GeT Seminar - April 29, 2022

 

Axiomatizing Geometry from a Transformation Approach

Friday, April 29, 2022
11:00 am PT | 12:00 pm MT | 1:00 pm CT | 2:00 pm ET
Presenter: Dr. Yvonne Lai

Summary: Historically, educators have held up the study of Euclidean geometry as a model of learning deductive reasoning rooted in axioms. However, axioms based solely on the Elements may not get a high school student all the way to clean, rigorous proofs of congruence and similarity from a transformation approach. While Euclid did allude to superposition by isometries, he did not axiomatize this idea. In this talk, I will discuss an axiomatic system for College Geometry that satisfies the following properties: (1) The system supports proofs of congruence and similarity of all polygons as well as curves defined as a locus of points such as conic sections; (2) it has the potential, with minimal modification, be suitable for use with high school students; (3) it treats angles in a way that generalize easily to angle usage in trigonometry and precalculus. This system combines and adapts Wu’s (2013) and Picciotto and Douglas’s (2017) systems.

Registration Closed

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.

Presenter:

Yvonne Lai has been fascinated by geometry since she was young, and wrote her doctoral dissertation in the area of hyperbolic geometry and geometric group theory — in other words, an area where geometric transformations are key. Following her PhD, she studied under Deborah Ball as a post-doctoral fellow to learn the research area of Mathematical Knowledge for Teaching. This project combines her love of geometry and her passion for teaching prospective teachers.