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. If you would like the STL fikles themselves contact me by email. 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.

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. (jzweck 'at' nyit 'dot' edu)

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.

Funding

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

Software and Talks

• Mathematica Code
• Other Mathematicians with 3D Printed Models

Active Learning Projects with 3D Printed Models

A Menagerie of Mathematical Models

Paraboloid [Rectangular Grid] Mathematica Code Project 1, Project 5	Paraboloid [Polar Grid] Mathematica Code Project 1, Project 5	Hyperboloid of One Sheet [Rectangular Grid] Mathematica Code Lecture Demo	Hyperboloid of One Sheet [Polar Grid] Mathematica Code Project 5
Saddle Surface [Rectangular Grid] Mathematica Code Project 2	Saddle Surface [Level Curves] Mathematica Code Project 2	Helix [Left/Right] Mathematica Code Project 3	Spiral Staircase [Helicoid] Mathematica Code -
Saddle Surface [Ruled] Mathematica Code Project 6	Hyperboloid of One Sheet [Ruled] Mathematica Code Project 6	Humpty Dumpty [Elliptical Paraboloid] Mathematica Code Lecture Demo	The Horse's Saddle [Saddle Surface] Mathematica Code Lecture Demo
Humpty Dumpty on a Horse - Lecture Demo	Intersecting Half Cylinders [You need more than 1!] Mathematica Code	Intersecting Cylinders [You need more than 1!] Mathematica Code	Temple of Viviani Mathematica Code Connection to MH370
Limit DNE [via Rays] Mathematica Code Project 4	Limit DNE [via Parabolas, I] Mathematica Code Project 4	Limits DNE [[via Parabolas, II]] Mathematica Code Project 4	Double Slippery Dip [For Critical Points] Mathematica Code Project 7
Sting Ray [For Critical Points] Mathematica Code Project 7	Two Local Max [Only 2 Critical Points!] Mathematica Code Project 8	Local Max Not Global [Only 1 Critical Point] Mathematica Code Project 8	Easter Egg In Toblerone Box [Global Max/Min] Mathematica Code 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