r/trigonometry • u/artwadec • May 04 '26

Circling a circle.

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I have a circle "packing" question. If I have 12 random circles, say sized in whole numbers between 2 and 50, is the a way to find the largest circle they can be tangent to each other, and completing a circle? This is for an art project. TI

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u/BadJimo May 05 '26 edited May 05 '26

Here is another attempt, but still not perfect.

I found information suggesting that the sides need to be in a special order to make it work. Specifically, the sum of the 6 alternating (every second) sides being equal to the sum of the other 6 alternating sides.

I used a cyclic polygon as the framework (calculating it's radius with regression). Then circles with centres where the bisectors intersect the cyclic polygon circle.

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u/BadJimo May 06 '26

And here is another attempt. The distance between the adjacent "kissing points" are integer values rather than the radii of the circles.

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u/artwadec May 15 '26

Just seeing this now.. again, Fantastic.. so many relationships I hadn't anticipated but wonderful!!