Rob Salgado

We present the foundations for a unified treatment of three planar geometries used in physics: Euclidean space, Galilean spacetime, and Minkowskian spacetime. Following I.M. Yaglom, using techniques familiar from the analytic geometry and trigonometry of Euclidean space, we develop the corresponding analogues for Galilean and Minkowskian spacetimes and suggest extensions to the constant-curvature de-Sitter space-times. We comment on how this unified treatment suggests a faithful visualization of tensors and their algebra [consistent with the pictorial representations in Schouten, Misner-Thorne-Wheeler, and Burke]. We feel that this provides a new geometric framework for teaching relativity.

 
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