A395466 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.

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, 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, 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

Offset

0,2

Comments

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

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

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.

Brian J. Shelburne, The Five Quadrable (Squarable) Lunes, Wittenberg University Springfield, 2005.

Index entries for algebraic numbers, degree 4.

Formula

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

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

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

Example

0.142031526333085112689793906561431961141056652520154...

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A106220 A176066 A376742 * A309987 A350358 A104689

Adjacent sequences: A395463 A395464 A395465 * A395467 A395468 A395469

Keyword

nonn,cons

Author

Amiram Eldar, Apr 24 2026

Status

approved