perplexus.info :: Geometry : 5 circles in a hexagon.

5 circles in a hexagon. (Posted on 2018-11-25)

Pack five unit circles in the smallest regular hexagon possible.

The exact solution for the smallest possible side length of the hexagon is given by the largest real root of a fourth degree polynomial:

P(x)=ax⁴+b√(3)x³+cx²+d√(3)x+e

Where a,b,c,d,e are integers. Find them.

No Solution Yet Submitted by Jer

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Picturing it.....

| Comment 1 of 9

On the internet I found a drawing of the figure. The side length (root) is given as well, but not the polynomial nor its derivation. For me, this is a good place to start, but one might also fairly regard this as a spoiler:

https://www2.stetson.edu/~efriedma/cirinhex/

Edited on November 25, 2018, 11:01 am

Posted by Steven Lord on 2018-11-25 10:56:17

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