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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re(4): soln

Comment 9 of 9 |

(In reply to re(3): soln by Jer)

Jer,

Thank you again. The broken "here" link was actually a typo. Fixed. "Here" was written simply as meant (i.e. I do not know any proof of why this arrangement is optimal, although the citation for Erich Friedman '99 might hold the answer.)

Edited on December 1, 2018, 10:49 am

Posted by Steven Lord on 2018-12-01 10:42:51

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