Projective Geometry: GSP Sam and it’s Unique Educational Tool
                        ACapston Paper
                  Submitted to the Department of Mathematics
                         Georgia College
                      requirements for the degree of
                        Bachelor of Science
                            in
                         Mathematics
                            by
                         Joel Rapkin
                         November 2014
          Acknowledgments
          This capstone project would not be possible without Dr. Cazacu. It is a pleasure
          to thank Dr. Rodica Cazaci for her guidance as my advisor
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                    Contents
                    Acknowledgments ................................................     ii
                    Abstract .........................................................  iv
                    Introduction .....................................................   1
                    Introduction to Geometrical Planes ..............................    2
                    The Origins of the Projective Plane ..............................   4
                    Extending the Euclidean Plane ...................................    7
                    Introducing the Real Projective Plane Using the “swap infinite and
                       finite point” Function .........................................   9
                    MyVision ....................................................... 13
                    Bibliography ..................................................... 15
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          Abstract
          Projective geometry originated in the context of art, but evolved into a much more
          mathematical research field as more and more mathematicians started questioning
          the uniqueness of the very popular Euclidean geometry. In this talk we will intro-
          ducetherealprojective plane and explore it using the Dynamic Geometry Software
          Sam. With its “swap finite & infinite points” function, students will be able to
          see connected geometrical figures and explore some theorems from the Euclidean
          plane in the projective plane.
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