|
|
A126774
|
|
Decimal expansion of volume of the Weeks manifold.
|
|
0
|
|
|
9, 4, 2, 7, 0, 7, 3, 6, 2, 7, 7, 6, 9, 2, 7, 7, 2, 0, 9, 2, 1, 2, 9, 9, 6, 0, 3, 0, 9, 2, 2, 1, 1, 6, 4, 7, 5, 9, 0, 3, 2, 7, 1, 0, 5, 7, 6, 6, 8, 8, 3, 1, 5, 9, 0, 1, 4, 5, 0, 6, 7, 7, 5, 7, 5, 2, 9, 3, 4, 1, 8, 2, 7, 7, 4, 1, 5, 7, 2, 1, 0, 3, 1, 2, 3, 1, 5, 6, 7, 2, 6, 4, 3, 3, 3, 3, 0, 3, 5, 8, 0, 4, 1, 8, 0
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
Gabai, Meyerhoff and Milley show that the Weeks manifold is the unique closed orientable hyperbolic 3-manifold of smallest volume. This constant gives the volume. - Jeremy Tan, Nov 19 2016
|
|
LINKS
|
|
|
FORMULA
|
Formula: Im(dilog(z0)+log(|z0|)*log(1-z0)) where z0 = 0.8774.. + 0.7448..i is the root of z^3-z^2+1 with Im(z)>0. - Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 15 2007
|
|
EXAMPLE
|
0.9427073627769277209212996030922116475903...
|
|
MATHEMATICA
|
z0 = Roots[z^3 - z^2 + 1 == 0, z][[3, 2]]; RealDigits[ Im[ PolyLog[2, z0] + Log[ Abs[ z0]] Log[1 - z0]], 10, 111][[1]] (* Robert G. Wilson v, Nov 19 2016 *)
|
|
PROG
|
(PARI) z0=polroots(z^3-z^2+1)[3]; imag(dilog(z0)+log(abs(z0))*log(1-z0)) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 15 2007
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 15 2007
|
|
STATUS
|
approved
|
|
|
|