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 constantcurvature deSitter
spacetimes. We comment on how this unified treatment suggests a
faithful visualization of tensors and their algebra [consistent with the
pictorial representations in Schouten, MisnerThorneWheeler, and
Burke]. We feel that this provides a new geometric framework for
teaching relativity.
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SpaceTime Trigonometry
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