A395472 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.

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, 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, 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

Offset

0,1

Comments

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.

See A395465 for details, references and more links.

Links

Table of n, a(n) for n=0..104.

Amiram Eldar, Illustration.

Mikhail Mikhailovich Postnikov, The Problem of Squarable Lunes, The American Mathematical Monthly, Vol. 107, No. 7 (2000), pp. 645-651. Translated from Russian by Abe Shenitzer.

Index entries for transcendental numbers.

Formula

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

Example

0.293109197301404358232893099155098839281045160270675...

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A339203 A179451 A124918 * A348763 A011240 A021345

Adjacent sequences: A395469 A395470 A395471 * A395473 A395474 A395475

Keyword

nonn,cons

Author

Amiram Eldar, Apr 24 2026

Status

approved