2012/05/01 by Melvin Royer · 1 citation
Mathematics · #Mathematical and Theoretical Analysis #Advanced Mathematical Theories #History and Theory of Mathematics #CITES #Calculus (dental) #Fractal #French horn #Algebra over a field #Mathematics #Pure mathematics #Computer science #Sociology #Mathematical analysis
paper · doi:10.1080/10511970.2010.517601
openalex publication_date 2012/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
Gabriel's Horn is a solid of revolution commonly featured in calculus textbooks as a counter-intuitive example of a solid having finite volume but infinite surface area. Other examples of solids with surprising geometrical finitude relationships have also appeared in the literature. This article cites several intriguing examples (some of fractal type), adds additional ones, and discusses how these topics can enhance a Calculus II or Real Analysis course by adding cohesiveness between topics, challenging students at multiple levels, and illustrating both the power and limitations of a computer algebra system.