Imaginary Numbers Are Real [Part 12: Riemann's Solution]

In parts 12 and 13, we get to spend some time inside the head of arguably the most important mathematician of the 19th Century - Bernhard Riemann. We're going to begin our next episode by creating a Riemann Surface from our 2 w-planes. This surface will have the wonderful property of making our colored path continuous! While the full theory of Riemann surfaces is far more complex than we can cover here, the baby Riemann Surface we'll create will be sufficient to elegantly visualize our 4 dimensional multifunction, and explain the weird path behavior we saw in back in part 11. You can download a pdf version of the w-planes here.

Your very own w-planes to cutout!