The mathematics of the projections

Website created August 2009. Last update September 2013.


This web page is a portal to an article (3.3MB) on the Normal and Transverse Mercator projections on the sphere and ellipsoid:



  • 1: Introduction
  • 2: Normal Mercator on the sphere: NMS
  • 3: Transverse Mercator on the sphere: TMS
  • 4: NMS to TMS by complex variables
  • 5: The geometry of the ellipsoid
  • 6: Normal Mercator on the ellipsoid (NME)
  • 7: Transverse Mercator on the ellipsoid (TME)
  • 8: The UTM and NGGB projections
  • Appendices

  • A: Curvature in two and three dimensions
  • B: Inversion of series by Lagrange expansions
  • C: Plane Trigonometry
  • D: Spherical Trigonometry
  • E: Series expansions
  • F: Calculus of variations
  • G: Complex variable theory
  • H: Maxima code
  • Latex source code

    Source files: mercator.rar

    Maxima files

    Maxima files: maxima.rar


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