The Unit Square: Geometric Construction and Locus Exploration

① This example demonstrates the construction of a unit square and various geometric elements (points, rays, circles, polygons, curves) within it, along with dynamic loci showing paths of points or curves as parameters change. ② Core mathematical concepts include the definition of a unit square, rotation and symmetry, polygon area, quadratic functions, ellipse equations, sequences and series in geometric form, and geometric transformations (rotation, translation) with locus generation. ③ Construction highlights: from the summary, GeoGebra commands used include Ray, Point, Circle, Rotate, Polygon, Intersect, Angle, Segment, CurveCartesian, and Locus; objects include α (angle), B, i, A, c, D, D', poly1, e, f, g, h, E, F, G, C, β, a, b, j, d, loc1, k, l, driven by sliders or parameters for dynamic interaction. ④ Suitable for middle/high school geometry and algebra teaching, as well as university-level analytic geometry or dynamic geometry demonstrations, helping students intuitively understand geometric relationships and locus formation.