Wikipedia:Reference desk/Archives/Mathematics/2014 March 22

= March 22 =

OEIS text
I have great difficulty interpreting the comment text given with OEIS entries. Take for example http://oeis.org/A086089 which is " Decimal expansion of 3*sqrt(3)/(2*Pi). " and says:

"

OFFSET 0,1 COMMENTS Limiting ratio of areas in the disk-covering problem.

From Daniel Forgues, May 26 2010: (Start)

Consider: A060544, Centered 9-gonal (or nonagonal) numbers, starting with

a(1)=1, P_c(9, n), n >= 1. Every third triangular number, starting with a(1)=1, P(3, 3n-2), n >= 1. Then:

1/(sum_{n=0..infinity} 1/binomial(3n+2,2)) = 1/(sum_{n=1..infinity} 1/binomial(3n-1,2)) = 1/(sum_{n=1..infinity} 1/P_c(9,n)) = 1/(sum_{n=1..infinity} 1/P(3,3n-2)) = 1/(sum_{n=1..infinity} 1/A060544(n)) = this constant. (End)

Also, decimal expansion of product_{n>=1} (1 - 1/(3n)^2). [Bruno Berselli, Apr 02 2013] LINKS Table of n, a(n) for n=0..101. EXAMPLE 0.8269933431326880742669897474694541620960797205499609791990... MATHEMATICA  RealDigits[3 Sqrt[3]/(2 Pi), 10, 110]1 (* or, from the third comment: *) RealDigits[N[Product[1 - 1/(3 n)^2, {n, 1, Infinity}], 110]]1 (* Bruno Berselli, Apr 02 2013 *)

"

I understand that this series is that value (though why one would want that value I'm not sure...) and that the value is approximated in the EXAMPLE.

But why has it anything to do with disk covering? What are nonagonal numbers and why are they relevant? And what does the Consider part from 'start' to 'end' actually say - I can't read the formulae in this ascii presentation.

-- SGBailey (talk) 16:46, 22 March 2014 (UTC)


 * Disk covering problem links to http://mathworld.wolfram.com/DiskCoveringProblem.html which has the number at the bottom. We also have an article about centered nonagonal numbers: 1, 10, 28, 55, 91, ... Let s = sum of the reciprocals of the centered nonagonal numbers = 1/1 + 1/10 + 1/28 + 1/55 + 1/91 + ... Then 1/s = 3*sqrt(3)/(2*Pi). Mathematicians often want to know the sum of the reciprocals of a sequence. PrimeHunter (talk) 19:40, 22 March 2014 (UTC)
 * One thing is OEIS tries to use ascii for mathematical notation, which takes some getting used to. Another is that OEIS is a reference work for people who already know the subject, so it doesn't explain jargon or specialized notation. Also, like many reference works, it has information that is useful to some but gibberish to others, for example Mathematica scripts are cryptic unless you happen to be a Mathematica user. In other words, treat it like a buffet: Take what you understand and leave the rest. --RDBury (talk) 17:40, 23 March 2014 (UTC)