BEATS Logo: Composite Construction with Vectors and Geometric Transformations

① This GeoGebra example constructs a graphic logo named 'BEATS', demonstrating how basic geometric elements such as vectors, midpoints, perpendicular lines, circles, and circular arcs can be combined to form a symmetric and rotational composite pattern. ② Core mathematical concepts include two-dimensional vectors, parallelogram properties, reflection and rotation transformations, midpoint and perpendicular relationships, and definitions of circles and arcs; although tags also mention statistics (histogram, means, hypothesis testing), the main focus is geometric construction. ③ Construction highlights: from the summary, commands used include Line, Midpoint, Circle, Intersect, Vector, OrthogonalLine, Polygon, and CircleArc, with objects such as points B, A, C, D, E, F, G, H, I, J, K, L, M, N, O, P, lines f, e, g, h, j, k, p, circles c and c1, vector u, plus text and image objects; the construction builds symmetric structures step by step using intersections and perpendiculars. ④ Suitable for middle school to high school levels, as a comprehensive practice case for geometric construction, vectors, and transformations, also useful for mathematical art design or interdisciplinary projects to help students understand geometric command logic and pattern generation.