Imaginary Numbers Are Real [Part 13: Riemann Surfaces]

It took over a year, but the Imaginary Numbers Series is finally complete. By far the most labor intensive parts were part 1 and part 13. When I began the series I had no idea where it would end up. I originally planned on 6 parts, but the deeper I got into imaginary numbers, the cooler things got - and I just couldn't deal with telling an incomplete story. 

I couldn't be happier with where the series ended up - I'm so happy I was able to talk about Riemann Surfaces. I'm sure a mathematician or two will take issue with my presentation (there's a reason Riemann Surface are a graduate level mathematics topic!), but I hope I was able to give a broad audience a taste for these beautiful mathematical structures without oversimplifying the meaning out of things.

I wanted to share a few of the visualizations I used in Part 13. I used the wonderful visualization tool plotly for all 3D graphics. Here are a few visualization from Part 13:

Riemann Surface for \(w=\sqrt{z}\) 

Paths on Riemann Surface. This one's a bit slow, it takes lots of points to make that path!

3D surface plot from opening scene. 

Thanks for watching!