A279037 Decimal expansion of the total area of Ford circles.

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

Offset: 0

Author

Jean-François Alcover, Dec 04 2016

Keywords

• nonn
• cons

Comments

Named after the American mathematician Lester Randolph Ford, Sr. (1886-1967). - Amiram Eldar, Jun 24 2021

Examples

			0.8722840410656279761751975321712258706402777808899330325203521...
		

Links

• L. R. Ford, Fractions, The American Mathematical Monthly, Vol. 45, No. 9 (1938), pp. 586-601.
• Wieslaw Marszalek, Circuits with Oscillatory Hierarchical Farey Sequences and Fractal Properties, Circuits Syst Signal Process, Vol. 31 (2012), pp. 1279-1296.
• Eric Weisstein's World of Mathematics, Ford Circle.
• Wikipedia, Ford circle.

Crossrefs

Cf. A000010, A002117, A013662.

Programs

Mathematica

RealDigits[Pi/4 * Zeta[3]/Zeta[4], 10, 107][[1]]

PARI

Pi/4 * zeta(3)/zeta(4) \\ Michel Marcus, Dec 04 2016

Formula

Equals (Pi/4) * Sum_{n >= 1} EulerPhi(n)/n^4.

Equals (Pi/4) * zeta(3)/zeta(4).

Equals 45*zeta(3) / (2*Pi^3).