Van Kampen Diagrams and Pictures: Definitions, Operations, and Conversions

Abstract

Van Kampen diagrams are an important and powerful tool in many areas of mathematics and engineering. These diagrams are used to visually and intuitively represent the relationships and interactions between different elements, making complex structures easier to understand and analyze. Van Kampen diagrams are distinguished by their ability to analyze structures consisting of multiple elements and identify common points between them.

In this paper, we initially explained Van Kampen diagrams and showed two ways of finding them. Subsequently, we explained Van Kampen pictures and demonstrated four ways of obtaining them. Finally, using various methods, we were able to show how these diagrams can be converted into pictures and vice versa.