A254604 Decimal expansion of the half of a single half-wave constant.

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

Offset: 0

Author

Roman Witula, Feb 02 2015

Keywords

• nonn
• cons

Comments

By the definition this constant takes the value 0 < x < Pi such that the horizontal line y = sin x divides the region bounded by the sine curve and the interval [0,Pi] on the x-axis into two shapes of equal area.

Examples

			x = 0.368305390596661399946991689932336338080760158209792727276899496553...
		

Programs

Mathematica

FindRoot[2 Cos[x] - (Pi - 2 x) Sin[x] - 1 == 0, {x, 0, Pi}, WorkingPrecision -> 150] (* Bruno Berselli, Feb 03 2015 *)

PARI

solve(x=0, Pi, 2*cos(x) - (Pi - 2*x)*sin(x) - 1) \\ Michel Marcus, Feb 03 2015

Formula

2*cos(x) - (Pi - 2*x)*sin(x) = 1, 0 < x < Pi.