Möbius Transformations Interactive Demo

① This GeoGebra example dynamically illustrates Möbius transformations (fractional linear maps) on the complex plane, showing how lines and circles are mapped to lines or circles while preserving angles. ② Core mathematical concepts include complex analysis, Möbius transformation formula (az+b)/(cz+d), conformal mapping, and the interplay between complex numbers and geometric objects like parabolas and secant lines. ③ Construction details: The summary lists objects a, eq1, eq2, f, eq3 — likely a slider 'a' controlling transformation parameters, equations eq1/eq2/eq3 defining initial curves (e.g., a parabola or line), and function f representing the transformed image. GeoGebra's linked algebra and geometry views allow real-time manipulation and observation of how the mapping alters shapes. ④ Suitable for university-level complex analysis courses or advanced high school enrichment, this demo helps learners visualize the geometric essence of Möbius transformations, including circle/line preservation and angle invariance, and serves as an effective teaching tool for instructors.