Level sets which are one and two sheeted hyperboloids

For two-variable functions, the level  sets {(x,y): c = f(x,y)} are curves in the plane. For three-variable functions, the level sets {(x,y,z): c = f(x,y,z)} are surfaces in three-space.  This surface show the level surfaces of 

for c = -1, 1. The level sets are hyperboloids of one and two sheets.  It is designed and printed by Chloe Ham, GMU Math Makerlab. 

First laser print: Symmetry group tiling

by Evelyn Sander 

In a foray beyond 3D printing, here is my first test of laser cutting math, cut at the Mason MixLab at Innovation Hall, designed in http://math.hws.edu/eck/js/symmetry/wallpaper.html and prepared as an svg file for laser cutting in Inkscape.

This was inspired by the work shown below by students from last semester Savannah Crawford, who designed it, and Katherine McCabe, who transferred the design to laser format and cut it in acrylic.  This is in my office, and it will soon hang in the department not in my office.

Since it's hard to read the text, I have included it below the photo. 

Tiling the Plane

These laser cut objects are designed by Savannah Crawford and cut by Katherine McCabe, students in Math 401 Fall 2019. The class was taught by Dr. Evelyn Sander with the assistance of Chloe Ham and Colin Chung.

More info: gmumathmaker.blogspot.com

There are 17 distinct symmetry groups which periodically tile the plane 

This dragonfly tiling has symmetry group 4*2. It has one point of rotational symmetry of order 4, and one point of intersecting 2 mirror lines. 

Level surfaces of exp(xyz)

For two-variable functions, the level  sets {(x,y): c = f(x,y)} are curves in the plane. For three-variable functions, the level sets {(x,y,z): c = f(x,y,z)} are surfaces in three-space.  This surface show the level surfaces of exp(xyz) for c=0,1,2,3. It is designed and printed by Colin Chung, GMU Math Makerlab, inspired by a previous version designed by former student Anneliese Slaton which she wrote about on: http://gmumathmaker.blogspot.com/2016/04/level-sets.html

Construct3D 2020

Check out the code from my Construct3D 2020 talk. OpenSCAD and Mathematica tutorials and  files for creating math:

http://math.gmu.edu/~sander/EvelynSite/construct3d2020.html