Points on Curves: Animation of Parametric Curves with Tangent and Curvature Vect

This GeoGebra example demonstrates animated points moving along parametric curves, with tangent lines and curvature vectors displayed in real time, making local curve properties visually intuitive. Core mathematical concepts include parametric curves, derivatives, tangent lines, curvature vectors, trigonometric functions, and vector operations. Construction highlights: the CurveCartesian command defines the parametric curve, Derivative computes tangent vectors, CurvatureVector calculates curvature, Vector draws vectors, Circle creates auxiliary circles, and Text/Textfield add dynamic labels and input fields. Sliders (e.g., a, ω) drive the animation. Suitable for high school to undergraduate mathematics, especially for teaching parametric equations, introductory differential geometry, and dynamic geometric visualization.