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Some features of the general Fermat point

Published online by Cambridge University Press:  01 August 2016

S. Simons
S. Simons*
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS
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Given a triangle with vertices P 1, P 2, P 3 its Fermat point is defined as that point F which minimises the sum P 1 F + P 2 F + P 3 F. It is known that if each of the angles P 1, P 2, P 3 is less than 120°, then F will be the point inside the triangle at which each pair of P 1, P 2, P 3 subtend an angle of 120°, while if any of the angles at P 1, P 2, P 3 exceed 120° then F will coincide with that vertex – see Figure (1).

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Articles
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The Mathematical Gazette , Volume 87 , Issue 508 , March 2003 , pp. 60 - 70
Copyright
Copyright © The Mathematical Association 2003

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References

1. Abu-Abbas, Z. and Hajja, M., A note on the Fermat point of a tetrahedron, Math. Gaz. 79 (March 1995).Google Scholar
2. Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flannery, B. P., Numerical recipes: the art of scientific computing, Cambridge University Press (1992).Google Scholar