Riemann Surface

The Auger (Riemann Surface)
By: Colston DiBlasi
Math 401 Mathematics Through 3D Printing
George Mason University
10/29/19

This I call the Auger. This is a Riemann Surface. The reason why I call this the auger is because its round shape reminds me of a lawn auger on the lawn. This print uses complex variables and complex functions. 

The definition for a Riemann surface is a surface-like configuration that covers the complex plane with several, and in general infinitely many, "sheets." These sheets can have very complicated structures and interconnections. Riemann surfaces are one way of representing multiple-valued functions; another is branch cuts. 

The function that I used was z^(1/4). This is what the code looked like.

When writing the code to print some struggles that I encountered the majority of my problems. The main problem that I encountered was when trying to figure out how to get the thickness increases. This was a problem because it seemed like when I increase it .1 it would drastically change the thickness to where you couldn’t see the individual surfaces. Another problem was trying to get my print time down. When I printed it vertically it was over 8 hours long. I figured out that if I turned the entire thing and printed it on its side that it cut the print time down to around 2.5 hours. I did print it on a raft on the makers bot. It was a little rough when the print came out but all in all it turned out well. This is what my final print looked like.

 

 A good site to look at different Riemann Surface graphs is https://en.wikipedia.org/wiki/Riemann_surface.