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Articles 1 - 4 of 4

Full-Text Articles in Physical Sciences and Mathematics

Outer Median Triangles, Árpád Bényi, Branko Ćurgus Jan 2014

Outer Median Triangles, Árpád Bényi, Branko Ćurgus

Árpád Bényi

We define the notions of outer medians and outer median triangles. We show that outer median triangles enjoy similar properties to that of the median triangle.


A Generalization Of Routh's Triangle Theorem, Árpád Bényi, Branko Ćurgus Jan 2013

A Generalization Of Routh's Triangle Theorem, Árpád Bényi, Branko Ćurgus

Árpád Bényi

No abstract provided.


Pompeiu's Theorem Revisited, Árpád Bényi Jan 2009

Pompeiu's Theorem Revisited, Árpád Bényi

Árpád Bényi

Pompeiu's theorem states that if ABC is an equilateral triangle and M a point in its plane, then MA, MB, and MC form a new triangle. In this article, we have a new look at this theorem in the realm of arbitrary triangles. We discover what we call Pompeiu's Area Formula, a neat equality relating areas of triangles determined by the points A, B, C, and M.


The Simple Random Walk On A Random Voronoi Tiling, Amites Sarkar, Louigi Addario-Berry Oct 2005

The Simple Random Walk On A Random Voronoi Tiling, Amites Sarkar, Louigi Addario-Berry

Amites Sarkar

Let P be a Poisson point process in ℝd with intensity 1. We show that the simple random walk on the cells of the Voronoi diagram of P is almost surely recurrent in dimensions d = 1 and d = 2 and is almost surely transient in dimension d ≥ 3.