Mathematics

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Mario thinks he recognizes these from building 54. No, that's not it... maybe building 28? Something like that. It’s all Greek to him, but then mathematical expressions usually are.

  • z=w3 with z, w ∈ ℂ near 0
  • z2 + 1 = x2 + 4y2, marked with lines of the form (tcos θ + sin θ,±(tsin θ − cos θ)/2,t) for various values of θ
  • y2 = x2z3 + 3x2z
  • x2 + 2y2 +3z2 = 1, marked with curves in the principal directions. A point where the principal directions are not well-defined is indicated
  • The shape of a soap film stretched between two parallel wire hoops
  • z4 + 2z2 + 1 = x2 + y2, marked with curves along which the normal curvature vanishes
  • x2 + y2/4 + z2/9 = 1 and z2/3 = 1 + x2/5 + y2/2
  • z = Re{(x + iy)2}
  • A surface, locally isometric to the hyperbolic plane, with an isolated singularity

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