1 citations · 1 across the 7 of their papers we have counts for
7 papers
Minimal Sum of Powered Distances from the Sides of a Triangle
Elias Abboud
In this paper we apply the KKT conditions to find the minimal sum of powered distances from the sides of an arbitrary triangle.
Loci of Points Inspired by Viviani's Theorem
Elias Abboud
We consider loci of points such that their sum of distances or sum of squared distances to each of the sides of a given triangle is constant. These loci are inspired by Viviani's t…
On Word Equations Originated from Discrete Dynamical Systems Related to Antisymmetric Cubic Maps With Some Applications
Elias Abboud
In this article, we solve some word equations originated from discrete dynamical systems related to antisymmetric cubic map. These equations emerge when we work with primitive and…
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…
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…
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…
Algorithms for Producing and Ordering Lexical and Nonlexical Sequences out of one Element
Elias Abboud
This paper deals with algorithms for producing and ordering lexical and nonlexical sequences of a given degree. The notion of "elementary operations" on positive integral sequences…