The Secret Life of y=x²

misc

I just discovered this languishing on my flash drive and thought I’d put it up….

Anyone who’s taken grade-school math is, of course, familiar with the graph y=x² in the real plane.

We quickly move to discussing functions with complex roots, but little effort is put into trying to visualize those roots – thinking in four dimensions is hard, as is visualizing a graph with a 2-dimensional range.

But, being bored in algebra a couple years ago, I decided to graph y=x² on the complex plane and see what would happen. Here’s what it looks like:

The blue surface shows the real part of the solution and the red surface shows the imaginary part.

If that’s still hard to figure out, a video of the above image being rotated to give a better sense of depth.

Nothing terribly new or exciting, but pretty cool for us public school kids without Mathematica licenses.