login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A237558 Decimal expansion of (1/Pi)*arccos(1/sqrt(3)). 0
3, 0, 4, 0, 8, 6, 7, 2, 3, 9, 8, 4, 6, 9, 6, 3, 6, 4, 9, 1, 4, 5, 7, 2, 2, 2, 0, 3, 8, 8, 7, 8, 4, 5, 4, 4, 3, 4, 1, 6, 8, 5, 6, 7, 5, 2, 8, 0, 2, 9, 9, 8, 5, 6, 3, 5, 6, 0, 3, 0, 8, 5, 0, 9, 8, 8, 9, 9, 9, 2, 9, 5, 6, 6, 1, 2, 7, 8, 8, 7, 6, 5, 6, 4, 8, 9, 4, 0, 8, 6, 9, 1, 2, 1, 1, 2, 7, 4, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Known to be irrational. If m is a positive integer (1/Pi)*arccos(1/sqrt(m)) is rational iff m=1,2 or 4.

A constant giving the location (x = y) of the thermodynamic center (also called warmest point or "hot spot") of a unit isosceles right triangle. The thermodynamic center is the warmest point in a convex heat conductor with unitary initial temperature and with boundary grounded at zero temperature. The convex heat conductor here considered is the isosceles right triangle x>0, y>0, x+y <= 1. - Jean-François Alcover, Jul 26 2016

REFERENCES

M. Aigner and G. M. Ziegler, Proofs from The Book, Chap. 7, p. 40, Springer-Verlag, Berlin, 1999.

LINKS

Table of n, a(n) for n=0..98.

Steven R. Finch, In limbo: Three triangle centers, arXiv:1406.0836 [math.HO] 2014 p. 11.

FORMULA

0 < x < 1/2 maximizing sin(Pi x)*sin(2Pi x), that is x = arctan(sqrt(2)) / Pi, solution to sin(Pi x) = 3 sin(3 Pi x). - Jean-François Alcover, Jul 26 2016

EXAMPLE

0.30408672...

MAPLE

arccos(1/sqrt(3))/Pi; evalf(%) ; # R. J. Mathar, Aug 02 2016

MATHEMATICA

Join[{0}, RealDigits[1/Pi ArcCos[1/Sqrt[3]], 10, 120][[1]]] (* Harvey P. Dale, Feb 22 2015 *)

CROSSREFS

Cf. A275336.

Sequence in context: A027636 A173425 A289445 * A060034 A308216 A035544

Adjacent sequences:  A237555 A237556 A237557 * A237559 A237560 A237561

KEYWORD

nonn,cons

AUTHOR

Benoit Cloitre, Feb 09 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 10 12:25 EST 2019. Contains 329895 sequences. (Running on oeis4.)