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 A319905 Decimal expansion of 4*(sqrt(2) - 1)/3. 0
 5, 5, 2, 2, 8, 4, 7, 4, 9, 8, 3, 0, 7, 9, 3, 3, 9, 8, 4, 0, 2, 2, 5, 1, 6, 3, 2, 2, 7, 9, 5, 9, 7, 4, 3, 8, 0, 9, 2, 8, 9, 5, 8, 3, 3, 8, 3, 5, 9, 3, 0, 7, 6, 4, 2, 3, 5, 5, 7, 2, 9, 8, 3, 9, 8, 7, 6, 4, 3, 3, 0, 4, 6, 1, 6, 1, 4, 2, 7, 1, 8, 4, 6, 7, 1, 8, 3 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS A 90-degree unit-circular arc in the first quadrant can be approximated by a cubic Bézier curve. In this case, L = 4*(sqrt(2) - 1)/3 is the unit tangent vector scaling factor that minimizes the distance between the curve and the unit circle segment, provided its endpoints and midpoint are interpolated. Riškus referred to this constant as "magic number". LINKS Tor Dokken, Morten Dæhlen, Tom Lyche and Knut Mørken, Good approximation of circles by curvature-continuous Bézier curves, Computer Aided Geometric Design Vol. 7 (1990), 33-41. Aleksas Riškus, Approximation of a cubic Bézier curve by circular arcs and vice versa, Information Technology And Control Vol. 35 (2006), 371-378. Adam G. Stanislav, Drawing a circle with Bézier Curves Wikipedia, Bézier curve Wikipedia, Composite Bézier curve FORMULA Equals (4/3)*tan(Pi/8). Irrational number represented by the periodic continued fraction [0; [1, 1, 4, 3]]; positive real root of 9*x^2 + 24*x - 16. - Peter Luschny, Oct 04 2018 EXAMPLE 0.552284749830793398402251632279597438092895833835930... MAPLE Digits:=1000; evalf(4*(sqrt(2) - 1)/3); MATHEMATICA RealDigits[4*(Sqrt[2] - 1)/3, 10, 100][[1]] PROG (PARI) 4*(sqrt(2) - 1)/3 CROSSREFS Cf. A002193, A156309, A188582, A268683. Sequence in context: A011501 A319305 A196614 * A319593 A335321 A172125 Adjacent sequences:  A319902 A319903 A319904 * A319906 A319907 A319908 KEYWORD nonn,cons,easy AUTHOR Franck Maminirina Ramaharo, Oct 01 2018 STATUS approved

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Last modified August 4 21:32 EDT 2021. Contains 346455 sequences. (Running on oeis4.)