67 lines
1.4 KiB
Markdown
67 lines
1.4 KiB
Markdown
---
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id: 5900f5431000cf542c510056
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challengeType: 5
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title: 'Problem 471: Triangle inscribed in ellipse'
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forumTopicId: 302148
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---
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## Description
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<section id='description'>
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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.
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Let r(a,b) be the radius of the incircle of ΔABC when the incircle has center (2b, 0) and A has coordinates $\left( \frac a 2, \frac {\sqrt 3} 2 b\right)$.
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For example, r(3,1) = ½, r(6,2) = 1, r(12,3) = 2.
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Let $G(n) = \sum_{a=3}^n \sum_{b=1}^{\lfloor \frac {a - 1} 2 \rfloor} r(a, b)$
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You are given G(10) = 20.59722222, G(100) = 19223.60980 (rounded to 10 significant digits).
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Find G(1011).
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Give your answer in scientific notation rounded to 10 significant digits. Use a lowercase e to separate mantissa and exponent.
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For G(10) the answer would have been 2.059722222e1.
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler471()</code> should return 1.895093981e+31.
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testString: assert.strictEqual(euler471(), 1.895093981e+31);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler471() {
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return true;
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}
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euler471();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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