Proving the solution of Malfatti’s marble problem. (English) Zbl 1528.52012
Summary: Malfatti’s problem is more than 200 years old and its solution given by the greedy arrangement has been stated first in 1994. The solution was obtained at that time by considering 14 arrangements and by justifying the exclusion of the non-greedy ones through a complex reasoning relying purely on numerical simulations in several crucial steps. By significantly improving the underlying methods and by filling still extant gaps, a full purely analytical proof of the solution is provided for the first time in the present work, especially based on a mixture of synthetic and analytic Euclidean geometry and on the theory of convex functions.
MSC:
| 52C26 | Circle packings and discrete conformal geometry |
| 26B25 | Convexity of real functions of several variables, generalizations |
| 97G99 | Geometry education |
| 51M04 | Elementary problems in Euclidean geometries |
| 52A40 | Inequalities and extremum problems involving convexity in convex geometry |
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