Tangent lines

Tiptoeing into calculus.
February 15, 2019

While getting to know the basics of machine learning, I encountered (unsurprisingly) some notions of calculus. I’m very unfamiliar with calculus but I would very much love to understand it. I have been thinking for a while about devising some small experiments that would allow me to familiarize myself with mathematical concepts in an intuitive way. So this sudden need to understand a bit of calculus seemed like a good opportunity to delve into this.

The animation below is one of those experiments. It helped me to familiarize myself with the notions of limits and tangents. A line is tangent to a circle when its slope is identical to the slope of the circle at the point where they meet. This slope is calculated by taking two different points on the circle, and by then diminishing almost infinitely the distance between those two points. This is what I have done while writing the code for this animation. I was interested in what kinds of shapes I would obtain by playing with these notions, and I ended up with this dense mesh of tangent lines evenly distributed around a circle. And then, why not make the circle morph to see what movements would the mesh end up making?

The code written to make this animation can be found on GitHub. I also created a few variations of the animation using the p5.js web editor. You can find some variations here, here, and here.

Context

This blog post is part of my research project Towards an algorithmic cinema, started in April 2018. I invite you to read the first blog post of the project to learn more about it.