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

Author

N. J. A. Sloane

Keywords

• nonn
• cons
• easy

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

Surface area of a gyroelongated square bipyramid (Johnson solid J_17) with unit edges. - Paolo Xausa, Aug 02 2025

Examples

			6.928203230275509174109785366023489467771221015241522512223227917807732...
		

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
• Wikipedia, Gyroelongated square bipyramid.
• Index entries for algebraic numbers, degree 2

Crossrefs

Cf. A040041 (continued fraction).

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

Programs

Mathematica

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

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

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