yaworsw/euler-manager

---
:id: 392
:name: Enmeshed unit circle
:url: https://projecteuler.net/problem=392
:content: "A rectilinear grid is an orthogonal grid where the spacing between the
  gridlines does not have to be equidistant.  \nAn example of such grid is logarithmic
  graph paper.\n\nConsider rectilinear grids in the Cartesian coordinate system with
  the following properties:\n\n- The gridlines are parallel to the axes of the Cartesian
  coordinate system.\n- There are N+2 vertical and N+2 horizontal gridlines. Hence
  there are (N+1) x (N+1) rectangular cells.\n- The equations of the two outer vertical
  gridlines are x = -1 and x = 1.\n- The equations of the two outer horizontal gridlines
  are y = -1 and y = 1.\n- The grid cells are colored red if they overlap with the
  <dfn title=\"The unit circle is the circle that has radius 1 and is centered at
  the origin\">unit circle</dfn>, black otherwise.\nFor 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.\n\nE.g. here
  is a picture of the solution for N = 10:\n\n![p392_gridlines.png]({{ images_dir
  }}/p392_gridlines.png)\n\nThe area occupied by the red cells for N = 10 rounded
  to 10 digits behind the decimal point is 3.3469640797.\n\nFind the positions for
  N = 400.  \n Give as your answer the area occupied by the red cells rounded to 10
  digits behind the decimal point.\n\n"