This talk explores the beauty of dynamic geometry in calculus through animated visualizations and a variety of practical examples. It highlights the close connections between mathematical concepts and geometric figures, encouraging learners to appreciate the beauty of mathematics from a visual perspective. Topics include straight lines, spirals, line-segment folding, Bézier curves, and fractal geometry. Through visual representations of roses, sunflowers, hummingbirds, geometric cityscapes, and Koch snowflakes, the talk illustrates the diverse ways in which mathematics appears in nature, artistic creations, and everyday life. In addition, dynamic visualizations are used to demonstrate calculus-related concepts, including polar coordinates and parametric equations, double integrals and spatial grids, volume calculations, line integrals, and three-dimensional geometry. These visual representations help learners develop an intuitive understanding of abstract mathematical concepts. By integrating mathematics with poetry, music, and visual arts, the talk highlights the interplay between logical reasoning and aesthetic creativity in mathematics. It encourages learners to recognize that mathematics is more than formulas and calculations. Through dynamic geometric representations, mathematics can inspire imagination and creativity, ultimately enhancing students’ interest in learning calculus and geometry.

Implemented by Department of Data Science and Mathematics
Date: 2026/10/12