Math + Making

A student blog for Math 189AH: Making Mathematics at Harvey Mudd College

Making Math with Savva

Savva Ignatov

Over the course of making math I learned a lot more about some math topics that I was interested in and got to try out technologies I was too scared of touching before as I didn’t have an assignment that required using them. Over the course of this blog post I will do a summary of my semester doing Making Math.

Project 0A

Sierpinski Triangle

To start off the making math semester, I was interested in looking at fractal geometry, so I picked the sierpinski triangle. I learned that it was pretty simple to write python code that would make a turtle put the pen up, go to a midpoint, put the pen down and go to the next midpoint. I wrote a python script so that it would redo the whole loop 3 times in order to get a basic Sierpinski triangle.

 I then exported the PDF it produced into the laser cutter. The laser cutter was a technology that seemed really scary, mostly because it had “laser” in its name, but after doing the maker space safety quiz it turned out to be quite simple. I then cut the wood I had laser cut on with a band saw in order to give the rest of the wood a triangular shape, and to have grip.

I turned out to be very happy with the project since I had tried so many different apparatus that I had never used or seen before.

Project 0B 

Sphericoin art

During the Sphericoin art project, I collaborated with Lucie where first we put the coin straight down the middle until its center using a Dremel saw. The Dremel saw was one of the scarier new technologies I ended up using, as it also took more than 1 try to get right. We then hammered the two coins together to get a spherical coin shape, which would produce an interesting pattern when rolled down.

We then got lots of different paint and just rolled the coins down the page using gravity. I felt like this part of the project was much more artistic and calming than the cutting and hammering side of it.

I was happy collaborating instead of doing the project myself as it was more entertaining and felt easier to tackle the new technologies as Lucie had already done it once before with Vicente.

Project 1

Creating the Gömböc

For the first long term project, Lucie, Vicente and I joined up together to try and create a Gömböc. We were at first interested with this shape, as it was the first self-righting shape that had uniform density. The shape had one stable equilibrium point, where it wouldn’t move even if pushed gently, and an unstable equilibrium point where the shape would return to the stable equilibrium point if pushed gently, but otherwise would stay still. We found out that the whole group felt passionate about this topic and we all wanted to get our hands on a shape like that.

After finding an STL file that could work we wanted to try out a new technology, being the 3D printer. We didn’t expect the printing process to be so hard, as our prints would fail over and over again even when we used LSUN, Resin and Prusa.

Then Prof. Kagey heard about our troubles and helped by printing a beautiful carbon fiber Gömböc.

Project 2

Wooden Klein Bottle

I was really interested in shapes that had non orientable surfaces such as Mobius strips, a real projective plane. I found it really intriguing how those shapes were found and how they have many interesting properties, such as a Klein Bottle not having a volume.

Even though I was interested in this object, I wanted to try and work with wood a bit and try doing some more complicated wood work than just cutting the shape in half with a blade. So I came up with the idea of trying to make a vase shape out of the wood and then try to make a straw out of wood connecting those pieces together in the end to make a Klein Bottle.

I asked Zeneve Jacotin for some help as she was an engineer and told me to start with powered Lathe. The powered Lathe turned out to be problematic, as it would shoot out the spindle across the room multiple times even with the steward at the time repeatedly telling me it’s safe.

I ended up sanding the wood down and managing to lathe it into a curved vase shape, after which I drilled holes in the side and in the top to create a non orientable surface inside the wood. To finish up the Klein Bottle, I needed to make a straw, however that turned out to be very hard so I tried buying one instead.

Project 3

Klein Bottle in Blender

After doing the wooden Klein Bottle, I was a bit disappointed how hard it was to see that the shape was a non orientable surface, so I wanted to make it look more like a Klein Bottle by using more accurate software. What I didn’t expect was Blender to be so hard. 

At first I tried creating the Klein Bottle, after watching some basic tutorials and ended up with version 1.

I felt disappointed with this version, as I saw people do very complicated things in Blender and make them look much better. So, I went back to watching more tutorials and learned more about blender to create version 2.

I was much happier with this version, and I felt like I improved a lot in Blender which was another technology I wanted to learn to use.


Over the course of this semester I looked into the following math topics

  • 0A Fractal Geometry
  • 0B Sphericons
  • 1 Gömböc, Equilibrium Points
  • 2,3 Non orientable surfaces with Euler characteristic 0, Klein Bottle

Over the course of the semester I tried the following technologies

  • Band saw
  • Laser cutter
  • Dremel Saw
  • 3D printers
  • Powered Lathe
  • Horizontal, vertical powered sander
  • Powered drill
  • Blender

I really enjoyed doing these projects, as I felt they pushed me to try something on my own without guidance which is a challenge that is rarely found in other mudd classes. I felt like this class really pushed you to try new things and go out of your comfort zone in the machine shop and maker space to make you feel more used to not knowing the answer and being forced to ask for help. I felt like over the course of trying all these technologies, I also learned a lot on math topics I was interested in but didn’t have time to understand.


Leave a Reply

Your email address will not be published. Required fields are marked *