No, This is not a Circle
This addresses a specific educational challenge in mathematics teaching by clarifying a common visual illusion for students and teachers, but it is incremental as it applies existing tools to a known pedagogical issue.
The paper tackles the problem of identifying a geometric curve that appears circular but is not, using elementary approaches and GeoGebra to refute misconceptions, suggest conjectures, and provide proofs, with methods applicable in middle to high school classrooms.
A popular curve shown in introductory maths textbooks, seems like a circle. But it is actually a different curve. This paper discusses some elementary approaches to identify the geometric object, including novel technological means by using GeoGebra. We demonstrate two ways to refute the false impression, two suggestions to find a correct conjecture, and four ways to confirm the result by proving it rigorously. All of the discussed approaches can be introduced in classrooms at various levels from middle school to high school.