Viviani's Theorem and its Extensions Revisited; Canghareeb, Sanghareeb and a New Definition of the Ellipse

TL;DR

This paper revisits Viviani's Theorem and explores geometric creatures Canghareeb and Sanghareeb, revealing their properties and introducing a novel definition of the ellipse based on their behaviors.

Contribution

It provides new insights into Viviani's Theorem, analyzes the properties of Canghareeb and Sanghareeb, and proposes a fresh geometric definition of the ellipse.

Findings

Canghareeb lives on a line segment inside a triangle

Sanghareeb moves along an ellipse

A new geometric definition of the ellipse is introduced

Abstract

Canghareeb and Sanghareeb are described to be "geometric creatures" living in the plane under certain conditions relative to a triangle. They have common and different features. The former lives on a line segment inside a triangle and the latter lives along an ellipse. Their story ends with a new definition of the ellipse.