Three Things

[Three
things]

  • Four out of Eight Octants in a Sphere, radius 1/2:
  • Exact Area = 5 pi / 4
  • Approximate Area = 3.9267
  • Exact Volume = pi / 12
  • Approximate Volume = 0.2618
  • A Roman surface, x2y2+x2z2+y2z2-xyz = 0:
  • Exact Area = ????
  • Approximate Area = 3.195
  • Exact Volume = 1 / 6
  • Approximate Volume = 0.1666
  • Four out of Eight Octants in an Octahedron (distance from center to vertex = 1/2):
  • Exact Area = (sqrt(3) + 3) / 2
  • Approximate Area = 2.366
  • Exact Volume = 1 / 12
  • Approximate Volume = 0.08333


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