Square Spiral: Limits and Iterative Construction

This GeoGebra example demonstrates a spiral formed by repeatedly rotating, scaling, and nesting squares, visually illustrating iterative processes and the concept of limits. Core mathematical concepts include squares, midpoints, rotation, dilation (homothety), limits, and infinite sequences generated by iteration. The construction uses the Polygon command to create the initial square, then applies Midpoint, Dilate, and Rotate commands successively to generate a series of nested squares (poly1, poly1', poly1'', etc.), with auxiliary objects (q1, q2, etc.) guiding the spiral's progression. This resource is suitable for high school or early college students to explore geometric transformations, the geometric meaning of sequence limits, and iterative construction techniques in dynamic geometry software. It also serves as a visual aid for teaching limits in calculus.