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Can a single projection be both conformal and equal-area?

  • A.Yes, on any azimuthal projection at all
  • B.Yes, along the central meridian only
  • C.No, the two properties are incompatible
  • D.Yes, if the scale is small enough

Answer: C

It follows from Gauss's theorem that no projection can preserve both angles and areas, so the two must be traded against one another. That impossibility is the reason so many projections exist rather than one correct answer.

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