A395466 - OEIS

%I #10 Apr 25 2026 10:47:40

%S 1,4,2,0,3,1,5,2,6,3,3,3,0,8,5,1,1,2,6,8,9,7,9,3,9,0,6,5,6,1,4,3,1,9,

%T 6,1,1,4,1,0,5,6,6,5,2,5,2,0,1,5,4,9,3,7,2,1,1,6,1,7,5,8,5,0,8,2,6,7,

%U 4,8,3,8,7,1,9,5,1,3,9,5,9,5,4,5,9,0,5,7,5,6,1,2,6,5,3,3,0,2,9,8,3,5,3,2,3

%N Decimal expansion of the area of the constructible squarable lune whose circular arcs have central angles in a 3:2 ratio and common chord of unit length.

%C One of the five constructible squarable lunes. It was discovered by Hippocrates of Chios in the 5th century BC.

%C Called the "concave pentagon lune" by Shelburne (2005).

%C See A395465 for details, references and more links.

%H Amiram Eldar, <a href="/A395466/a395466.png">Illustration</a>.

%H Mikhail Mikhailovich Postnikov, <a href="https://www.jstor.org/stable/2589121">The Problem of Squarable Lunes</a>, The American Mathematical Monthly, Vol. 107, No. 7 (2000), pp. 645-651. Translated from Russian by Abe Shenitzer.

%H Brian J. Shelburne, <a href="https://bshelburne.wittenberguniversity.org/TheFiveLunes120408.pdf">The Five Quadrable (Squarable) Lunes</a>, Wittenberg University Springfield, 2005.

%H <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.

%F Equals sqrt((69 - 11*sqrt(33))/2)/12.

%F Equals f(3*theta) - f(2*theta), where theta = A395470, and f(x) = x/sin(x)^2 - cot(x)/4.

%F Minimal polynomial: 432*x^4 - 207*x^2 + 4.

%e 0.142031526333085112689793906561431961141056652520154...

%t RealDigits[Sqrt[(69 - 11*Sqrt[33])/2]/12, 10, 120][[1]]

%o (PARI) sqrt((69 - 11*sqrt(33))/2)/12

%Y Cf. A395465, A395467, A395468, A395469, A395470, A395471, A395472.

%K nonn,cons

%O 0,2

%A _Amiram Eldar_, Apr 24 2026