Year 2024,
Volume: 12 Issue: 4, 178 - 186
Oğuzhan Kaya
,
Zeki Topçu
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
Oğuzhan Kaya
,
Zeki Topçu
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)