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

2014/10/23 by Abboud, Elias
#51N20 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1410.6442

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.

Related

• Loci of Points Inspired by Viviani's Theorem
• Quadri-Figures in Cayley-Klein Planes: All Around the Newton Line
• Counterexamples of the Geometrization Conjecture
• Euler's explorations of extremal ellipses
• Miquel circles and Cevian lines