Mathematics, geometry, Euclid, projective geometry
Applied Mathematics | Mathematics | Physical Sciences and Mathematics
There are two ways to study projective geometry: 1) an extension fo the Eucildean geometry taught in high schools, and 2) as an independent system, with its own definitions, acioms, and theorems. The first of these ways corresponds to the actual historical development of the subject.
Each of the two ways to study projective geometry has its own disadvantages. One disadvantage with the first method is that the high schools frequently are not very definite about Euclid's axioms. Another problem is that in projective geometry some of Euclid's axioms are not valid. These problems create confusion, not only about what Euclid's axioms really say, but also about which axioms are valid in projective geometry and which are not valid.
Department 1 Awarding Honors Status
Batchelor, D. L. (1978). Euclidean Geometry: A Descendant of Projective Geometry (Undergraduate honors thesis, University of Redlands). Retrieved from https://inspire.redlands.edu/cas_honors/580