yaworsw/euler-manager

---
:id: 332
:name: Spherical triangles
:url: https://projecteuler.net/problem=332
:content: "A **spherical triangle** is a figure formed on the surface of a sphere
  by three **great circular arcs** intersecting pairwise in three vertices.\n\n ![p332_spherical.jpg]({{
  images_dir }}/p332_spherical.jpg)\n\nLet C(<var>r</var>) be the sphere with the
  centre (0,0,0) and radius <var>r</var>.  \nLet Z(<var>r</var>) be the set of points
  on the surface of C(<var>r</var>) with integer coordinates.  \nLet T(<var>r</var>)
  be the set of spherical triangles with vertices in Z(<var>r</var>). Degenerate spherical
  triangles, formed by three points on the same great arc, are <u>not</u> included
  in T(<var>r</var>).  \nLet A(<var>r</var>) be the area of the smallest spherical
  triangle in T(<var>r</var>).\n\nFor example A(14) is 3.294040 rounded to six decimal
  places.\n\nFind ![p332_sum.gif]({{ images_dir }}/p332_sum.gif) A(<var>r</var>).
  Give your answer rounded to six decimal places.\n\n"