# Spacetime and Euclidean geometry

@article{Brill2004SpacetimeAE, title={Spacetime and Euclidean geometry}, author={Dieter R. Brill and Ted Jacobson}, journal={General Relativity and Gravitation}, year={2004}, volume={38}, pages={643-651} }

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.

## 7 Citations

### From Einstein's 1905 postulates to the geometry of flat space‐time

- Physics
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Minkowski diagrams in 1+1 dimensional flat space‐time are given a strictly geometric derivation, directly from two gedanken experiments incorporating the principle of the constancy of the velocity of…

### Relativity on Rotated Graph Paper

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It is shown that many quantitative results can be read off a spacetime diagram by counting boxes, using a minimal amount of algebra, in the spirit of the Bondi k-calculus.

### Alice and Bob and Hendrik

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This paper offers an alternative approach to discussing both the principle of relativity and the derivation of the Lorentz transformations. This approach uses the idea that there may not be a…

### Physics and the Pythagorean Theorem

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Pythagoras' theorem lies at the heart of physics as well as mathematics, yet its historical origins are obscure. We highlight a purely pictorial, gestalt-like proof that may have originated during…

### Plane Geometry in Spacetime

- Physics
- 2009

Minkowski’s spacetime diagrams are extracted directly from Einstein’s 1905 postulates, using only some very elementary plane geometry. I have spent a significant part of my career looking at familiar…

### Theory of Relativity – Biggest Mistake of the 20th Century?

- PhysicsInternational Journal of Theoretical and Mathematical Physics
- 2021

According to the thesis presented here, the correct model of reality should be based on two major discoveries of the 20th century: Einstein's discovery that reality is four-dimensional (1905) and de…

### The cissoid of Diocles in the Lorentz–Minkowski plane

- MathematicsTURKISH JOURNAL OF MATHEMATICS
- 2019

This article presents the cissoid of Diocles and the cissoid of two circles with respect to origin in the Lorentz-Minkowski plane.

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