Ratio of a Circle: Dynamic Visualization of Area and Circumference

This GeoGebra example dynamically demonstrates the ratio of a circle (i.e., π) and its relationship to the area and circumference, visually showing how sector divisions, angle changes, and numerical proportions interrelate. Core mathematical concepts include circle geometry, π, sector area, angle and arc length, limits, and natural number accumulation. Construction uses commands such as Point, Semicircle, Segment, Angle, Textfield, and Vector, creating objects like f, a, g, A, B, c, d, C, D, h, F, G, H, α, E, I, i, InputBox1, text1, b, v, text2, J, j, K, k, text3. Suitable for middle school geometry learning about circle properties and π approximation, as well as introductory calculus for deriving the area formula of a circle.