Fermat Point of a Triangle

① This example demonstrates how to construct the Fermat point of a triangle, the point inside the triangle that minimizes the sum of distances to the three vertices. ② Core mathematical concepts include the definition of the Fermat point, its property as an equiangular point (when all angles are less than 120°, the Fermat point satisfies ∠AFB = ∠BFC = ∠CFA = 120°), and the geometric meaning of the shortest network (Steiner tree). ③ Construction details: Based on the construction summary, the example uses GeoGebra commands such as Segment and LaTeX, involving objects P, A, B, C, segments g and h, point E, function f, TotalNetwork, and text1. It likely constructs equilateral triangles or rotates segments to locate the Fermat point and computes the total network length. ④ Suitable for high school and above to explore geometric optimization, triangle properties, or mathematical modeling, and also useful for university geometry courses to visualize the Fermat point and Steiner problem.