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An irreducibly simple derivation of the Hausdorff dimension of spacetime

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  • El Naschie, M.S.

Abstract

Starting from the simple picture of a three-dimensional cube, we construct a four-dimensional cube hierarchy. The dimensions of infinitely concentric four-dimensional cubes naturally lead to a corresponding construction of a continued fraction converging to D=4.2360679. This is exactly the Hausdorff dimension found using E-infinity theory.

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  • El Naschie, M.S., 2009. "An irreducibly simple derivation of the Hausdorff dimension of spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1902-1904.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:4:p:1902-1904
    DOI: 10.1016/j.chaos.2008.07.043
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    References listed on IDEAS

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    1. Elnaschie, M.S., 2008. "From classical gauge theory back to Weyl scaling via E-Infinity spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 980-985.
    2. He, Ji-Huan & Xu, Lan & Zhang, Li-Na & Wu, Xu-Hong, 2007. "Twenty-six dimensional polytope and high energy spacetime physics," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 5-13.
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    Cited by:

    1. He, Ji-Huan, 2009. "Hilbert cube model for fractal spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2754-2759.
    2. Zmeskal, Oldrich & Vala, Martin & Weiter, Martin & Stefkova, Pavla, 2009. "Fractal–cantorian geometry of space-time," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1878-1892.
    3. El Naschie, M.S., 2009. "The theory of Cantorian spacetime and high energy particle physics (an informal review)," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2635-2646.
    4. Zmeskal, Oldrich & Weiter, Martin & Vala, Martin, 2009. "Notes to “An irreducibly simple derivation of the Hausdorff dimension of spacetime” by M.S. El Naschie," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 532-533.
    5. El Naschie, M.S., 2009. "Arguments for the compactness and multiple connectivity of our cosmic spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2787-2789.

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