A395470 Decimal expansion of the angle theta (in radians) such that 3*theta and 2*theta are the half central angles of the circular arcs of a constructible squarable lune.

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

Offset

0,1

Comments

The angle in degrees is 26.812... . The two half central angles are 3*theta = 1.403... = 80.437... degrees, and 2*theta = 0.935... = 53.624... 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(33)-1)/8)/2.

Equals arcsin(sqrt(9-sqrt(33))/4).

Example

0.467964727830662986803279867689423001766006742525581...

Mathematica

RealDigits[ArcCos[(Sqrt[33] - 1)/8]/2, 10, 120][[1]]

Prog

(PARI) acos((sqrt(33)-1)/8)/2

Crossrefs

Cf. A395465, A395466, A395467, A395468, A395469, A395471, A395472.

Sequence in context: A363375 A382107 A269330 * A213627 A225871 A288383

Adjacent sequences: A395467 A395468 A395469 * A395471 A395472 A395473

Keyword

nonn,cons

Author

Amiram Eldar, Apr 24 2026

Status

approved