The Point? Dimensions

“The Point of Evolution” started as a Mathober doodle and led to this GIF.

Dimensions are fun – what do you see? what do you notice?

Side Note: I talk about dimensions when covering combining like terms. One analogy – A 3D banana can’t combine with a 2D banana (or whatever noun seems to go with the variable you have). We have fun with expressions using various animals/objects and their dimensions. Variables (things) and their exponents (dimensions) need to match to be able to combine them.

Moiré GIF: by Opal

My daughter started playing with moiré in procreate after I fiddled with it in a previous post. You know we breathe math in our home. She wanted to share:

Parallel to a Parabola

I received a question today about what curve is parallel to a parabola. I sat for a minute and realized that it wasn’t another parabola. It required parametric equations (at least if you wanted to keep it simple). That of course lead to code:

See the Pen jOqzMJb by Sophia (@fractalkitty) on CodePen.

The parametric equations for the parabola are:

  • x = 2at
  • y = at2

The parallel curve equations are:

  • x = 2at+ct/sqrt(1+t2)
  • y = at2 – c/sqrt(1+t2)


So I doodled and was pleasantly surprised when Sierpinski-like triangles formed. I am sure that a million people have discovered this before me, but I felt like I found a magic portal.

And that lead to coding (of which is currently a mess, and I will post later).

And one more version:

Popping Apollonian Gasket

I doodled this GIF after two days of painting the canvas below. I think I am in the process of preparing for my fall classes and students. Art is definitely an outlet – especially when it’s math + art.