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A367480 Decimal expansion of the radius of a common circle surrounded by seven tangent unit circles. 0
1, 3, 0, 4, 7, 6, 4, 8, 7, 0, 9, 6, 2, 4, 8, 6, 5, 0, 5, 2, 4, 1, 1, 5, 0, 2, 2, 3, 5, 4, 6, 8, 5, 5, 1, 1, 3, 4, 4, 4, 5, 0, 1, 8, 8, 7, 6, 0, 6, 3, 2, 1, 1, 6, 2, 0, 6, 3, 1, 0, 6, 2, 9, 6, 4, 6, 6, 8, 5, 3, 3, 4, 2, 7, 7, 8, 4, 7, 9, 5, 9, 6, 3, 7, 9, 1, 1, 1, 4, 2, 1, 9, 7, 4, 7, 6, 1, 7, 9, 3, 6, 1, 5, 1, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The radius of a common circle surrounded by n tangent unit circles (n > 2) is r = 1/sin(Pi/n) - 1.
n=7 is the smallest number for which the radius cannot be expressed using square roots, since the regular heptagon formed by the centers of the tangent circles is non-constructible (see A246724, A188582, and A121570 for n=3, 4, 5).
LINKS
Andrew M. Gleason, Angle Trisection, the Heptagon, and the Triskaidecagon, The American Mathematical Monthly 95, no. 3 (March 1988), pp. 185-194.
FORMULA
Equals 1 / sin(Pi/7) - 1.
Equals A121598 - 1.
EXAMPLE
1.3047648709624865052...
MATHEMATICA
RealDigits[Csc[Pi/7] - 1, 10, 120][[1]] (* Amiram Eldar, Dec 28 2023 *)
PROG
(PARI) 1/sin(Pi/7) - 1
CROSSREFS
Cf. A121598.
Sequence in context: A210878 A355977 A356581 * A320373 A303274 A199608
KEYWORD
nonn,cons,easy
AUTHOR
Thomas Otten, Dec 23 2023
EXTENSIONS
More digits from Jon E. Schoenfield, Dec 24 2023
Comments edited by Michal Paulovic, Dec 26 2023
STATUS
approved

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Last modified April 14 09:06 EDT 2024. Contains 371657 sequences. (Running on oeis4.)