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 A294968 #37 Sep 08 2022 08:46:20
%S A294968 1,7,7,8,8,2,3,6,4,5,6,6,3,9,2,4,4,5,0,8,5,8,3,3,4,8,2,0,4,1,5,0,2,6,
%T A294968 7,6,0,7,6,5,0,1,7,3,7,2,9,5,2,5,7,8,5,4,4,0,7,9,2,2,8,5,1,0,5,0,8,1,
%U A294968 8,3,5,3,5,4,5,4,7,6,7,2,3,1,0,6,4,7,0,1,9,7,1,1,0,7,9,9,9,5
%N A294968 Decimal expansion of sqrt(7 + 4*sqrt(2))/2.
%C A294968 A construction of this length using a circle of radius of 1 (length unit) and the circumscribed and inscribed square as well as a square in the middle between them is given in figure 15 of the footnote 13 on p. 26 of M. Gardner's book. Point A is on the middle of one side, say the left, of the middle square and point B is at the intersection of the prolonged right side of the inscribed square with the middle square. Then the length AB is sqrt(AC^2 + CB^2) with point C on the middle of the right side of the inscribed square. AC = (2 - sqrt(2))/4 and CB = 1/sqrt(2) + (2 - sqrt(2))/2 = (2 + sqrt(2))/4. Therefore, AB = sqrt(7 + 4*sqrt(2))/2. See the link.
%C A294968 This is a not a good approximation to the squaring of the circle problem: (AB)^2 is not Pi, or AB = 1.778... is not sqrt(Pi) = A002161 = 1.772... Gardner writes that he was told "of an extremely good approximation".
%C A294968 An elegant construction for the reflexible Archimedean solids was devised by Alicia Boole Stott. In the process called expansion, certain sets of elements (i.e., edges or faces) are moved directly away from the center, retaining their size and orientation, until the consequent interstices can be filled with new regular faces. The reverse process is called contraction. The final edge length is the same as that of the starting solid. By contracting the truncated cube according to its triangles, the cuboctahedron is obtained. (Cf. W. W. Rouse Ball, H. S. M. Coxeter, Mathematical recreations and essays, pp. 139-140.) The factor of this contraction is 1/{a(n)} = (2/17)*sqrt(119-68*sqrt(2)) = 0.56216927542964050970... - _Martin Renner_, Dec 31 2019
%D A294968 Martin Gardner, Logic Machines and Diagrams, Second Ed., 1982, The Harvester Press, p. 26, Figure 15.
%D A294968 W. W. Rouse Ball, H. S. M. Coxeter, Mathematical recreations and essays, New York, Dover, 13th ed., 1987, pp. 139-140 (Mrs. Stott's Construction), fig. 3.
%H A294968 G. C. Greubel, <a href="/A294968/b294968.txt">Table of n, a(n) for n = 1..10000</a>
%H A294968 Alicia Boole Stott, <a href="https://www.dwc.knaw.nl/DL/publications/PU00011492.pdf">Geometrical deduction of semiregular from regular polytopes and space fillings.</a> In: Verhandelingen der Koninklijke Akademie van Wetenschappen, section 1, part 11, nr. 1. Amsterdam, Müller 1910, pp. 3-24.
%H A294968 Wolfdieter Lang, <a href="/A294968/a294968_1.pdf">Some poor approximation of sqrt(Pi).</a>
%e A294968 1.778823645663924450858334820415026760765017372952578...
%t A294968 RealDigits[Sqrt[7 + 4*Sqrt[2]]/2, 10, 100][[1]] (* _G. C. Greubel_, Sep 30 2018 *)
%o A294968 (PARI) sqrt(7+4*sqrt(2))/2 \\ _Felix Fröhlich_, Nov 16 2017
%o A294968 (Magma) SetDefaultRealField(RealField(100)); Sqrt(7+4*Sqrt(2))/2; // _G. C. Greubel_, Sep 30 2018
%K A294968 nonn,cons
%O A294968 1,2
%A A294968 _Wolfdieter Lang_, Nov 16 2017