Riemann Spires

Vincent Vu
December 4th, 2021
George Mason University MATH 401: Mathematics through 3D Printing

These prints represent the real and imaginary parts of the complex function f(z)=csch((1/3)*z^2). The topic of this week’s print was Riemann Surfaces, which helps us visualize multi-valued functions that are 4-dimensional that would otherwise not be possible. There are many ways to use Riemann Surfaces to represent a complex function, such as having two surfaces for the real and imaginary parts (as I did) f(z) or two surfaces for the modulus and arguments of f(z). I ended up going with the real and imaginary parts for my function since it was tedious but still possible to break into real and imaginary parts while not looking possible to do the other way.


The standout of both the real and imaginary surfaces are the spire-like protrusions above and below the base of the surface. These are the poles, which in complex analysis means that the function is undefined at this value and th