To start off I gave this project to my students in my “Excursions in Mathematics” course. They quickly came up with some interesting work.

I’m not much of an artist but after seeing what could be done with pencil and paper I decided to sketch my favorite video game character, MARIO!

That was fun, but given by inability to draw well I thought I would let my computer handle the work for my next piece of art. To do so I took a quick photo of myself and imported it into Mathematica. From there I applied a transformation of the photo into polar coordinates to give me the following picture.

I’m not sure which of the two photos is scarier. Either way, I definitely needed a haircut at the time.

From there I converted the distorted image to greyscale and imported it into Easel where is was carved by UNH’s desktop cnc router Carvey.

This thing makes a mess but luckily it is completely enclosed so it is easy to clean up. I decided to use a piece of two-color HDPE plastic to carve out my self portrait.

Overall, I am pretty pleased with this project. It’s a little hard to make out but if you look closely you should be able to read the title I added above my head. You can also make out a QR code that links to this webpage. I think they will both make a nice addition to place in the window of my office at work.

]]>The design that we chose to work with is called a penny trap and credit for both the idea and the design goes to Laura Taalman. I have been following Laura’s work for a while at her website http://mathgrrl.com/hacktastic/ and had the opportunity to meet her this summer at Brown’s ICERM conference.

The students designed the penny traps using the free online cad software called Tinkercad. This software has a very small learning curve so it is great to use while introducing students to 3D design. It also has the ability to export a .stl file ready to be printed.

Once the designs were complete the students were off to send them to the printers. We have four M3D printers that the university purchased through Kickstarter last spring. So far they have been great albeit a little bit slower than most printers. However, just like Tinkercad they are very user friendly and designed for “plug and play” applications.

Once the penny traps are half way through being printed it is time to insert the penny so it can be trapped inside.

In the end each student was able to take home their own penny trap to show off a 3D printed object. They all seemed to enjoy the day and hopefully learned a bit about STEM as well.

]]>The first one that really stood out to me was the following piece of pyrite, also known as fools gold.

The almost perfect rectangular solid formed by this mineral is due to its crystalline structure.

By Materialscientist – Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=10379959

Although other crystals may have a more intricate shape that involves more complicated geometry I was struck by the simplicity of this particular mineral.

Next up I found a fossilized sea urchin.

I like how the five-fold (72 degree rotation) symmetry of the sea urchin’s anatomy is so clearly shown in this fossil. Each of the five marks on the side of the urchin are formed by it’s stone canals. They can be seen in the following diagram of a sea urchin’s anatomy.

And last, but certainly not least, is my favorite find of the day. A fossilized nautilus shell showing off the Fibonacci sequence and golden ratio in all of its glory.

The colors in this particular shell are just beautiful and the spiral stands out exceptionally well. This spiral shape can be formed by joining the corners of squares with arcs that from a quarter of a circle. You just need to make sure that the sides of the squares have lengths corresponding to the Fibonacci sequence:

1,1,2,3,5,8,13,21,34,55,89,144,…

Starting with two 1’s for the first two terms in the sequence new ones are formed by adding together the two previous terms. For example, the seventh term in the sequence, 13, is formed by adding together the two terms that come before it, 5 and 8. Below is the spiral with its squares illustrated to the tenth term in the sequence.

So the next time you’re on a vacation in a new place make sure to keep an eye out for some math. You never know where it is going to show up!

]]>Of course for a test print I decided to make Sierpinski’s triangle out of a piece of plywood. Below you can see Carvey removing the triangles one by one as well as the final product before it was taken out of the machine.

Once Carvey finished doing its thing I had to sand some of the edges but that was about it.

You can see how rough the initial cut was. I think this mostly had to do with the fact that the triangle was cut from cheap plywood rather than a nice piece of hardwood.

All cleaned up I think it looks rather nice in my window.

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I just attended a conference held at Brown Universities ICERM called “Illustrating Mathematics”. Many topics were discussed that involved cutting edge methods for creating 3D prints of various mathematical models. This has inspired me to start a blog of the same name to show off some of my own work.

I have been inspired by Henry Segerman’s work with 3D printed fractal formations so I attempted to create my own in Tinkered. To start off simple I wanted to show the evolution of the classic cantor set.

This was printed in PLA to show the continuous transformation of the line segment [0,1] into the 4th level of the Cantor set. I also made the the dimensions of the overall rectangle match the golden ratio and printed it in gold to give the comb some style.

Next, I wanted to see if I could model something a little more difficult so I set my eyes on the evolution of the Cantor Dust fractal.

This was also made in Tinkered but printed in ABS on a Lulzbot Taz 5. The evolution from the original square goes down to the 4th level of the fractal. It starts with one cube and ends with 4^4=256 cubes.

I also included arches in the transformation to give it the look of the Arc de Triomphe. Like the golden Cantor Comb I scaled this fractal’s main arch to have similar dimensions to the real Arc de Triomphe.

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