397a9f0c3e
* fix: clean-up Project Euler 462-480 * fix: missing image extension * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
61 lines
2.0 KiB
Markdown
61 lines
2.0 KiB
Markdown
---
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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, $r(3, 1) = \frac{1}{2}, r(6, 2) = 1, r(12, 3) = 2$.
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<img class="img-responsive center-block" alt="triangle ΔABC inscribed in an ellipse, radius of the incircle of ΔABC r(6, 2) = 1" src="https://cdn.freecodecamp.org/curriculum/project-euler/triangle-inscribed-in-ellipse-1.png" style="background-color: white; padding: 10px;">
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<img class="img-responsive center-block" alt="triangle ΔABC inscribed in an ellipse, radius of the incircle of ΔABC r(12, 3) = 2" src="https://cdn.freecodecamp.org/curriculum/project-euler/triangle-inscribed-in-ellipse-2.png" style="background-color: white; padding: 10px;">
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Let $G(n) = \sum_{a = 3}^n \sum_{b = 1}^{\left\lfloor\frac{a - 1}{2} \right\rfloor} r(a, b)$
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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 $G({10}^{11})$. Give your answer as a string 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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# --hints--
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`triangleInscribedInEllipse()` should return a string.
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```js
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assert(typeof triangleInscribedInEllipse() === 'string');
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```
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`triangleInscribedInEllipse()` should return the string `1.895093981e31`.
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```js
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assert.strictEqual(triangleInscribedInEllipse(), '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 triangleInscribedInEllipse() {
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return true;
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}
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triangleInscribedInEllipse();
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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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