Designing Apollonian Earrings

art
Coding Apollonian circle packings into 3D-printed earrings, and asking Twitter to vote on the final design.
Author

Christopher R. H. Hanusa

Published

May 1, 2020

This post was originally a Twitter thread with three polls; their final results are shown below each poll. See also More Interesting Math Jewelry and An Apollonian Necklace.

I had wanted to create Apollonian jewelry for @hanusadesign but I couldn’t figure out how to code them. During @anniek_p’s #mathartchallenge, @SWCHS_Maths linked to Brent Yorgey’s https://mathlesstraveled.com/2016/04/27/apollonian-gaskets/, so now they exist. The prototypes came from @shapeways and they look great!

Six 3D-printed white Apollonian circle packing pendants on a purple background. The three on the left have a solid outer circle, and the three on the right have no outer circle, so their small circles form a bumpy edge.

Now I need your help to choose the design of the official @hanusadesign earrings! (Polls below.)

First up: Do you like the design better when it has the outer circle (left models) or without the outer circle (right models)?

Poll choice Votes Share
Keep the outer circle! 15 65%
No outer circle! 8 35%

Next up: Do you like the idea of two copies of the same model (a matched pair) or would you prefer the earrings be two different models (a mismatched pair)?

Poll choice Votes Share
Matched Pair 14 56%
Mismatched Pair 11 44%

Last up: I created five different models by starting with different random starting circles.

Five white Apollonian circle packing pendants on a red background, labeled 1 through 5, each generated from different random starting circles

Which design is your favorite? (Oh no! Twitter only allows four choices! I’ll have to consolidate the two most similar ones!)

Poll choice Votes Share
1 4 15%
2 or 4 10 38%
3 4 15%
5 8 31%

Thanks for your votes! May I suggest that you follow @hanusadesign here or on Instagram? And a reminder that to celebrate #mathartchallenge I’m offering 20% off the entire site http://hanusadesign.com with code “mathartchallenge”.

Citation

BibTeX citation:
@online{hanusa2020,
  author = {Hanusa, Christopher R. H.},
  title = {Designing {Apollonian} {Earrings}},
  date = {2020-05-01},
  url = {https://hanusa.xyz/blog/posts/2020-05-01-designing-apollonian-earrings/},
  langid = {en}
}
For attribution, please cite this work as:
Hanusa, Christopher R. H. 2020. “Designing Apollonian Earrings.” May 1. https://hanusa.xyz/blog/posts/2020-05-01-designing-apollonian-earrings/.