Mathematical, experimental and metaversal approaches to catenoid in geometry education

Mathematical, experimental and metaversal approaches to catenoid in geometry education

The catenoid is formed between two coaxial circular rings and is mathematically classified as a minimal surface. The shape of the catenoid is very interesting and can be used for educational purposes as it explains curvatures and equilibrium shapes in nature. There are many interesting ways to create a catenoid with two ends, i.e. mathematical, experimental and metaversal approaches. This paper details the mathematical formulation and then creates and observes the catenoid for mathematics education. We also provide a tutorial video to create and observe the catenoid in the metaverse. This paper explores the mathematical properties of the catenoid for educators and highlights its use in experiments and virtual environments for educational purposes. Geometric surfaces have been studied extensively from a mathematical perspective. Mathematical concepts are physically invisible but difficult to understand because a mathematical surface has no volume and no mass. The catenoid is a minimal surface found in nature (e.g. soap films). This surface, classified as a minimal surface, can be understood through simple calculus and remains a subject of ongoing research in the field of differential geometry as one of the problems related to the classification of minimal surfaces. In mathematics education, the catenoid can motivate studies from basic calculus to differential equations, mathematical analysis and geometry. The aim of this paper is to mathematically explore the catenoid, which can be used in different ways depending on the objectives of the educator or the different levels of learning, and to inform educators about its application in experiments and computer simulations within virtual environments.