|
%I #82 Jan 25 2024 07:42:39
%S 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,
%T 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,
%U 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
%N Decimal expansion of the radius of a common circle surrounded by seven tangent unit circles.
%C The radius of a common circle surrounded by n tangent unit circles (n > 2) is r = 1/sin(Pi/n) - 1.
%C 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).
%H Andrew M. Gleason, <a href="https://doi.org/10.2307/2323624">Angle Trisection, the Heptagon, and the Triskaidecagon</a>, The American Mathematical Monthly 95, no. 3 (March 1988), pp. 185-194.
%F Equals 1 / sin(Pi/7) - 1.
%F Equals A121598 - 1.
%e 1.3047648709624865052...
%t RealDigits[Csc[Pi/7] - 1, 10, 120][[1]] (* _Amiram Eldar_, Dec 28 2023 *)
%o (PARI) 1/sin(Pi/7) - 1
%Y Cf. A121598.
%Y Cf. A121570, A188582, A246724.
%K nonn,cons,easy
%O 1,2
%A _Thomas Otten_, Dec 23 2023
%E More digits from _Jon E. Schoenfield_, Dec 24 2023
%E Comments edited by _Michal Paulovic_, Dec 26 2023
|
