A232717 Decimal expansion of the ratio of the length of the boundary of any arbelos to the length of the boundary of its associated parbelos: Pi / (sqrt(2) + log(1 + sqrt(2))).

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

Offset: 1

Author

Jonathan Sondow, Nov 28 2013

Keywords

• cons
• easy
• nonn

Comments

Same as decimal expansion of Pi/P, where P is the Universal parabolic constant (A103710). - Jonathan Sondow, Jan 19 2015

Examples

			1.36853556373191478886062626593258810842142480010621734905399...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• M. Hajja, Review Zbl 1291.51018, zbMATH 2015.
• M. Hajja, Review Zbl 1291.51016, zbMATH 2015.
• J. Sondow, The parbelos, a parabolic analog of the arbelos, arXiv 2012, Amer. Math. Monthly, 120 (2013), 929-935.
• E. Tsukerman, Solution of Sondow's problem: a synthetic proof of the tangency property of the parbelos, arXiv 2012, Amer. Math. Monthly, 121 (2014), 438-443.

Crossrefs

Reciprocal of A232716. Ratio of areas is A232715.

Cf. A000796, A103710.

Programs

Magma

R:= RealField(); Pi(R)/(Sqrt(2) + Log(1 + Sqrt(2))) // G. C. Greubel, Jul 27 2018

Mathematica

RealDigits[Pi/(Sqrt[2] + Log[1 + Sqrt[2]]),10,100]

PARI

Pi/(sqrt(2) + log(1 + sqrt(2))) \\ G. C. Greubel, Jul 27 2018

Formula

Equals A000796 / A103710.