can either run the Mathematica notebook or you can use the open source software MeshLab which can read in the STL file.

You may download and modify the code in any way you like. However, I would appreciate a short email to let me know how you are using the models. (zweck 'at' utdallas 'dot' edu)

I am also writing a series of Active Learning Projects that we are using in Problem (Tutorial) Sessions for the Calculus III course I teach at UT Dallas.

Thanks to Stephanie Taylor, Ximone Willis, Mary Urquhart, Sue Minkoff, Sonny Skaaning, Abdullah Helal, Yanping Chen, Arafat Khan, Jing Guo, Johnathan Popa, Sonam Lama, Jordan Kaderli, Mikaela McMurtry, Henry Curtis, Carl Finley, Dalia Franco Cortes, Jonathan Sok, Erik Rinqvist, Andrew Marder, Ariel Dezeeuw, Danika Lelina, and the SME Interns for their invaluable assistance with this project.

This project is supported by the National Science Foundation through a Supplement to the UTeach Dallas Robert Noyce Scholarship Program (DUE 1544159).

News Stories

Software and Talks

Active Learning Projects with 3D Printed Models

Project 1: Circular Paraboloids
Project 2: Saddle Surfaces
Project 3: Helices
Project 4: Limits
Project 5: Parametrized Surfaces
Project 6: Ruled Surfaces
Project 7: Max/Min/Saddle
Project 8: Hills and Valleys

A Menagerie of Mathematical Models


Paraboloid
[Rectangular Grid]

Mathematica Code
STL File
Project 1, Project 5

Paraboloid
[Polar Grid]

Mathematica Code
STL File
Project 1, Project 5

Hyperboloid of One Sheet
[Rectangular Grid]

Mathematica Code
STL File
Lecture Demo

Hyperboloid of One Sheet
[Polar Grid]

Mathematica Code
STL File
Project 5

Saddle Surface
[Rectangular Grid]

Mathematica Code
STL File
Project 2

Saddle Surface
[Level Curves]

Mathematica Code
STL File
Project 2

Helix
[Left/Right]

Mathematica Code
STL Files: Left, Right
Project 3

Spiral Staircase
[Helicoid]

Mathematica Code
STL File
-

Saddle Surface
[Ruled]

Mathematica Code
STL File
Project 6

Hyperboloid of One Sheet
[Ruled]

Mathematica Code
STL File
Project 6

Humpty Dumpty
[Elliptical Paraboloid]

Mathematica Code
STL File
Lecture Demo

The Horse's Saddle
[Saddle Surface]

Mathematica Code
STL File
Lecture Demo

Humpty Dumpty
on a Horse

-
Lecture Demo

Intersecting Half Cylinders
[You need more than 1!]

Mathematica Code
STL File

Intersecting Cylinders
[You need more than 1!]

Mathematica Code
STL File

Temple of Viviani
Mathematica Code
STL File
Connection to MH370

Limit DNE
[via Rays]

Mathematica Code
STL File
Project 4

Limit DNE
[via Parabolas, I]

Mathematica Code
STL File
Project 4

Limits DNE
[[via Parabolas, II]]

Mathematica Code
STL File
Project 4

Double Slippery Dip
[For Critical Points]

Mathematica Code
STL File
Project 7

Sting Ray
[For Critical Points]

Mathematica Code
STL File
Project 7

Two Local Max
[Only 2 Critical Points!]

Mathematica Code
STL File
Project 8

Local Max Not Global
[Only 1 Critical Point]

Mathematica Code
STL File
Project 8

Easter Egg In
Toblerone Box
[Global Max/Min]

Mathematica Code
STL File
Lecture Demo

Helix as Intersection
of Cylinder and Wave
Mathematica Code
Virtual Model

Helix as Intersection
of Two Orthogonal Waves
Mathematica Code
Virtual Model

Intersection of
Paraboloid and Vertical Plane
Mathematica Code
Virtual Model