Mathematical Impressions: Printing 3-D Models
It’s getting easier to make physical models of mathematical objects. This video surveys some examples of surfaces and polytope models. A variety of software packages are used to create a description of the geometry (an “stl file”), which is then sent to a 3-D printer to be fabricated. The software used for these models is:
Many other programs are available and may be useful:
http://reprap.org/wiki/Useful_Software_Packages
http://www.shapeways.com/tutorials/supported-applications
The 3-D printer shown is a Replicator.
Tori parametrically defined as 0 < u < 2Pi, 0 < v < 2Pi:
x = (3 + cos(v)) * sin(u)
y = (3 + cos(v)) * cos(u)
z = sin(v)
x = (3 + 0.2 * cos(20 * u) + cos(v)) * sin(u)
y = (3 + 0.2 * cos(20 * u) + cos(v)) * cos(u)
z = sin(v)
Triply periodic surface:
cos(x) + cos(y) + cos(z) + 3/2 cos(x)cos(y)cos(z) = 0
