Folding Paper: Dynamic Demonstration of Mathematical Patterns in Origami

This GeoGebra example dynamically simulates the process of paper folding, visually revealing the geometric shapes and mathematical patterns that emerge. The core mathematical concepts include sequences (Sequence), curve sketching, complex numbers, root finding, and combinatorial counting ideas. The construction uses the Sequence command to generate a series of crease lines or folding points, along with multiple objects such as f_1, f_2, list1 through list6, text1 through text4, points A and B, and parameters a, b, c, d, e, f. By adjusting sliders or parameters, users can observe how the figure changes with different numbers of folds, and analyze properties such as crease trajectories, intersection points, or areas. This example is suitable for upper secondary or early university students, serving as a resource for exploring geometric transformations, sequence patterns, and the application of complex numbers in geometry, as well as for mathematical modeling or inquiry-based learning.