Anamorphic Cylindrical Art

I wanted to try my hand at creating a piece of anamorphic art in the style of the artist István Orosz.  He created several works in polar coordinates that appear normal when viewed in the reflection of a cylindrical mirror.  Below is an example of his impressive artwork.

István Orosz cylinder painting

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.

EXCELL in STEM at UNH Manchester

Its been about two months since the EXCELL in STEM program took place on the Manchester campus of UNH but it was such a great time that I still wanted to share it with all of you.  The activity that I ran introduced students to 3D printing and design.  We had both middle school and high school students in attendance, and both were awesome to work with!

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 and had the opportunity to meet her this summer at Brown’s ICERM conference.

penny trap
Penny Trap

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.

Designing Penny Traps in Tinkercad

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.

Starting the M3D Printers

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

insert penny

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.

Math at a Rock Shop

I recently went on a Vacation to Bar Harbor in the beautiful state of Maine.  While enjoying bicycling through Acadia National Park and eating more than my fair share of lobster, I found some time to stop in the local rock shop.  Of course math was to be found absolutely everywhere!  I just knew that I couldn’t leave Maine without at least a few souvenirs so I brought the following three “math rocks” back home with me.

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. FeS2structure

By Materialscientist – Own work, CC BY-SA 3.0,

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.

By Alex Ries –, CC BY-SA 4.0

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:


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.  spiral

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!

Carvey is up and Running!

Hello everyone,  Today I wanted to share my first project with UNH’s new CNC milling machine. It’s a new machine made by Inventables that got going on Kickstarter.  It’s called “Carvey”!  The machine is a three axis CNC so it has some limitations for mathematical design although I think it has a ton of potential.

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.

IMG_8444 IMG_8447

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

IMG_8450You 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.

Level 3 Sierpinski Triangle


Evolution of the Golden Cantor Comb and Fractal Arc de Triomphe

Hello, My name is Dr. Donald Plante and I have always been interested in visualizing mathematics through the use of models.  With the advent of 3D printing this has recently become much easier to do.  No more nights glueing 400 cubes together to make a level 2 Menger sponge!  Now I can design and print one in much greater detail in a matter of hours instead of days.

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.

Evolution of the Cantor Dust fractal
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.

All 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.

Fractal Arc de Triomphe
A look inside the Fractal Arc de Triomphe