the weighted fermat triangle problem
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ID: 220261
2008
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Abstract
We completely solve the generalized Fermat problem: given a triangle ๐1, ๐2, ๐3 and
three positive numbers ๐1, ๐2, ๐3, find a point ๐ for which the sum ๐1๐1๐+๐2๐2๐+๐3๐3๐
is minimal. We show that the point always exists and is unique, and indicate necessary
and sufficient conditions for the point to lie inside the triangle. We provide geometric
interpretations of the conditions and briefly indicate a connection with dynamical systems.
| Reference Key |
shen2008internationalthe
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|---|---|
| Authors | ;Yujin Shen;Juan Tolosa |
| Journal | structural engineering and mechanics |
| Year | 2008 |
| DOI |
10.1155/2008/283846
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| URL | |
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