Monday, March 21, 2016

Art and Mathematics - Zentangle

It's been awhile since I've posted. In fact, it's been awhile since I've created any art. So here's what I've been up to lately.  Perhaps some of you know that I went back to teaching after many years of being a stay-at-home mom. I thought I would ease into it by substituting for a math teacher who was having surgery. For a week, I taught Algebra, Geometry and Precalculus using prepared lessons, interacting with students, rediscovering how much I loved teaching. And then, the school asked me if I wanted to teach my own classes. The school needed a teacher for IB Math Standard Level. It is a two year course that covers trigonometry, statistics, and AB calculus. Were they crazy? Was I crazy enough to take the position? Of course! And so began my crazy return to teaching which has taken over my life. It's been two months and I'm finally beginning to feel like I can breathe. And it's my spring break! Though I still have plenty of things to keep me busy, I wanted to get back to doing art again.

IB stands for International Baccalaureate and without going into detail, the IB Math that I teach is a two-year course covering trigonometry, statistics and AB level calculus. One of the interesting part of this program is that students must write a paper that explores the math concepts they learned in class in real life. My seniors are working on topics ranging from statistics in sports to mathematics of Islamic geometry. And so I thought I would focus on some connections between art and mathematics this week.

If you have been following me on this blog, you know that I love zentangles. It is a stress reliever for me to just doodle some favorite patterns without worrying about what I'm creating. There have been many nights that I would simply pick up a pen and began drawing patterns in my notebook just to brain-dump so I can sleep.

Last week, my precalculus students worked on a project about graphing polar equations. You must remember graphing points and equations on a rectangular or Cartesian coordinate system.

The points are placed on the graph based on the distance away from the two reference lines called the y-axis (vertical) and the x-axis (horizontal). This is the system all of us learn in school.

There is another coordinate system that uses the distance from the reference point (the radius) and an angle from a reference direction. This system is called the polar coordinate system and is often used to graph cyclical equations. I'm not going to bore you with the details, but here are some cool polar graphs.

The last one is called an Archimedes spiral and it's what I used to graph my zentangle pattern. My original attempt on my TI-Nspire graphing calculator looked like this.

I increased the number of revolutions and also increased the step size (how often the calculator puts a point and since I increased the step size, it puts the point less frequently). This made the spiral less smooth. To get the original graph that looks like Rick's paradox, I did 80 revolutions and used a step size of 6.5. Using a simple polar equation r = Θ, I was able to create a replica of Rick's paradox. Pretty cool!

And here is an old zentangle piece I did using only Rick's paradox..

I hope do more math-inspired art this week! Stay tuned!


  1. Angelcake! Welcome back, sort of! Math and art, huh? It must be wonderful to be able to use both sides of your brain! I must say that I don't understand any of this. I loathe math and I love art and I can't do either. Does this mean that I use neither side of my "brain"? I'm so glad that you are enjoying yourself. <3 <3


    1. Lol, Deedles! I'm sure your brain is always working overtime! I'm hoping for some non-math related art this week too.. 😊

  2. Firstly. This was one of the mist ontetesting posts i have ever read. 2nd its so good to hear your voice again and to know you are finding your math/teaching sea legs again. 3rd the graphic is beautiful and i guess i have to admit that there is beauty in math after all. Lol. Dont disapeat again!

    1. Thanks, Suzala! I'm finding it difficult to balance my work, family and my art.. I'm hoping I won't be gone for so long again.. ❤️

  3. It is so cool how your love of art and math intersect. Glad to read your posts again. :)