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

Author

Muthu Veerappan Ramalingam, Dec 22 2019

Keywords

• nonn
• cons

Examples

			0.302848349804097933375691303492564570884596990578285814558...
		

Links

• Muthu Veerappan Ramalingam, An Expected Value Problem III

Crossrefs

Cf. A093064.

Programs

Mathematica

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

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.