Axiomatizing Geometry from a Transformation Approach

Completed
Friday, April 29th, 2022
11:00AM  PT
12:00PM MT
1:00PM CT
2:00PM ET
PRESENTED BY: Yvonne Lai


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:
Registration is 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(s):
Yvonne Lai
Yvonne Lai is an expert in the field of Mathematical Knowledge for Teaching. Her current research program seeks to improve the education of secondary mathematics teachers and early mathematics majors by bridging disciplinary perspectives from mathematics and education. Lai is a member of the National Academies Mathematical Sciences Education Board, a Steering Committee member of the CBMS Mathematical Education of Teachers, III, a member at large on the Council of the AMS, past chair of the MAA’s Committee on the Mathematical Education of Teachers, and Vice President-elect of the MAA. Lai received the 2025 AMS Award for Impact on the Teaching and Learning of Mathematics and the 2025 MAA Haimo Award.

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