What is Geometry?
                      (an introduction to modern geometry)
                             Kapil Hari Paranjape
                 Indian Institute of Science Education and Research, Mohali
                     KVPYSummer Camp, 2nd June 2010
      Kapil Paranjape (IISERM)    What is Geometry?        KVPYCamp2010  1 / 14
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                Didn’t Euclid do all that there is to be done?
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                What does a geometer do to earn his salary?
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 To give a satisfactory answer is difficult since:
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   ◮ we must re-write modern geometry to make it easier to understand
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   ◮ we must provide better training in mathematics for the rest.∗
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 “The rest” is how mathematicians usually refer to non-mathematicians!
                                 Introduction
  Difficult Questions
                Is there geometry beyond high school geometry?
      Kapil Paranjape (IISERM)     What is Geometry?          KVPYCamp2010  2 / 14
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                What does a geometer do to earn his salary?
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 To give a satisfactory answer is difficult since:
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   ◮ we must re-write modern geometry to make it easier to understand
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   ◮ we must provide better training in mathematics for the rest.∗
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 “The rest” is how mathematicians usually refer to non-mathematicians!
                                 Introduction
  Difficult Questions
                Is there geometry beyond high school geometry?
                  Didn’t Euclid do all that there is to be done?
      Kapil Paranjape (IISERM)     What is Geometry?          KVPYCamp2010  2 / 14
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 To give a satisfactory answer is difficult since:
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   ◮ we must re-write modern geometry to make it easier to understand
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   ◮ we must provide better training in mathematics for the rest.∗
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 “The rest” is how mathematicians usually refer to non-mathematicians!
                                 Introduction
  Difficult Questions
                Is there geometry beyond high school geometry?
                  Didn’t Euclid do all that there is to be done?
                  What does a geometer do to earn his salary?
      Kapil Paranjape (IISERM)     What is Geometry?          KVPYCamp2010  2 / 14