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The golden ratio in special relativity

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  • Sigalotti, Leonardo Di G.
  • Mejias, Antonio

Abstract

In this note we show that Euclid’s construction of the golden rectangle can be used to derive both the dilation of time intervals and the Lorentz contraction of lengths as predicted by Einstein’s theory of special relativity. In this simple exercise, the Lorentz factor arises as a direct consequence of the Pythagorean theorem, while the golden ratio, ϕ=1+5/2, is found to govern the transition from Newton’s physics to relativistic mechanics.

Suggested Citation

  • Sigalotti, Leonardo Di G. & Mejias, Antonio, 2006. "The golden ratio in special relativity," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 521-524.
    • Handle: RePEc:eee:chsofr:v:30:y:2006:i:3:p:521-524
    DOI: 10.1016/j.chaos.2006.03.005
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    References listed on IDEAS

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    1. Marek-Crnjac, L., 2006. "The golden mean in the topology of four-manifolds, in conformal field theory, in the mathematical probability theory and in Cantorian space-time," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1113-1118.
    2. El Naschie, M.S., 2005. "A new solution for the two-slit experiment," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 935-939.
    3. El Naschie, M.S., 2005. "A guide to the mathematics of E-infinity Cantorian spacetime theory," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 955-964.
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    1. El Naschie, M.S., 2006. "Is Einstein’s general field equation more fundamental than quantum field theory and particle physics?," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 525-531.
    2. Crasmareanu, Mircea & Hreţcanu, Cristina-Elena, 2008. "Golden differential geometry," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1229-1238.
    3. Estrada, Ernesto, 2007. "Graphs (networks) with golden spectral ratio," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1168-1182.

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