d269909faa
* fix: clean-up Project Euler 381-400 * fix: missing image extension * fix: missing subscripts Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
59 lines
1.8 KiB
Markdown
59 lines
1.8 KiB
Markdown
---
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id: 5900f4f41000cf542c510007
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title: 'Problem 392: Enmeshed unit circle'
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challengeType: 5
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forumTopicId: 302057
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dashedName: problem-392-enmeshed-unit-circle
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---
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# --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:
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- The gridlines are parallel to the axes of the Cartesian coordinate system.
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- There are $N + 2$ vertical and $N + 2$ horizontal gridlines. Hence there are $(N + 1) \times (N + 1)$ rectangular cells.
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- The equations of the two outer vertical gridlines are $x = -1$ and $x = 1$.
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- The equations of the two outer horizontal gridlines are $y = -1$ and $y = 1$.
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- The grid cells are colored red if they overlap with the unit circle, black otherwise.
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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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<img class="img-responsive center-block" alt="solution for N = 10" src="https://cdn.freecodecamp.org/curriculum/project-euler/enmeshed-unit-circle.png" style="background-color: white; padding: 10px;">
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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 $N = 400$. Give as your answer the area occupied by the red cells rounded to 10 digits behind the decimal point.
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# --hints--
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`enmeshedUnitCircle()` should return `3.1486734435`.
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```js
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assert.strictEqual(enmeshedUnitCircle(), 3.1486734435);
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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 enmeshedUnitCircle() {
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return true;
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}
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enmeshedUnitCircle();
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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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