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math.MG2014
Viviani's Theorem and its Extensions Revisited; Canghareeb, Sanghareeb and a New Definition of the Ellipse
Elias Abboud
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. Th…
math.MG2014
On Routh-Steiner Theorem and Generalizations
Elias Abboud
Following Coxeter we use barycentric coordinates in affine geometry to prove theorems on ratios of areas. In particular, we prove a version of Routh-Steiner theorem for parallelogr…
math.MG2009★ 1 cited
On Viviani's Theorem and its Extensions
Elias Abboud
Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. We consider extensions of the theorem and show that any c…