Knowra Fermat point Fermat point The Fermat point of a triangle minimizes the sum of its distances to the three vertices. For triangles with all angles below 120°, its segments to the vertices meet at 120° angles.
Torricelli's construction : A geometric construction locating the Fermat point using equilateral triangles and intersecting lines. It constructs the point by turning the 120° condition into intersections of straight lines.
Triangle : A polygon with three sides, three vertices, and three interior angles. The Fermat point is defined from the three vertices of this figure.
Facility location problem : The problem of choosing a site that optimizes distances or costs to a set of locations. The Fermat point is an exact solution for minimizing summed Euclidean travel distances to three sites.
Pierre de Fermat : A French mathematician whose work shaped number theory, probability, and analytic geometry. The point bears his name, though the classical triangle problem is also associated with Torricelli.
First Fermat point : The Fermat point inside a triangle whose angles are all less than 120°. This is the minimizing point in the acute-angle case, with three 120° segments.
Distance : A measure of separation between two points, usually the length of the straight segment joining them. The objective adds three distances from one candidate point to the vertices.
Steiner minimal tree : A shortest network connecting specified points, allowed to include additional junctions. Its junction geometry uses the Fermat point when connecting three triangle vertices.
Evangelista Torricelli : An Italian mathematician and physicist known for work on geometry, fluid mechanics, and the barometer. He is credited with an early solution and construction of the three-distance minimization problem.
Second Fermat point : A triangle center associated with external equilateral-triangle constructions and oriented 120° geometry. It complements the first point in constructions involving equilateral triangles.
Centroid : The intersection of a triangle's medians, which is also its center of mass when uniform. It is a familiar triangle center, but it does not generally minimize total vertex distance.
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