1.1 Example 1: Exploring Ratio Relationships in Polygons with Differential Calcu

This GeoGebra example demonstrates the construction of polygons such as rhombi and trapezoids, along with associated line segments, to explore how ratio relationships within geometric figures connect to concepts from differential calculus. The core mathematical ideas involve polygon properties, ratios, and the intersection of geometric paths. The construction uses GeoGebra commands like IntersectPath to find intersection points of paths and Line to create straight lines, with objects including eq1, eq2, f, A, B, d, P, g, t₀, S, and d₀. By manipulating these elements, learners can observe how ratios change dynamically. This resource is suitable for high school or early college students studying geometry and introductory calculus, and can serve as a classroom demonstration or a self-guided exploration tool.