OFFSET
0,1
COMMENTS
The largest disk that can be covered by six unit disks has radius 1/r = 1.79886782...
Piezas (see Mathematics Stack Exchange link) notes that the minimal polynomials for both this constant and A133077 have unsolvable Galois groups.
LINKS
Erich Friedman, Circles Covering Circles
Jeremy Tan, What is the exact value of the radius in the Six Disks Problem?, Mathematics Stack Exchange, Feb 15 2018
Jeremy Tan, Python/Singular program
Eric Weisstein's World of Mathematics, Disk Covering Problem
FORMULA
r is the smallest positive root of 7841367r^18 - 33449976r^16 + 62607492r^14 - 63156942r^12 + 41451480r^10 - 19376280r^8 + 5156603r^6 - 746832r^4 + 54016r^2 + 3072.
EXAMPLE
0.55590521141658870482629555069659...
MATHEMATICA
First@ RealDigits@ N[Root[7841367x^18 -33449976x^16 +62607492x^14 -63156942x^12 +41451480x^10 -19376280x^8 +5156603x^6 -746832x^4 +54016x^2 +3072, x, 3], 102]
PROG
(PARI) polrootsreal(7841367*x^18 -33449976*x^16 +62607492*x^14 -63156942*x^12 +41451480*x^10 -19376280*x^8 +5156603*x^6 -746832*x^4 +54016*x^2 +3072)[3]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jeremy Tan, Feb 16 2018
STATUS
approved