A020837 Decimal expansion of 1/sqrt(80) = sqrt(5)/20.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• cons

Comments

Multiplied by 100, this is sqrt(125). - Alonso del Arte, Jan 06 2013

Multiplied by 10, this is sqrt(5)/2. As such, it appears in the Pythagorean tree as the ratio of the distance between 2 consecutive square centers divided by the length of the initial square (see CNRS link). - Michel Marcus, Feb 20 2013

The two-dimensional Steinitz constant K_2(0,0), related to sum of vectors, is sqrt(5)/2. - Jean-François Alcover, Jun 04 2014

sqrt(5)/2 is the length of the shortest line segment needed to dissect the unit square into 4 regions with equal areas if all the line segments start at the same vertex of the square. - Wesley Ivan Hurt, May 18 2021

sqrt(5)/2 is the standard deviation of rolling a 4-sided die. - Mohammed Yaseen, Feb 23 2023

Examples

			sqrt(5)/20 = 0.111803398874989484820458683436563811772...
sqrt(5)/2  = 1.118033988749894848204586834365638117720...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.13 Steinitz constants, p. 241.

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• Étienne Ghys and Jos Leys, Un arbre pythagoricien — Images des Mathématiques, CNRS, 2013.
• Index entries for algebraic numbers, degree 2

Crossrefs

c = (1/10)*(A001622 - 1/2) = (1/10)*(7/2 - A079585) = (A176055 - 1)/10.

Programs

Mathematica

RealDigits[1/Sqrt[80], 10, 120][[1]] (* Harvey P. Dale, May 01 2012 *)

PARI

sqrt(1/80) \\ Charles R Greathouse IV, Apr 25 2016

Formula

Equals 1/sqrt(80) = sqrt(5)/20 = (-1 + 2*phi)/20, with phi from A001622.

Equals 0.1 * Sum_{k>=0} binomial(2*k,k)/20^k. - Amiram Eldar, Aug 04 2022