# Problem 471: Triangle inscribed in ellipse
The triangle ΔABC is inscribed in an ellipse with equation \$\\frac
{x\^2} {a\^2} + \\frac {y\^2} {b\^2} = 1\$, 0 < 2b < a, a and b
integers. Let r(a,b) be the radius of the incircle of ΔABC when the
incircle has center (2b, 0) and A has coordinates \$\\left( \\frac a 2,
\\frac {\\sqrt 3} 2 b\\right)\$. For example, r(3,1) = ½, r(6,2) = 1,
r(12,3) = 2. Let \$G(n) = \\sum\_{a=3}\^n \\sum\_{b=1}\^{\\lfloor \\frac
{a - 1} 2 \\rfloor} r(a, b)\$ You are given G(10) = 20.59722222, G(100)
= 19223.60980 (rounded to 10 significant digits). Find G(1011). Give
your answer in scientific notation rounded to 10 significant digits. Use
a lowercase e to separate mantissa and exponent. For G(10) the answer
would have been 2.059722222e1.