Approximation of Pi by Inscribed and Circumscribed Polygons

① This example dynamically demonstrates how the areas of an inscribed polygon and a circumscribed polygon around a circle approach the circle's area as the number of sides n increases, thereby approximating the value of π. ② Core mathematical concepts include pi, polygon area, the concept of limits, and the squeeze theorem (sandwich theorem) — as n grows, the inscribed area increases from below and the circumscribed area decreases from above, both converging to the circle's area and bounding π. ③ Construction details: using GeoGebra commands such as Circle to draw the circle, Intersect to find intersection points, Sequence to generate vertex lists, Polygon to construct the inscribed polygon (poly1) and circumscribed polygon (poly2), Area to compute areas, and a slider n to control the number of sides; text objects (text1, text2) display the computed areas and the resulting approximation of π. ④ Suitable for high school or early college students learning limits and numerical approximation of π, as well as for math lab activities or inquiry-based learning to illustrate the idea of approximating curved shapes with polygons.