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 A233700 Decimal expansion of 1/sin(arctan(1/t)) or t/sin(arctan(t)) where t = 2*Pi: hypotenuse for a right triangle of equal area to a disk. 1
 6, 3, 6, 2, 2, 6, 5, 1, 3, 1, 5, 6, 7, 3, 2, 8, 3, 9, 3, 6, 9, 1, 2, 4, 5, 4, 4, 0, 5, 8, 6, 8, 0, 4, 4, 1, 0, 6, 9, 9, 7, 1, 4, 9, 8, 5, 1, 3, 8, 9, 8, 9, 6, 8, 6, 5, 8, 2, 0, 4, 1, 6, 1, 7, 0, 4, 5, 9, 9, 8, 5, 8, 7, 3, 3, 1, 7, 8, 4, 8, 5, 4, 1, 3, 4, 5, 5, 0, 8, 7, 7, 1, 3 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS "The great mathematician Archimedes used the tools of Euclidean geometry to show that the area inside a circle is equal to that of a right triangle whose base has the length of the circle's circumference and whose height equals the circle's radius in his book Measurement of a Circle." (Quote from Wikipedia link) LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 Wikipedia, Area of a disk: Triangle method FORMULA Equals sqrt(1+(2*Pi)^2) = sqrt(1 + (A019692)^2) = sqrt(1 + A212002) = 1/sin(A233527) = A019692/sin(A233528) = 1/cos(A233528) = A019692/cos(A233527). EXAMPLE 6.362265131567328393691245440586804410699714985138989686582041617045998587331... MATHEMATICA RealDigits[(2*Pi)/Sin[ArcTan[2*Pi]], 10, 120][] (* Harvey P. Dale, Jul 12 2014 *) RealDigits[ Sqrt[1 + 4*Pi^2], 10, 111][] (* Robert G. Wilson v, Mar 12 2015 *) PROG (PARI) sqrt(1+(2*Pi)^2) (MAGMA) C := ComplexField(); Sqrt(1 + 4*Pi(C)^2) // G. C. Greubel, Jan 08 2018 (MAGMA) R:=RealField(110); SetDefaultRealField(R); n:=Sqrt(1+4*Pi(R)^2); Reverse(Intseq(Floor(10^108*n))); // Bruno Berselli, Mar 13 2018 (Julia) using Nemo RR = RealField(310) t = const_pi(RR) + const_pi(RR) t/sin(atan(t)) |> println # Peter Luschny, Mar 13 2018 CROSSREFS Cf. A233527, A019692, A233528. Sequence in context: A143506 A248580 A008567 * A195436 A194625 A165065 Adjacent sequences:  A233697 A233698 A233699 * A233701 A233702 A233703 KEYWORD nonn,cons,nice AUTHOR John W. Nicholson, Dec 16 2013 STATUS approved

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Last modified November 27 01:16 EST 2021. Contains 349344 sequences. (Running on oeis4.)