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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 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

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