Growing from a Point: Dynamic Similarity and Geometric Construction

This example demonstrates a dynamic geometric figure that grows from an initial point through ray rotation, orthogonal line construction, and vector translation, generating a sequence of similar shapes that illustrate expansion from a single origin. The core mathematical concepts include angles, line segments, similarity transformation, exponential functions, vectors, and geometric construction. The construction relies on GeoGebra commands such as Rotate, Ray, Intersect, Vector, OrthogonalLine, Point, Line, Segment, Angle, and Circle, together with point objects A, B, C, D, E, F, G, H, angle parameters α, β, γ, δ, and vector/auxiliary objects vec_{ray}, perpen_{ray}. It is suitable for secondary school geometry and function instruction, serving as a classroom demonstration of similarity, the geometric meaning of exponential growth, and interactive GeoGebra construction.