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

## Description
<section id='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.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

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

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

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

euler471();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>