A333202 Decimal expansion of arclength from (0,0) to (1,1) on y = x^2.

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

Offset: 1

Author

Clark Kimberling, May 13 2020

Keywords

• nonn
• cons
• easy

Examples

			Equals 1.478942857544597433827906...
		

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A333203, A333204, A335996.

Programs

Mathematica

s = Integrate[Sqrt[1 + 4 x^2], {x, 0, 1}]
r = N[s, 200]
RealDigits[r][[1]]

PARI

sqrt(5)/2 + asinh(2)/4 \\ Charles R Greathouse IV, Sep 02 2024

Formula

arclength = (2 sqrt(5) + arcsinh(2))/4.

arclength = (2 sqrt(5) + log(2 + sqrt(5)))/4.