A330646 Decimal expansion of the mean length of a line segment drawn by picking a random point on a unit length equilateral triangle and extending it in a random direction until it meets an edge.

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

Offset

0,1

Links

Table of n, a(n) for n=0..109.

Muthu Veerappan Ramalingam, An Expected Value Problem III

Formula

Equals sqrt(3) * log(3) / (2 * Pi).

Equals (h_a/(3*Pi))*cosech^{-1}((1/2)*((b+c)/a-a/(b+c)))+(h_b/(3*Pi))*cosech^{-1}((1/2)*((c+a)/b-b/(c+a)))+(h_c/(3*Pi))*cosech^{-1}((1/2)*((a+b)/c-c/(a+b))) for an arbitrary triangle with sides a, b and c with corresponding altitudes h_a, h_b and h_c.

Example

0.302848349804097933375691303492564570884596990578285814558...

Mathematica

RealDigits[Sqrt[3] Log[3]/2/Pi, 10, 110][[1]]

Crossrefs

Cf. A093064.

Sequence in context: A325447 A240660 A347418 * A341905 A354905 A099095

Adjacent sequences: A330643 A330644 A330645 * A330647 A330648 A330649

Keyword

nonn,cons

Author

Muthu Veerappan Ramalingam, Dec 22 2019

Status

approved