1.8 KiB
id | challengeType | title | forumTopicId |
---|---|---|---|
5900f4f41000cf542c510007 | 5 | Problem 392: Enmeshed unit circle | 302057 |
Description
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.
E.g. here is a picture of the solution for N = 10:
The area occupied by the red cells for N = 10 rounded to 10 digits behind the decimal point is 3.3469640797.
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.
Instructions
Tests
tests:
- text: <code>euler392()</code> should return 3.1486734435.
testString: assert.strictEqual(euler392(), 3.1486734435);
Challenge Seed
function euler392() {
// Good luck!
return true;
}
euler392();
Solution
// solution required