# No, This is not a Circle

## TL;DR

This paper explores methods to correctly identify a geometric curve often mistaken for a circle, using elementary and technological approaches suitable for classroom teaching at various educational levels.

## Contribution

It introduces novel technological methods with GeoGebra to distinguish the curve from a circle and provides multiple approaches for verification, enhancing geometric understanding.

## Key findings

- Two methods to refute the false impression of the curve as a circle
- Two suggestions to formulate correct conjectures
- Four rigorous proof techniques for confirmation

## Abstract

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.