56 lines
1.6 KiB
Markdown
56 lines
1.6 KiB
Markdown
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---
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id: 5900f4ee1000cf542c510000
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challengeType: 5
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title: 'Problem 385: Ellipses inside triangles'
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videoUrl: ''
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localeTitle: 问题385:三角形内的椭圆
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---
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## Description
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<section id="description">对于平面中的任何三角形T,可以显示存在唯一的椭圆,其中最大区域完全在T内。 <p>对于给定的n,考虑三角形T,使得: </p><ul><li> T的顶点具有绝对值≤n的整数坐标,和</li><li> T内最大面积椭圆的焦点是(√13,0)和(-√13,0)。设A(n)为所有这些三角形的面积之和。 </li></ul><p>例如,如果n = 8,则存在两个这样的三角形。它们的顶点是(-4,-3),( - 4,3),(8,0)和(4,3),(4,-3),( - 8,0),每个三角形的面积因此A(8)= 36 + 36 = 72。 </p><p>可以证实A(10)= 252,A(100)= 34632和A(1000)= 3529008。 </p><p>找A(1 000 000 000)。 </p><p> 1椭圆的焦点(多个焦点)是两个点A和B,使得对于椭圆边界上的每个点P,AP + PB是恒定的。 </p></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>euler385()</code>应该返回3776957309612154000。
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testString: 'assert.strictEqual(euler385(), 3776957309612154000, "<code>euler385()</code> should return 3776957309612154000.");'
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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 euler385() {
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// Good luck!
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return true;
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}
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euler385();
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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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