45 lines
1.2 KiB
Markdown
45 lines
1.2 KiB
Markdown
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---
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id: 5900f5431000cf542c510056
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title: 'Problem 471: Triangle inscribed in ellipse'
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challengeType: 5
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forumTopicId: 302148
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dashedName: problem-471-triangle-inscribed-in-ellipse
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---
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# --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 $G(n) = \\sum*{a=3}^n \\sum*{b=1}^{\\lfloor \\frac {a - 1} 2 \\rfloor} r(a, b)$ 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.
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# --hints--
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`euler471()` should return 1.895093981e+31.
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```js
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assert.strictEqual(euler471(), 1.895093981e31);
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```
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# --seed--
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## --seed-contents--
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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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# --solutions--
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```js
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// solution required
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```
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