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A333202 Decimal expansion of arclength from (0,0) to (1,1) on y = x^2. 19
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
arclength = (2 sqrt(5) + arcsinh(2))/4.
arclength = (2 sqrt(5) + log(2 + sqrt(5)))/4.
EXAMPLE
Equals 1.478942857544597433827906...
MATHEMATICA
s = Integrate[Sqrt[1 + 4 x^2], {x, 0, 1}]
r = N[s, 200]
RealDigits[r][[1]]
CROSSREFS
Sequence in context: A090383 A179620 A310936 * A082390 A011517 A000934
KEYWORD
nonn,cons,easy
AUTHOR
Clark Kimberling, May 13 2020
STATUS
approved

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Last modified July 19 02:27 EDT 2024. Contains 374388 sequences. (Running on oeis4.)