About the maximum and minimum areas of the necklace
Abstract
An extreme problem related to finding the maximal and minimal areas of the set of circles inscribed into the bounded by two tangent circles
About the Author
R. R. Gazizov
Kazan Federal University, Lobachevskii Institute of Mathematics and Mechanics
Russian Federation
Russian Federation
18 Kremlyovskaya str., Kazan 420008
References
1. [1] I. D. Zhizhilkin, Inversion transformation, MCCME, M., 2009 (in Russian).
2. [2] E. A. Avksentyev, V.Yu. Protasov, Universal measure for Poncele-type theorems, Proc. Amer. Math. Soc. 146 (11), 4843–4854 (2018). DOI: https://doi.org/10.1090/proc/13838
3. [3] M. N. Gurov, M. A. Volkov, Chains of tangent circles inscribed in curvilinear triangles, Int. J. Geom. 7 (1), 105–118 (2018). URL: https://ijgeometry.com/product/mikhail-n-gurov-and-makar-a-volkov-chains-oftangent-circles-inscribed-in-curvilinear-triangles/
4. [4] B. V. Shabat, Introduction to complex analysis, p. 1. 2nd ed., Nauka, M., 1976 (in Russian).
5. [5] L. B. W. Jolley, Summation of series. 2nd revised ed. Dover Books on Advanced Mathematics. Dover Publ., Inc., New York, 1961.
Review
For citations:
Gazizov R.R. About the maximum and minimum areas of the necklace. Mathematics and Theoretical Computer Science. 2023;1(2):50-61. (In Russ.)
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