Polyline Approximation of a Rose Curve to Find Self-Intersection Points

This example demonstrates how to approximate a rose curve with a polyline (piecewise linear path) and then compute its self-intersection points, making the overlapping “petals” geometry visually clear. The key math ideas include rose-curve parameterization (typically linked to polar-form expressions), construction using trigonometric relationships, discretizing a curve into sample points, and using intersection computation to locate where the curve crosses itself. In GeoGebra, Textfield and input boxes manage parameters (such as n, k, and sampling controls); CurveCartesian defines the curve; LaTeX is used for formula/label rendering; Sequence generates a list of discrete sample values; PolyLine builds the polyline approximation; Intersect finds intersection points between curve segments/approximations; and Mod/Div help control periodic indexing and segmentation for consistent generation. Objects include the constructed function/curve (e.g., f), parameter variables, the polyline approximation, and the resulting intersection point set for display. Suitable for secondary school through early university lessons on parametric curves, trigonometry, and geometric constructions, as well as classroom visualization of numerical approximation and intersection-finding.