# Hyperbolic Paraboloid Inspiration

Inspired by a link from here, I just sent my multivariable calculus kids an email.

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Hi all,

I ran across something so neat I wanted to share it with you immediatamente! Google the “Philips Pavilion” — either in regular Google or Google Images. A stunning building.

Also, a mathematical building. HELLO HYPERBOLIC PARABOLOID!

I love this model that someone, somewhere built. I mean, it’s simple enough that one of you could build it. And the best part is… You can talk about the math and PROVE that the mesh forms a hyperbolic paraboloid. Anyway, and idea for a final project.

Last year I worked with Ms. TEACHER on a simpler problem — given this set of lines, what curve does this trace out:

In other words, what’s the equation of the blue line:

(In case you cared, we got $y=\frac{(\sqrt{5x}-5)^2}{5}$ using some nice calculus.)

In any case, I see this as the 3D extension to that problem.

So keep it in mind for your final project.

Best,
Mr. Shah