Equal Blue Puzzle: Rectangle Division and Centroid Exploration

① This example demonstrates an animated puzzle called 'Equal Blue Puzzle', where a rectangle is dynamically divided and regions are adjusted so that the blue areas remain equal, visually illustrating geometric area relationships. ② Core mathematical concepts include rectangle area, polygon subdivision, centroid (barycenter), and connections to conditional probability, median lines, and linear programming ideas. ③ Construction highlights: GeoGebra commands such as Point, Midpoint, Mirror, Polygon, and PointIn are used to create points, midpoints, mirrored objects, and polygons; objects include A, B, C, E, F, D, G, F', r, g_1, h_1, k_1, l_1, E', q, s, t, e, f_1, poly1, a, d, b, c, H, poly2, f, h, g, I, J, poly3, i, i_1, j, K, poly4, k, j_1, l, with mirroring and midpoints to build symmetric divisions and PointIn to test point-polygon relations. ④ Suitable for middle/high school geometry teaching, math competition training, or geometric animation demonstrations, helping students understand area conservation and geometric transformations.