Apollonian Cone

by IronOxide, published

Apollonian Cone by IronOxide May 8, 2012
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16041Views 7716Downloads Found in Math


This is a simple design but since I havn't seen one on here I thought I would upload it. This is my first OpenSCAD project. An apollonian cone is a teaching tool to illustrate "conic sections." Starting with a basic cone: a horizontal slice reveals the circle, a slanted horizontal slice reveals the ellipse, a straight vertical cut reveals the hyperbola, and a slanted vertical cut reveals the parabola. Simple, elegant, conversation piece.


I have seen these made out of wood and usually stands about 10-12 inches high with alternating colors (brown/light brown). This should be easily achieved with the print volume available these days. The total cone height here is 5cm.

I have created insets on the inside to leave room for text such as "circle" in the circular section etc. Of course a logo/image can also be used.

The original solid pieces are easily recreated (simply intersect a cone with various boxs) but I will upload all the scad scripts in a zip file. caveat: I used a polyhedron to create the ellipse piece - not recommended! As I said this is my first project and now I know its much easier to create two planes(thin boxes) and hull them together

**Update: The files for the center piece and the SCAD scripts have been updated since original post...

I have hollowed out the center piece even more. This saves on materials and should make it easier/cheaper to print. I have also added a lip to the center piece to be sure the upper levels remain steady.

**Update #2: Text is in...
I have included both sets of stl files. The larger files are the ones with text.

If anyone plans to print it, two alternating colors looks good. (print the ellipse piece upside down - clearly) Would make a great gift for a math teacher. Let me know if you need me to make any adujustments.

Thanks to everyone out there making great tutorials for OpenSCAD!

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I would like permission to share a link to this project and physical examples at my 3D Printing in the Math Classroom presentation at the Virginia Council of Teachers of Mathematics conference. Thank you. -Josh

By all means. Please update me on how that turns out. I am a STEM educator myself and am polishing off my designs for the MakerEdChallenge as we speak.

Cool, reminds me of Donald Duck in Mathmagic Land!

Now we just need a tree with square roots...

"Mathematics? That's for eggheads!" "It is only in the mind that we can conceive infinity"

-A tree with square roots sounds great with the proper support.

-How about the funky looking 3D numbers in the first scene! A whole font could be developed around that awesome artwork.

-If anyone hasn't seen this Disney clip, your missing out. Can't say I agree with Disney's "greeks invented everything" mantra, but hey It's Disney, what do you expect?

" union a lip on the bottom piece to hold it steady " or turn it upside down! I like it. (retired math teacher)