Yesterday I was able to watch the Global Math Project presentations (well, most of them) via the Facebook Live feed. Hopefully those videos will be preserved here:
The Global Math Project’s Facebook page
One tank that caught my eye was given by Henry Segerman. I’d guess that his work and Laura Taalman’s work account for at least 80% of what I know about exploring math through 3d printing.
As I write this post there are 96 prior posts with the “3D Printing” tag on my blog. 3D Printing is still pretty new, and I think many people around math are only starting to see its use in education. Segerman’s talk made me want to throw together a list of fun projects that we’ve done just in case anyone is looking for a starting point after seeing his talk.
Some of my original thoughts on exploring math through 3d printing can be found in this blog post from March 2014 which features two really neat videos from Brooklyn Tech and Laura Taalman:
Here are some sample projects:
(1) James Tanton’s Geometry Problem and 3d printing
Since this blog post was inspired by a talk a James Tanton’s Global Math Project, it seems appropriate to kick it off with a project inspired by Tanton:
Here are some of the shapes we printed as we explored what the shape itself looked like:
and here are the two projects that we’ve done exploring this problem
James Tanton’s geometry problem and 3d printing
Revisiting James Tanton’s Tetrahedron Problem
(2) Hard to highlight just one project that Segerman Inspired, so here’s the first of 2
One of the Segerman’s examples in yesterday’s talk was about bubbles. He showed a few complicated bubble examples but there are simple ones that are amazing, too. Here’s an example showing that the “bubble” formed by dipping a tetrahedron in soap is the same shape as a 4-dimensional shape:
Talking about Henry Segerman’s 5-cell with my 5th grader
(3) A second idea from Segerman – exploring shadows
One of Segerman’s most beautiful creations is on the cover of his book:
It is incredibly fun to have kids explore this shape:
Here’s the project we did after seeing Segerman give a talk last fall:
Playing with Sahdows inspired by Henry Segerman
Here’s a link to all of our project inspired by him:
All of our Henry Segerman-inspired projects
(4) There is also no way to limit Laura Taalman’s work to one example.
Here’s a project where we explored some of here 3d printed knots – one of which was featured in Segerman’s talk yesterday:
Playing with some 3d printed knots
(5) Here’s another project inspred by Taalman – tiling pentagons
Taalman’s 3d printed tiling pentagon designs are one of the most amazing pieces at the intersection of math and education:
We’ve used them for several projects including making cookies!
Here’s that project
Learning about tiling pentagons from Laura Taalman and Evelyn Lamb
and here’s a link to all of our projects inspired by Laura Taalman:
All of our projects inspired by Laura Taalman
(6) Exploring connections between algebra and geometry
3d printing can come in handy for looking at math ideas that previously you could only study on paper or on the computer screen. For example, a common algebra mistake is to think that:
Here’s what these two surfaces look like:
Here’s two projects exploring these algebra ideas with the boys:
Comparing x^2 + y^2 and (x + y)^2 with 3d printing/a>
Comparing Sqrt(x^2 + y^2) and Sqrt(x^2) + Sqrt(y^2) with 3d Printing
(7) 3D printing can also be surprisingly useful for studying 2d geometry
We’ve done a few neat projects in this area.
(i) Which triangle has larger area, a 5-5-6 triangle or a 5-5-8 one?
A few follow ups to the triangle puzzle
(ii) A neat geometry idea from Patrick Honner
Here’s how we used 3d printing to explore this triange:
Inequalities and Mr. Honner’s Triangles
(iii) A neat geometry problem shared by Tina Cardone
Here’s how I explored this problem with 3d printing
A Cool Geometry Problem Shared by Tina Cardone
which led to a fun and unexpected follow up:
A Follow Up to Our Tina Cardone Geometry Project
(8) 3d printing can be a fun way to review ideas from elementary geometry
In his talk yesterday Segerman mentioned a few prints that his undergraduate students created. As he showed this projects he talked about how the creation process really helps students understand and explore the underlying math.
In the project below, creating the shape of the tile helped me review and explore equations of lines with the boys:
Sharing a Craig Kaplan post with kids
(9) 3d printing can also make abstract math / advanced problems accessible
A few months back I saw this problem shared by Alexander Bogomolny:
Nassim Taleb’s look at the problem on Mathematica made me think that the problem could be shared with kids:
A project for kids inspired by Nassim Taleb and Alexander Bogomolny
After getting some intuition from this problem we extended the problem to 4 dimensions using Taleb’s approach. The prints were really fun to play with and it is amazing to hear kids talk about these shapes that come from 4 dimensions:
Here’s that project:
Extending our Bogomolny / Taleb project from 3 to 4 dimensions
(10) Using 3d printing for calculus and beyond
I’m written a few posts and done a few projects about how to use 3d printing to explore some basic ideas from Calculus.
That collection of posts is here:
Posts about 3d printing and calculus
But 3d printing can help you see even more advanced ideas. Here’s a cube inside of a dodecahedron, for example:
and, of course, many (most!) of examples that Henry Segerman showed in his talk yesterday are perfect for showing how 3d printing can help everyone experience some advanced ideas in mathematics.
I’ll end with the project we did yesterday, which is a delightful example of how 3d printing can help you explore a math idea:
Revisiting the Volume of a Sphere with 3d printing