

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
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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 nonconstructible (see A246724, A188582, and A121570 for n=3, 4, 5).


LINKS



FORMULA

Equals 1 / sin(Pi/7)  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



AUTHOR



EXTENSIONS



STATUS

approved



