John Cook’s neat surface example

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

A function with two local maxima and no other critical points.https://t.co/AQ5hAqzUMO pic.twitter.com/Cx5l7lchoq

— Analysis Fact (@AnalysisFact) October 4, 2017

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).

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

3d print of @JohnDCook ‘s surface with two local maximums but no local minimums cc: @AnalysisFact pic.twitter.com/hyBC2aAVbY

— Mike Lawler (@mikeandallie) October 5, 2017

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.