The Theory on Loops and Spaces -- Part 2

The study of loops and spaces in mathematics has been the subject of much interest among researchers. In Part 1 of "The Theory on Loops and Spaces," published in the "Mathematics Teaching Research Journal," introduced the concept and the basic underlying idea of this theory. This article continues the exploration of this topic and aims to advance the understanding of the theory through observation and analysis of patterns. A systematic examination of intersection points and their numerical Sum is conducted, and the effect of the order of numbering on the analysis is analyzed. Furthermore, the physical implications of the theory are discussed, and the validity of the theory in the third dimension is confirmed through analysis. This article provides a solid foundation for the understanding of the elementary principles of Graph Theory and paves the way for the development of more advanced theorems in the field. Additionally, the article demonstrates how patterns in nature can be analyzed and expressed mathematically, offering a unique perspective on the interplay between mathematics and the natural world. The work is inspired by the video posted by mathematician Dr. James Tanton on his YouTube channel on September 27th, 2021. [For "The Theory on Loops and Spaces. Part 1," see EJ1350656.]