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id	challengeType	title	forumTopicId
5900f5431000cf542c510056	5	Problem 471: Triangle inscribed in ellipse	302148

Description

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.

Instructions

Tests

tests:
  - text: <code>euler471()</code> should return 1.895093981e+31.
    testString: assert.strictEqual(euler471(), 1.895093981e+31);

Challenge Seed

function euler471() {
  // Good luck!
  return true;
}

euler471();

Solution

// solution required

1.4 KiB Raw Blame History