Difference between revisions of "Fermat point"

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Also called '''Torricelli point'''.
 
Also called '''Torricelli point'''.
  
In atriangle <math>\triangle ABC</math>, a point <math>p</math> which has the minimum total distance to three [[vertices]]. (i.e., <math>|Ap|+|Bp|+|Cp|)</math> is called the first Fermat point or simply '''Fermat point''' in general.
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In a triangle <math>\triangle ABC</math>, a point <math>p</math> which has the minimum total distance to three [[vertices]]. (i.e., <math>|Ap|+|Bp|+|Cp|)</math> is called the first Fermat point or simply '''Fermat point''' in general.
  
 
A method to find the point is to construct three equilateral triangles out of the three sides from <math>\triangle ABC</math>, then connect each new vertex to each opposite vertex, as these three lines will concur at first Fermat point.
 
A method to find the point is to construct three equilateral triangles out of the three sides from <math>\triangle ABC</math>, then connect each new vertex to each opposite vertex, as these three lines will concur at first Fermat point.

Revision as of 20:40, 4 November 2006

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Also called Torricelli point.

In a triangle $\triangle ABC$, a point $p$ which has the minimum total distance to three vertices. (i.e., $|Ap|+|Bp|+|Cp|)$ is called the first Fermat point or simply Fermat point in general.

A method to find the point is to construct three equilateral triangles out of the three sides from $\triangle ABC$, then connect each new vertex to each opposite vertex, as these three lines will concur at first Fermat point.

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