Abstract
For the first time Malfatti's old problem about arranging three non-overlapping circles of greatest total area in a triangle is solved.
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References
J. Hadamard, Elementary Geometry Pt. I: Plane Geometry [Russian translation], Moscow (1957).
G. D. Balk and M. B. Balk, "Probability test," Kvant, No. 1, 20–25 (1972).
V. A. Zalgaller, "An inequality for acute triangles," Ukr. Geom. Sb., No. 34, 10–25 (1991).
G. A. Los', Malfatti's Optimization Problem [in Russian], Dep. Ukr. NIINTI July 5, 1988.
T. Saaty, Integer Optimization Methods and Related Extremal Problems [Russian translation], Moscow (1973).
A. B. Kharazishvili, Introduction to Combinatorial Geometry [in Russian], Tbilisi (1985).
H. Dörrie, Triumph der Mathematik (Hundert berühmte Probleme aus zwei Jahrtausend mathematischer Kultur), Physica-Verlag, Würzburg (1958). [English translation: 100 Great Problems of Elementary Mathematics, Dover, New York (1965)].
H. Eves, in: A Survey of Geometry. 2, Allyn & Bacon (1965), pp. 50–66.
H. Gabai and E. Liban, "On Goldberg's inequality associated with the Malfatti problem," Math. Mag.,41, No. 5, 251–252 (1967).
M. Goldberg, "On the original Malfatti problem," Math. Mag.,40, No. 5, 241–247 (1967).
H. Lob and H. W. Richmond, "On the solutions of the Malfatti problem for a triangle," Proc. London Math. Soc.,2, No. 30, 287–301 (1930).
C. Malfatti, "Memoria sopra una problema stereotomico," Memoria di Matematica e di Fisica della Societa Italiana della Scienze,10, No. 1, 235–244 (1803).
A. Procissi, "Questioni connesse col problema di Malfatti e bibliografia," Period. Math.,4, No. 12, 189–205 (1932).
Additional information
Translated from Ukrainskii Geometricheskii Sbornik, No. 35, pp. 14–33, 1992.
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Zalgaller, V.A., Los', G.A. The solution of Malfatti's problem. J Math Sci 72, 3163–3177 (1994). https://doi.org/10.1007/BF01249514
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DOI: https://doi.org/10.1007/BF01249514