A334843 Decimal expansion of arclength between (0,0) and (Pi/6,1/2) on y = sin x.

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

Offset: 0

Author

Clark Kimberling, Jun 15 2020

Keywords

• nonn
• cons
• easy

Examples

			arclength = 0.63397459621556135323627682924706381652859737309480968...
		

Links

• Index entries for algebraic numbers, degree 2.

Crossrefs

Cf. A333202, A332633, A334842.

Programs

Mathematica

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

PARI

(3 - sqrt(3))/2 \\ Charles R Greathouse IV, Feb 11 2025

Formula

arclength = (3 - sqrt(3))/2.