login
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
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
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