Baravelle's Spiral: Infinite Series in Geometry

This GeoGebra example demonstrates a spiral-like shrinking pattern formed by repeatedly constructing similar polygons and mirroring them, visually representing the summation of a geometric series. The core mathematical concepts involve infinite series, limits, and geometric distribution—each successive polygon's area decreases by a fixed ratio, and the total area converges to a finite value. Construction highlights: using GeoGebra commands Polygon to create the initial polygon poly1, Sequence to generate a chain of nested polygons, and Mirror to flip each new polygon, producing the spiral effect. Key objects include poly1, poly2, poly3, auxiliary points a-j, variable n, color labels lred, lblue, lblack, and text2. This is suitable for high school and above, for learning sequence limits and geometric series, or as a mathematical exploration activity; it also serves as an intuitive visual aid for introductory calculus, linking abstract infinite series to concrete geometric shapes.