A dual visualizer method for interactive topology

A new method for visual and interactive topology is presented. While many classical and modern textbooks on topology contain beautiful illustrations for learners, and much excellent video software has been produced for animating geometrical phenomena, they are all based on static scenarios. This means their geometrical presentations fail to meet the demand for interactivity. With the progress of multimedia technology, dynamic scenarios, which enable learners to make mathematical experiments as many times as they like, are now well within reach. However, an appropriate methodology for interactive mathematical visualization is still lacking. The authors present a dual visualizer method in which the operational visualizer and the geometrical visualizer play complementary roles. The process graph is a key technique in the operational visualizer The method illuminates crucial factors to be considered in the methodology.