Research on the Dynamic Path of the “Bench Dragon” Based on the Spiral Theorem and Geometric Reasoning

The "Bench Dragon," or Panlong, is a vibrant traditional folk performance celebrated during major festivals like the Lantern Festival in Zhejiang and Fujian, China, where performers link dozens, sometimes hundreds, of benches together to mimic the shape of a dragon and skillfully maneuver it within tight spaces to create a stunning visual spectacle. To enhance the performance, the Archimedean spiral is used to design the dragon's path, while the cosine theorem simulates its motion, maximizing space efficiency and amplifying visual impact. Additionally, a collision detection algorithm from computational geometry assesses potential risks during sharp turns, and the bisection method refines the spacing of the spirals, minimizing space usage while ensuring smooth, safe movements. By integrating these techniques, an optimized motion model has been developed, allowing performers to execute this culturally rich and visually striking dance safely and efficiently, even in highly constrained spaces.