Diagrams in Euclidean Geometry: Logical, Philosophical, and Pedagogical Considerations
Summary: This talk will discuss the role of diagrams in geometric proofs. I will discuss some of the history of the use of diagrams in proof, leading up to a twentieth century bias against the use of diagrams. More recent work reveals that we can understand precise rules by which diagrams can be used in geometric proofs, and even formalized. We will discuss these rules, and I will demonstrate my computer program CDEG (“Computerized Diagramatic Euclidean Geometry”) for giving completely formal diagrammatic proofs. Understanding the rules by which diagrams can be used in geometry proofs has important implications for how we teach proof in geometry classes and how we help prospective teachers think about doing proofs with their own students.
Duration: 60 minutes
Format: Online seminar via Zoom web meeting software with questions and discussion. Detailed instructions for joining the seminar will be emailed to registered participants.
Dr. Nathaniel Miller is Professor of Mathematical Sciences at the University of Northern Colorado. He leads the Teaching GeT working group for the GRIP lab. He has published several sets of IBL Geometry course notes in the Journal of Inquiry-Based Learning in Mathematics, and is the current chair of the Special Interest Group of the MAA on Inquiry-Based Learning. A part of his research focuses on the use of diagrams in formal treatments of geometry, and he is the author of the book Euclid and his Twentieth-Century Rivals: Diagrams in the Logic of Euclidean Geometry.