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Year 2024, Volume: 12 Issue: 4, 178 - 186
https://doi.org/10.36753/mathenot.1448644

Abstract

References

  • [1] Taylor, L. R.:Aggregation, variance and the mean. Nature. 189, 732-735 (1961).
  • [2] Specht, E.: Packomania. http://www.packomania.com/. Circles in a Square Section, (2020).
  • [3] Hales, T. C.: The sphere packing problem. Journal of Computational and Applied Mathematics. 44(1) (1992).
  • [4] Cohen, J., Courgeau, D.: Modeling distances between humans using Taylor’s law and geometric probability. Mathematical Population Studies. 24 (4), 197-218 (2017).
  • [5] Tuckwell, H. C.: Elementary Applications of Probability Theory. CRC Press. 32 (1995).
  • [6] Cohen, J.: Human population grows up. Journal of Computational and Applied Mathematics. 288(3), 78-85 (2003)

Taylor's Power Law and Packing Circles

Year 2024, Volume: 12 Issue: 4, 178 - 186
https://doi.org/10.36753/mathenot.1448644

Abstract

The famous Taylor Power Law is in general observed in ecology and relates the variance of the population of a certain species in a unit area while Circle Packing is an arrangement of circles in a given area. We show that the circle packing problem in $\mathbb{R}^2$ satisfies the Taylor power law formula for $b = 2$.

References

  • [1] Taylor, L. R.:Aggregation, variance and the mean. Nature. 189, 732-735 (1961).
  • [2] Specht, E.: Packomania. http://www.packomania.com/. Circles in a Square Section, (2020).
  • [3] Hales, T. C.: The sphere packing problem. Journal of Computational and Applied Mathematics. 44(1) (1992).
  • [4] Cohen, J., Courgeau, D.: Modeling distances between humans using Taylor’s law and geometric probability. Mathematical Population Studies. 24 (4), 197-218 (2017).
  • [5] Tuckwell, H. C.: Elementary Applications of Probability Theory. CRC Press. 32 (1995).
  • [6] Cohen, J.: Human population grows up. Journal of Computational and Applied Mathematics. 288(3), 78-85 (2003)
There are 6 citations in total.

Details

Primary Language English
Subjects Applied Mathematics (Other)
Journal Section Articles
Authors

Oğuzhan Kaya 0000-0001-9756-1346

Zeki Topçu 0000-0002-8910-5612

Early Pub Date July 16, 2024
Publication Date
Submission Date March 7, 2024
Acceptance Date July 2, 2024
Published in Issue Year 2024 Volume: 12 Issue: 4

Cite

APA Kaya, O., & Topçu, Z. (2024). Taylor’s Power Law and Packing Circles. Mathematical Sciences and Applications E-Notes, 12(4), 178-186. https://doi.org/10.36753/mathenot.1448644
AMA Kaya O, Topçu Z. Taylor’s Power Law and Packing Circles. Math. Sci. Appl. E-Notes. July 2024;12(4):178-186. doi:10.36753/mathenot.1448644
Chicago Kaya, Oğuzhan, and Zeki Topçu. “Taylor’s Power Law and Packing Circles”. Mathematical Sciences and Applications E-Notes 12, no. 4 (July 2024): 178-86. https://doi.org/10.36753/mathenot.1448644.
EndNote Kaya O, Topçu Z (July 1, 2024) Taylor’s Power Law and Packing Circles. Mathematical Sciences and Applications E-Notes 12 4 178–186.
IEEE O. Kaya and Z. Topçu, “Taylor’s Power Law and Packing Circles”, Math. Sci. Appl. E-Notes, vol. 12, no. 4, pp. 178–186, 2024, doi: 10.36753/mathenot.1448644.
ISNAD Kaya, Oğuzhan - Topçu, Zeki. “Taylor’s Power Law and Packing Circles”. Mathematical Sciences and Applications E-Notes 12/4 (July 2024), 178-186. https://doi.org/10.36753/mathenot.1448644.
JAMA Kaya O, Topçu Z. Taylor’s Power Law and Packing Circles. Math. Sci. Appl. E-Notes. 2024;12:178–186.
MLA Kaya, Oğuzhan and Zeki Topçu. “Taylor’s Power Law and Packing Circles”. Mathematical Sciences and Applications E-Notes, vol. 12, no. 4, 2024, pp. 178-86, doi:10.36753/mathenot.1448644.
Vancouver Kaya O, Topçu Z. Taylor’s Power Law and Packing Circles. Math. Sci. Appl. E-Notes. 2024;12(4):178-86.

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