Defining π via Infinite Densification of the Sweeping Net and Reverse Integration

We present a novel approach to defining the mathematical constant π through the infinite den-sification of a sweeping net, which approximates a circle as the net becomes infinitely dense. Bydeveloping and enhancing notation related to sweeping nets and saddle maps, we establish a rigor-ous framework for expressing π in terms of the densification process using reverse integration. Thismethod, inspired by the concept that numbers ”come from infinity,” leverages a reverse integralapproach to model the transition from infinite densification to the finite circle. Our work not onlyoffers a new perspective on the geometric interpretation of π but also provides insights into reverseintegration techniques and their applications in mathematical analysis.