Hyperboloid of one sheet - with forumla

by dennedesigns, published

Hyperboloid of one sheet - with forumla by dennedesigns Jul 14, 2015

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11747Views 2600Downloads Found in Math


This model shows the hyperboloid of one sheet: x^2+y^2-z^2=1. The equation is imprinted in the surface. There is a second .stl file showing the surface without the equation.

This model was designed and printed by my WLU summer research student Emily Jaekle ('16). For more information see http://mathvis.academic.wlu.edu/2015/07/16/quadratic-surfaces-hyperboloid-of-one-sheet/.


This object was made on a MakerBot2X. We used the following settings:
2 shells
0.20mm layer height
10% infill (hexagonal pattern)
No supports
Raft off

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I tried printing this on a Lulzbot Mini, scaling it by 3.5, but the formula didn't appear as well defined as yours. Is that just a matter of scale (how large is the one in the image), or a limitation of the printer?

Thanks for the feedback. I designed the model to fit in the hand, so scaling by 3.5 probably put things off. However, you've given me a great idea - to design the model in a larger scale. I'm traveling right now, but will get to this in the next couple of weeks.

Thank you for making this model available. Your model was shared in my 3D Printing in the Math Classroom presentation at the Virginia Council of Teachers of Mathematics conference. The full presentation and resources links are available at http://designmaketeach.com/3dmath/

I've also created a collection of useful classroom models. http://www.thingiverse.com/DesignMakeTeach/collections/3d-printing-in-the-math-classroom. Please feel free to share any suggestions or resources that support 3D printing in the math classroom.

Very nice, great work!


If this could be made into a cup that would be awesome.

I'm considering doing something like this for volumes of revolution when I teach Calculus II next fall.....

Man, I wish I had these going through calc III. Cool!

Congrats on being featured! I'm going to pretend that my make helped catch the eye of one of the editors. :)