The Weighted Fermat Triangle Problem
We completely solve the generalized Fermat problem: given a triangle 𝑃1, 𝑃2, 𝑃3 and three positive numbers 𝜆1, 𝜆2, 𝜆3, find a point 𝑃 for which the sum 𝜆1𝑃1𝑃+𝜆2𝑃2𝑃+𝜆3𝑃3𝑃 is minimal. We show that the point always exists and is unique, and indicate necessary and sufficient conditions for the point to...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2008-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/283846 |
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| Summary: | We completely solve the generalized Fermat problem: given a triangle 𝑃1, 𝑃2, 𝑃3 and
three positive numbers 𝜆1, 𝜆2, 𝜆3, find a point 𝑃 for which the sum 𝜆1𝑃1𝑃+𝜆2𝑃2𝑃+𝜆3𝑃3𝑃
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. |
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| ISSN: | 0161-1712 1687-0425 |