### Abstract

Malfatti's problem, first published in 1803, is commonly understood to ask fitting three circles into a given triangle such that they are tangent to each other, externally, and such that each circle is tangent to a pair of the triangles sides. There are many solutions based on geometric constructions, as well as generalizations in which the triangle sides are assumed to be circle arcs. A generalization that asks to fit six circles into the triangle, tangent to each other and to the triangle sides, has been considered a good example of a problem that requires sophisticated numerical iteration to solve by computer. We analyze this problem and show how to solve it quickly.

*Keywords:*
Malfatti's problem, circle packing, geometric constraint solving,
GPU programming

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### Citation

Ching-Shoei Chiang, Christoph M. Hoffmann, and **Paul** **Rosen**. A generalized malfatti problem. *Computational Geometry: Theory and Applications*, 45(8):425--435, October 2012.

### Bibtex

@article{Chiang.2012.CGTA, author = {Ching-Shoei Chiang and Christoph M. Hoffmann and Paul {\bf Rosen}}, title = {A Generalized Malfatti Problem}, journal = {Computational Geometry: Theory and Applications}, year = {2012}, volume = {45}, pages = {425-435}, number = {8}, month = {October}, abstract = {Malfatti's problem, first published in 1803, is commonly understood to ask fitting three circles into a given triangle such that they are tangent to each other, externally, and such that each circle is tangent to a pair of the triangles sides. There are many solutions based on geometric constructions, as well as generalizations in which the triangle sides are assumed to be circle arcs. A generalization that asks to fit six circles into the triangle, tangent to each other and to the triangle sides, has been considered a good example of a problem that requires sophisticated numerical iteration to solve by computer. We analyze this problem and show how to solve it quickly.}, keywords = {Malfatti's problem, circle packing, geometric constraint solving, GPU programming} }