A343392 - OEIS

%I #24 Aug 31 2024 12:39:03

%S 8,8,8,5,7,6,5,8,7,6,3,1,6,7,3,2,4,9,4,0,3,1,7,6,1,9,8,0,1,2,1,3,8,7,

%T 3,9,7,2,2,9,2,4,3,3,7,8,7,5,1,3,8,0,4,4,6,1,7,0,7,9,1,2,1,3,9,1,2,8,

%U 6,9,5,8,6,1,9,8,9,4,7,8,2,1,1,5,0,6,5,3,8,6,9

%N Decimal expansion of 2*Pi*sqrt(2).

%C Circumference of the circumcircle of the square whose sides = 2.

%C Hypotenuse of the right isosceles triangle with the two legs = 2*Pi.

%C Perimeter of the closed curve with implicit Cartesian equation x^2 + y^2 = abs(x) + abs(y). This curve in the first quadrant is the half-circle with equation (x-1/2)^2 + (y-1/2)^2 = 1/2, hence, the curve is the union of 4 identical half-circles with diameter = sqrt(2) obtained by symmetries. (See link Curve.)

%C S. Ramanujan produced a curious approximation to 2*Pi*sqrt(2) by dividing 99^2 by 1103 (see link Prime Curios! and A343393).

%D David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 54.

%H Chris K. Caldwell and G. L. Honaker, Jr., <a href="https://primes.utm.edu/curios/page.php?short=1103">1103, 1st comment</a>, Prime Curios!

%H Bernard Schott, <a href="/A343392/a343392.jpg">Curve x^2+y^2 = abs(x)+abs(y)</a>.

%H <a href="/index/Cu#curves">Index to sequences related to curves</a>.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%F 2*Pi*sqrt(2) = A019692 * A002193 = A010466 * A000796 = 2 * A063448.

%e 8.88576587631673249403176198012138739722924337875138044617

%p evalf(2*Pi*sqrt(2),120);

%t RealDigits[2*Sqrt[2]*Pi, 10, 100][[1]] (* _Amiram Eldar_, Apr 13 2021 *)

%Y Cf. A000796, A002193, A010466, A019692, A063448, A343393.

%K nonn,cons

%O 1,1

%A _Bernard Schott_, Apr 13 2021