ArcTan Riemann Surface

thingiverse

This object embodies a Riemann surface, an intricate and fascinating entity that represents the complex function f(z) = arctan(z). The function's four-dimensional nature seamlessly merges its complex and imaginary parts, rendering Re(z) and Im(z) as the x and y components respectively, while the z component takes on the form (Re(f(z)) + Im(f(z))/2. This ingenious combination allows for a unique visualization of the real and imaginary components of the function's image, both exhibiting asymptotic behavior as |z| increases. Generated using Mathematica, this surface was brought to life, its supports crafted in openSCAD with code provided for both. The STL files were meticulously merged in MeshLab, resulting in a cohesive and intricate final product. This creation was born out of a course at George Mason University, "Math through 3D Printing," under the expert guidance of Dr. Evelyn Sander.