This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A194940 #58 Feb 16 2025 08:33:15 %S A194940 2,8,4,4,5,8,5,5,0,4,0,9,8,0,1,8,7,8,1,5,9,2,0,1,0,1,8,1,2,6,9,3,1,7, %T A194940 4,5,3,3,0,0,5,2,8,3,0,7,8,9,4,6,2,6,9,8,0,4,5,8,7,7,5,0,0,3,0,1,1,8, %U A194940 9,8,9,5,8,4,8,2,9,2,3,9,7,5,3,8,6,9,4,7,2,3,6,0,6,2,2,7,2,2,1,4,6,7,6,4,6,1,7,2,4,4,7 %N A194940 The Square Peg in the Round Hole constant. %C A194940 Given a unit circle and a square of equal area, what is the amount of the square peg shavings (or filings) which would allow the peg to be inserted into the circle? It turns out to be not quite two sevenths. %D A194940 Daniel Zwillinger, Editor, CRC Standard Mathematical Tables and Formulae, 31st Edition, Chapman & Hall/CRC, Boca Raton, Section 4.6.6 Circles, page 334 & figure 4.18, 2003. %H A194940 G. C. Greubel, <a href="/A194940/b194940.txt">Table of n, a(n) for n = 0..10000</a> %H A194940 1728 Software Systems, <a href="http://www.1728.org/circsect.htm">Circle Sector, Segment, Chord and Arc Calculator</a>. %H A194940 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CircularSegment.html">Circular Segment</a>. %H A194940 Wikipedia, <a href="http://en.wikipedia.org/wiki/Square_peg_in_a_round_hole">Square peg in a round hole</a>. %H A194940 Wikipedia, <a href="http://en.wikipedia.org/wiki/Squaring_the_circle">Squaring the circle</a>. %H A194940 Wikipedia, <a href="http://upload.wikimedia.org/wikipedia/commons/thumb/a/a7/Squaring_the_circle.svg/2000px-Squaring_the_circle.svg.png">Diagram of the problem</a>. %F A194940 Area = 4*arccos(sqrt(Pi)/2) - sqrt(Pi*(4-Pi)). %F A194940 Area = Pi + sqrt(2*Pi(2 - sqrt(Pi*(4 - Pi)))) - 4*arcsin(sqrt(Pi/4)). - _Robert G. Wilson v_, Mar 19 2014 %e A194940 0.28445855040980187815920101812693174533005283078946269804587750... %t A194940 RealDigits[ 4*ArcCos[ Sqrt[Pi]/2] - Sqrt[ Pi(4 - Pi)], 10, 111][[1]] %t A194940 RealDigits[Pi + Sqrt[ 2Pi(2 - Sqrt[Pi (4 - Pi)])] - 4 ArcSin[ Sqrt[Pi/4]], 10, 111][[1]] (* _Robert G. Wilson v_, Sep 20 2011 *) %o A194940 (PARI) 4*acos(sqrt(Pi)/2) - sqrt(Pi*(4-Pi)) \\ _G. C. Greubel_, Mar 28 2017 %Y A194940 Cf. A000796, A019704, A127454. %K A194940 cons,nonn %O A194940 0,1 %A A194940 _William H. Richardson_ and _Robert G. Wilson v_, Sep 05 2011