The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A019707

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A019707

Decimal expansion of sqrt(Pi)/5.
(history; published version)

#33 by Michael De Vlieger at Tue Mar 05 16:33:10 EST 2024

STATUS

reviewed

approved

#32 by Alois P. Heinz at Tue Mar 05 15:07:40 EST 2024

STATUS

proposed

reviewed

#31 by Stefano Spezia at Tue Mar 05 14:55:28 EST 2024

STATUS

editing

proposed

#30 by Stefano Spezia at Tue Mar 05 14:55:15 EST 2024

FORMULA

Equals -Gamma(-1/2)/10, where Gamma is Euler's gamma function. _- _Lee A. Newberg_, Mar 05 2024

STATUS

proposed

editing

#29 by Lee A. Newberg at Tue Mar 05 14:54:00 EST 2024

STATUS

editing

proposed

#28 by Lee A. Newberg at Tue Mar 05 14:50:34 EST 2024

COMMENTS

With offset 1 this is the decimal expansion of 2*sqrt(Pi) = 3.544907..., which is -Gamma(-1/2) and which is the smallest possible perimeter index eta=P/sqrt(A) of all figures (not necessarily connected) in the Euclidean plane with a continuous boundary of length P (perimeter) enclosing a finite area A. The smallest value is attained only by a Euclidean planar disk. For example, eta=4 for squares, eta=2(sqrt(a/b)+sqrt(b/a))>=4 for aXb rectangles, and eta=4.559014... (A268604) for equilateral triangles. - Stanislav Sykora, Feb 08 2016

FORMULA

Equals -Gamma(-1/2)/10, where Gamma is Euler's gamma function. Lee A. Newberg, Mar 05 2024

STATUS

proposed

editing

Discussion

Tue Mar 05

14:53

Lee A. Newberg: Thank you @Andrew Howroyd for the suggested edits.  Done.

#27 by Lee A. Newberg at Tue Mar 05 13:47:28 EST 2024

STATUS

editing

proposed

Discussion

Tue Mar 05

14:03

Andrew Howroyd: We don't usually just make such definitional changes on older sequences. This sequence has a b-file, several programs, and is referenced by 7 other sequences. All of this would need to be changed. (you can't just change the offset without fully dealing with all the consequences). So, I think in this case its no - such changes do occasionally happen, but they are not made lightly and probably only where the benefits seem high in relation to the amount of work involved.

14:05

Andrew Howroyd: You really have to accept that many sequences will have definitions that are suboptimal to your way of thinking - its true for everyone.

14:15

Andrew Howroyd: Perhaps rather than silently edit Stanislav Sykora's comment, just add to Formula's. "Equals -Gamma(-1/2)/10." and don't forget to sign with - ~~~~. Your observation will be more useful in the formula's section rather than buried in another's comments.

#26 by Lee A. Newberg at Tue Mar 05 13:42:56 EST 2024

COMMENTS

STATUS

approved

editing

Discussion

Tue Mar 05

13:47

Lee A. Newberg: I don't know whether this is allowed as a matter of policy, but should we also change the offset to be 1?  That is, should this be the decimal expansion for 2*sqrt(pi) rather than for sqrt(pi)/5?  The latter isn't described as remarkable anywhere in the entry, but the former is both a value of Euler's gamma function and a smallest possible perimeter.

#25 by Charles R Greathouse IV at Wed Sep 28 13:54:22 EDT 2022

STATUS

editing

approved

#24 by Charles R Greathouse IV at Wed Sep 28 13:54:19 EDT 2022

LINKS

<a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

PROG

(PARI) sqrt(Pi)/5 \\ Charles R Greathouse IV, Sep 28 2022

STATUS

approved

editing