|
|
A244921
|
|
Decimal expansion of (sqrt(2)+log(1+sqrt(2)))/3, the integral over the square [0,1]x[0,1] of sqrt(x^2+y^2) dx dy.
|
|
17
|
|
|
7, 6, 5, 1, 9, 5, 7, 1, 6, 4, 6, 4, 2, 1, 2, 6, 9, 1, 3, 4, 4, 7, 6, 6, 0, 1, 6, 3, 9, 6, 4, 9, 6, 7, 9, 5, 8, 6, 5, 9, 4, 4, 0, 6, 7, 8, 7, 9, 5, 2, 7, 8, 2, 7, 9, 7, 6, 6, 5, 8, 4, 4, 8, 8, 8, 1, 3, 6, 9, 8, 8, 7, 5, 6, 1, 3, 7, 7, 7, 0, 8, 8, 9, 4, 6, 9, 8, 1, 4, 2, 0, 7, 9, 2, 9, 9, 2, 0, 5, 1, 9, 7, 2, 5
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
This is also the expected distance from a randomly selected point in the unit square to a corner, as well as the expected distance from a randomly selected point in a 45-45-90 degree triangle of base length 1 to a vertex with an acute angle. - Derek Orr, Jul 27 2014
The average length of chords in a unit square drawn between two points uniformly and independently chosen at random on two adjacent sides. - Amiram Eldar, Aug 08 2020
|
|
LINKS
|
|
|
FORMULA
|
Also equals (sqrt(2) + arcsinh(1))/3.
|
|
EXAMPLE
|
0.76519571646421269134476601639649679586594406787952782797665844888136988756...
|
|
MATHEMATICA
|
RealDigits[(Sqrt[2] + Log[1 + Sqrt[2]])/3, 10, 104] // First
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|