General Relativity and Gravitation

, Volume 38, Issue 4, pp 643–651 | Cite as

Spacetime and Euclidean geometry

  • Dieter Brill
  • Ted JacobsonEmail author
Research Article


Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.


Special relativity Line element 


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.University of MarylandCollege ParkUSA

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