Important Points about Fermat Point
Some important points about Fermat Point are:
- The Fermat Point mostly be inside a triangle, and it is equidistant from the three medians of a triangle.
- It is the center of the smallest circle which can be inscribed in a triangle.
Fermat Point
Fermat Point is the point that Pierre de Fermat, the 17th-century French mathematician, posed as a challenge to his compatriot Evangelista Torricelli to geometrically determine, is named in Fermat’s honour as the solution that would minimize the total combined distance from each vertex of a triangular figure to any single internal locus. Torricelli solved the problem, therefore other than Fermat Point, it is also known as the Fermat Point or the Torricelli Point or Fermat Torricelli Point.
Although various methods exist to locate the Fermat point, connecting the vertices of the original triangle to those of the equilateral triangles constructed on each of its sides furnishes a straightforward technique. The intersection of these segments is the Fermat point.
The Fermat point gives a solution to the geometric median and Steiner tree problems for three points.
Table of Content
- What is Fermat Point or Torricelli Point?
- Fermat Point Definition
- How to find Fermat Point in Triangle?
- Different Cases of Fermat Point
- Case 1: Triangle has an Angle ≥ 120o
- Case 2: Triangle has no Angle ≥ 120o
- Properties of Fermat Point
- Important Point about Fermat Point
- Applications of Fermat Point
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