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

Author

Bernard Schott, Apr 13 2021

Keywords

• nonn
• cons

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).

Examples

			8.88576587631673249403176198012138739722924337875138044617
		

References

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

Links

• 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.

Crossrefs

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

Programs

Maple

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

Mathematica

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

Formula

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