Triangle center minimizing sum of distances to each vertex
Fig 1. Construction of the first isogonic center, X(13). When no angle of the triangle exceeds 120°, this point is the Fermat point.
In Euclidean geometry, the Fermat point of a triangle, also called the Torricelli point or Fermat–Torricelli point, is a point such that the sum of the three distances from each of the three vertices of the triangle to the point is the smallest possible[1] or, equivalently, the geometric median of the three vertices. It is so named because this problem was first raised by Fermat in a private letter to Evangelista Torricelli, who solved it.
The Fermat point gives a solution to the geometric median and Steiner tree problems for three points.
^Cut The Knot - The Fermat Point and Generalizations
known as the Fermatpoint of the triangle formed by the three vertices. (If the three points are collinear then the geometric median is the point between the...
Fermat number FermatpointFermat–Weber problem Fermat polygonal number theorem Fermat polynomial Fermat primality test Fermat pseudoprime Fermat quintic threefold...
three, and the three edges incident to such a point must form three 120 degree angles (see Fermatpoint). It follows that the maximum number of Steiner...
associated with a triangle like the Fermatpoint, nine-point center, Lemoine point, Gergonne point, and Feuerbach point were discovered. During the revival...
problem of computing the Fermatpoint, the geometric median of three points. For this reason it is sometimes called the Fermat–Weber problem, although...
any such point, depending on the specific triangle having that particular orthocentroidal disk. Furthermore, the Fermatpoint, the Gergonne point, and the...
near market. Weber's point of optimal transportation is a generalization of the Fermatpoint problem. In its simplest form, the Fermat problem consists in...
called the Fermat-Torricelli points, sometimes denoted F1 and F2. The intersection of the Fermat line (i.e., that line joining the two Fermat-Torricelli...
point inside a quadrilateral that minimizes the sum of distances to the vertices is the intersection of the diagonals. Hence that point is the Fermat...
as the area goes to zero, the circular triangle shrinks towards the Fermatpoint of the given three points. Hart circle, a circle associated with certain...
from 1640; in 1659, Fermat stated to Huygens that he had proven the latter statement by the method of infinite descent. In 1657, Fermat posed the problem...
Algebraic point Associated point Base point Closed point Divisor point Embedded point Extreme pointFermatpoint Fixed point Focal point Geometric point Hyperbolic...
entire domain (the global or absolute extrema) of a function. Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality...
Each point in the list is identified by an index number of the form X(n)—for example, X(1) is the incenter. The information recorded about each point includes...
the solution to the Steiner tree problem for those three vertices The Fermatpoint of a triangle, the solution to the Steiner tree problem for the three...
figure Torricelli point or Fermatpoint, a point such that the total distance from the three vertices of the triangle to the point is the minimum possible...
of Oxford, specialising in number theory. He is best known for proving Fermat's Last Theorem, for which he was awarded the 2016 Abel Prize and the 2017...
a point called the first isogonal center. In the case in which the original triangle has no angle greater than 120°, this point is also the Fermat point...
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