John Cook’s neat surface example

Yesterday John Cook shared a neat multivariable calculus idea through his “Analysis Fact” twitter feed:

He shared the equation for the function in his blog post and I was able to create a 3d printable version in Mathematica (using the totally secret / undocumented option “Extrusion” in Plot3D. Shhhhhh . . . don’t tell anyone).

3d Plot

The print came out so well that I couldn’t resist filming it while it was still on the build plate:

Here’s a better look at the print after I cleaned it up a bit:

Definitely a fun surface to see. I was pretty surprised by how steep it was when it printed – it looks much flatter when you see it on the screen in Mathematica. Cook’s example could be a fun way to introduce multivariable caluculus students to the strange world / strange properties of 2d surfaces.