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Numerical test of Palásti's conjecture on two-dimensional random packing density

Nature volume 254, pages 318–319 (1975)Cite this article

Abstract

RANDOM packing and random space-filling problems have received frequent attention1–5. In one dimension, this topic is usually called the car-parking problem6–10. Palásti11 generalised the parking problem to two dimensions and conjectured that the random packing density in the two-dimensional case is equal to the square of that in the one-dimensional case. Here we provide a thorough check on her conjecture and confirm its validity.

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References

  1. Bernal, J. D., Nature, 183, 141–147 (1959).

    Article  ADS  CAS  Google Scholar 

  2. Bernal, J. D., and Mason, J., Nature, 188, 910–911 (1960).

    Article  ADS  Google Scholar 

  3. Bernal, J. D., Mason, J., and Knight, K. R., Nature, 194, 956–958 (1962).

    Article  ADS  Google Scholar 

  4. Finney, J. L., Proc. R. Soc., A 319, 479–493 and 495–507 (1970).

    Article  ADS  CAS  Google Scholar 

  5. Adams, D. J., and Matheson, A. J., J. chem. Phys., 56, 1989–1994 (1972).

    Article  ADS  CAS  Google Scholar 

  6. Rényi, A., Magy. tudom. Akad. mat. Kut. Intéz. Közl., 3, 109–127 (1958).

    Google Scholar 

  7. Bánkövi, G., Magy. tudom. Akad. mat. Kut. Intéz. Közl., 7, 395–407 (1962).

    Google Scholar 

  8. Ney, P. E., Ann. math. Statist., 33, 702–718 (1962).

    Article  MathSciNet  Google Scholar 

  9. Mannion, D., Magy. tudom. Akad. mat. Kut. Intéz. Közl., 9, 143–153 (1964).

    MathSciNet  Google Scholar 

  10. Dvoretzky, A., and Robbins, H., Magy. tudom. Akad. mat. Kut. Intéz. Közl., 9, 209–225 (1964).

    Google Scholar 

  11. Palásti, I., Magy. tudom. Akad. mat. Kut. Intéz. Közl., 5, 353–359 (1960).

    MathSciNet  Google Scholar 

  12. Solomon, H., Proc. fifth Berkley Symp. math. Statist. Probability, 3, 119–134 (1966).

    ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Applied Physics, Tokyo Institute of Technology, Meguroku, Tokyo, 152, Japan

    YOSHIAKI AKEDA & MOTOO HORI

Authors
  1. YOSHIAKI AKEDA
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  2. MOTOO HORI
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AKEDA, Y., HORI, M. Numerical test of Palásti's conjecture on two-dimensional random packing density. Nature 254, 318–319 (1975). https://doi.org/10.1038/254318a0

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