OFFSET
0,4
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
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.
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
EXAMPLE
sqrt(5)/20 = 0.111803398874989484820458683436563811772...
sqrt(5)/2 = 1.118033988749894848204586834365638117720...
MATHEMATICA
RealDigits[1/Sqrt[80], 10, 120][[1]] (* Harvey P. Dale, May 01 2012 *)
PROG
(PARI) sqrt(1/80) \\ Charles R Greathouse IV, Apr 25 2016
CROSSREFS
KEYWORD
AUTHOR
STATUS
approved