Non-Euclidean Geometry and Modern Differential Geometry
           Non-Euclidean Geometry and
           Modern Differential Geometry
                           Zhiqin Lu
                        April 14, 2022
  Non-Euclidean Geometry and Modern Differential Geometry
   The fifth postulate
     The geometry we have learned in high school is the
     so-called Euclidean Geometry, named after the
     Greek mathematician Euclid.
     Euclid published The elements, which is a
     mathematical treatise consisting of 13 books in
     Alexandria, Ptolemaic Egypt c. 300 BC.
  Non-Euclidean Geometry and Modern Differential Geometry
    The fifth postulate
      Euclid’s Elements has been referred to as the most
      successful and influential textbook ever written. It
      was one of the very earliest mathematical works to
      be printed after the invention of the printing press
      and has been estimated to be second only to the
      Bible in the number of editions published since the
      first printing on May 25, 1482. It has about 1000
      versions.
  Non-Euclidean Geometry and Modern Differential Geometry
   The fifth postulate
     Why isThe Elements so important and...influential?
     It presented a set of formal logical arguments based
     on a few basic terms and axioms, provided a
     systematic method of rational exploration.
     Euclid is called the Father of Geometry not because
     he was the first man studied geometry – he was not
     – but he did a rigorous, thoughtful, and logical
     march through geometry.