A010502 Decimal expansion of square root of 48.

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

Offset

1,1

Comments

sqrt(48)/10 is the area enclosed by Koch's fractal snowflake based on unit-sided equilateral triangle (actually 8/5 times the latter's area). - Lekraj Beedassy, Jan 06 2005

7+sqrt(48) is the ratio of outer to inner Soddy circles' radii for three identical kissing circles (see Soddy circles link). - Lekraj Beedassy, Feb 14 2006

Continued fraction expansion is 6 followed by {1, 12} repeated. - Harry J. Smith, Jun 06 2009

Let a, b, c the sides of a triangle ABC of area S, then 4*sqrt(3) <= (a^2+b^2+c^2) / S; equality is obtained only when the triangle is equilateral (see Mitrinovic reference). - Bernard Schott, Sep 27 2022

References

J. N. Kapur, Mathematics Enjoyment For The Millions, Problem 47 pp. 64-67, Arya Book Depot, New Delhi 2000.

D. S. Mitrinovic, E. S. Barnes, D. C. B. Marsh, J. R. M. Radok, Elementary Inequalities, Tutorial Text 1 (1964), P. Noordhoff LTD, Groningen, problem 6.3, page 112.

Links

Harry J. Smith, Table of n, a(n) for n = 1..20000

L. Riddle, Area of the Koch Snowflake

Bernard Schott, Soddy circles

Index entries for algebraic numbers, degree 2

Formula

Equals 4*A002194. - R. J. Mathar, Jul 31 2010

Equals A176053/A246724 - 7 (2nd comment and Soddy link). - Bernard Schott, Mar 17 2022

Equals 1/A020805. - Bernard Schott, Sep 28 2022

Example

6.928203230275509174109785366023489467771221015241522512223227917807732...

Mathematica

RealDigits[N[Sqrt[48], 200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 24 2011 *)

Prog

(PARI)  default(realprecision, 20080); x=sqrt(48); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010502.txt", n, " ", d));  \\ Harry J. Smith, Jun 06 2009

Crossrefs

Cf. A040041 (continued fraction).

Cf. A002194, A104956, A010527, A152623 (other geometric inequalities).

Sequence in context: A198616 A215668 A344230 * A254292 A188618 A225125

Adjacent sequences: A010499 A010500 A010501 * A010503 A010504 A010505

Keyword

nonn,cons

Author

N. J. A. Sloane

Status

approved