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
EXAMPLE
6.362265131567328393691245440586804410699714985138989686582041617045998587331...
MATHEMATICA
RealDigits[(2*Pi)/Sin[ArcTan[2*Pi]], 10, 120][[1]] (* Harvey P. Dale, Jul 12 2014 *)
RealDigits[ Sqrt[1 + 4*Pi^2], 10, 111][[1]] (* Robert G. Wilson v, Mar 12 2015 *)
PROG
(PARI) sqrt(1+(2*Pi)^2)
(Magma) C<i> := 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
KEYWORD
AUTHOR
John W. Nicholson, Dec 16 2013
STATUS
approved