A367480 Decimal expansion of the radius of a common circle surrounded by seven tangent unit circles.

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

Table of n, a(n) for n=1..105.

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.

Cf. A121570, A188582, A246724.

Sequence in context: A210878 A355977 A356581 * A320373 A303274 A199608

Adjacent sequences: A367477 A367478 A367479 * A367481 A367482 A367483

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