Cycloid Curves

During the 2014-15 academic year, I became interested in drawing cycloid curves after receiving an old Spirograph set from my dad. Did you ever own one? At any rate, here are a few images I created in collaboration with David Hartz. They are each about 6×6 cm. On one level, they are about the concept of fading memories. But, on a different level, I was simply enjoying the mathematical simplicity of these geometric objects. For the record, I suppose these aren’t technically cycloids, but trochoids.




After creating the above images, I started exploring the creation of cycloid curves based on convergents from a given continued fraction. I wrote up an article describing this idea and posted it on the Research page. Below are a few examples of cycloids based on continued fractions that I produced using Mathematica 9. The first image corresponds to the continued fraction for 49/20.


The next image corresponds to the continued fraction for 23/18.


The next image corresponds to the continued fraction for 87/37.


Lastly, the next image corresponds to the continued fraction for411/131.411over131v1