A343392 Decimal expansion of 2*Pi*sqrt(2).

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

Offset

1,1

Comments

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

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

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.)

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

References

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

Links

Table of n, a(n) for n=1..91.

Chris K. Caldwell and G. L. Honaker, Jr., 1103, 1st comment, Prime Curios!

Bernard Schott, Curve x^2+y^2 = abs(x)+abs(y).

Index to sequences related to curves.

Index entries for transcendental numbers.

Formula

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

Example

8.88576587631673249403176198012138739722924337875138044617

Maple

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

Mathematica

RealDigits[2*Sqrt[2]*Pi, 10, 100][[1]] (* Amiram Eldar, Apr 13 2021 *)

Crossrefs

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

Sequence in context: A181122 A023412 A336211 * A343393 A023413 A188727

Adjacent sequences: A343389 A343390 A343391 * A343393 A343394 A343395

Keyword

nonn,cons

Author

Bernard Schott, Apr 13 2021

Status

approved