A395472 - OEIS

%I #7 Apr 25 2026 10:17:13

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

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

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

%N Decimal expansion of the angle theta (in radians) such that 5*theta and 3*theta are the half central angles of the circular arcs of a constructible squarable lune.

%C The angle in degrees is 16.793... . The two half central angles are 5*theta = 1.465... = 83.969... degrees, and 3*theta = 0.879... = 50.381... degrees.

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

%H Amiram Eldar, <a href="/A395468/a395468.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 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%F Equals arccos((sqrt(5/3) - 1 + sqrt(20/3 + sqrt(20/3)))/4)/2.

%e 0.293109197301404358232893099155098839281045160270675...

%t RealDigits[ArcCos[(Sqrt[5/3] - 1 + Sqrt[20/3 + Sqrt[20/3]])/4]/2, 10, 120][[1]]

%o (PARI) acos((sqrt(5/3) - 1 + sqrt(20/3 + sqrt(20/3)))/4)/2

%Y Cf. A395465, A395466, A395467, A395468, A395469, A395470, A395471.

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Apr 24 2026