Circumference of a Circle using 'i' (Riemann Sum & Derivative)

① This GeoGebra example dynamically demonstrates how the circumference of a circle can be approximated by summing small straight segments indexed by the natural number 'i', visually connecting to the concept of π. ② Core mathematical concepts include circle circumference, upper and lower Riemann sums, derivative intuition, limits, natural numbers, and angles. ③ Construction highlights: using GeoGebra commands such as Point, Semicircle, Mirror, Segment, Intersect, Vector, Polygon, and Integral, the applet builds multiple objects (A, B, c, c', f, text1, etc.) and uses a slider or parameter to increase the number of subdivisions, refining the approximation. ④ Suitable for high school or early college students to explore the fundamental ideas of calculus (approximation, limits) and to investigate the value of π interactively.