72 lines
1.8 KiB
Markdown
72 lines
1.8 KiB
Markdown
---
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id: 5900f4f41000cf542c510007
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challengeType: 5
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title: 'Problem 392: Enmeshed unit circle'
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---
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## Description
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<section id='description'>
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A rectilinear grid is an orthogonal grid where the spacing between the gridlines does not have to be equidistant.
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An example of such grid is logarithmic graph paper.
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Consider rectilinear grids in the Cartesian coordinate system with the following properties:The gridlines are parallel to the axes of the Cartesian coordinate system.There are N+2 vertical and N+2 horizontal gridlines. Hence there are (N+1) x (N+1) rectangular cells.The equations of the two outer vertical gridlines are x = -1 and x = 1.The equations of the two outer horizontal gridlines are y = -1 and y = 1.The grid cells are colored red if they overlap with the unit circle, black otherwise.For this problem we would like you to find the positions of the remaining N inner horizontal and N inner vertical gridlines so that the area occupied by the red cells is minimized.
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E.g. here is a picture of the solution for N = 10:
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The area occupied by the red cells for N = 10 rounded to 10 digits behind the decimal point is 3.3469640797.
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Find the positions for N = 400.
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Give as your answer the area occupied by the red cells rounded to 10 digits behind the decimal point.
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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>euler392()</code> should return 3.1486734435.
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testString: 'assert.strictEqual(euler392(), 3.1486734435, "<code>euler392()</code> should return 3.1486734435.");'
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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 euler392() {
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// Good luck!
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return true;
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}
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euler392();
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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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