Research Article

Taylor's Power Law and Packing Circles

Volume: 12 Number: 4 December 8, 2024
EN

Taylor's Power Law and Packing Circles

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 $b = 2$.

Keywords

Density, Distance, Packing circles, Population, Taylor

References

  1. [1] Taylor, L. R.:Aggregation, variance and the mean. Nature. 189, 732-735 (1961).
  2. [2] Specht, E.: Packomania. http://www.packomania.com/. Circles in a Square Section, (2020).
  3. [3] Hales, T. C.: The sphere packing problem. Journal of Computational and Applied Mathematics. 44(1) (1992).
  4. [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. [5] Tuckwell, H. C.: Elementary Applications of Probability Theory. CRC Press. 32 (1995).
  6. [6] Cohen, J.: Human population grows up. Journal of Computational and Applied Mathematics. 288(3), 78-85 (2003)
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
1.Kaya O, Topçu Z. Taylor’s Power Law and Packing Circles. Math. Sci. Appl. E-Notes. 2024;12(4):178-186. doi:10.36753/mathenot.1448644
Chicago
Kaya, Oğuzhan, and Zeki Topçu. 2024. “Taylor’s Power Law and Packing Circles”. Mathematical Sciences and Applications E-Notes 12 (4): 178-86. https://doi.org/10.36753/mathenot.1448644.
EndNote
Kaya O, Topçu Z (December 1, 2024) Taylor’s Power Law and Packing Circles. Mathematical Sciences and Applications E-Notes 12 4 178–186.
IEEE
[1]O. Kaya and Z. Topçu, “Taylor’s Power Law and Packing Circles”, Math. Sci. Appl. E-Notes, vol. 12, no. 4, pp. 178–186, Dec. 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 (December 1, 2024): 178-186. https://doi.org/10.36753/mathenot.1448644.
JAMA
1.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, Dec. 2024, pp. 178-86, doi:10.36753/mathenot.1448644.
Vancouver
1.Oğuzhan Kaya, Zeki Topçu. Taylor’s Power Law and Packing Circles. Math. Sci. Appl. E-Notes. 2024 Dec. 1;12(4):178-86. doi:10.36753/mathenot.1448644