Neutral Geometry is plane geometry without any assumptions about parallel lines (i.e. No Euclidean Parallel Postulate or Hyperbolic Parallel Postulate). One axiom used to construct Neutral Geometry is the Side-Angle-Side axiom for congruence of triangles. After giving a brief introduction to Neutral Geometry, the speaker shows that we can replace the Side-Angle-Side axiom with the Side-Angle-Angle axiom for congruence of triangles and still get all of Neutral geometry. In particular, we get Side-Angle-Side as a theorem.
This talk is accessible to students of all levels.
John Donnelly is a graduate student at Binghamton University currently working towards his PhD in mathematics. He is a fellow in the "Preparing Future Faculty" program in the Department of Mathematical Sciences.