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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Outer Median Triangles, Árpád Bényi, Branko Ćurgus
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
A Generalization Of Routh's Triangle Theorem, Árpád Bényi, Branko Ćurgus
Árpád Bényi
No abstract provided.
Pompeiu's Theorem Revisited, Árpád Bényi
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
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.