Fibonacci Sequence: Geometric Construction and Visualization

This GeoGebra example dynamically illustrates the generation of the Fibonacci sequence and integrates it with geometric elements such as cylinders, rhombi, and translations, offering a visual representation of the sequence's recursive nature. The core mathematical concept is the Fibonacci recurrence (each term is the sum of the previous two), along with its connection to geometric transformations like translation and rotation. The construction uses GeoGebra commands: Point to define key points, Sequence to generate point lists corresponding to sequence terms, and Segment to connect points into polygonal chains or spiral-like structures. Key objects include fi (the Fibonacci sequence), C, p, f, Valores (value list), L, T3, and toggles for natural, integer, and real number sets (verNaturales, verEnteros, verReales), plus text labels (text1, text2, text3) to annotate terms. This example is suitable for secondary school or early university mathematics, helping students grasp recursive definitions, the geometric interpretation of sequence formulas, and how dynamic geometry software can reveal mathematical patterns. It also serves as a resource for interdisciplinary teaching linking algebra and geometry.