Random triangles

Bachelor thesis Czech RESTRICTED
Matula, Dominik (2013)
  • Subject: trojúhelník vepsaný trojúhelníku; inscribed triangle in a triangle; trojúhelník v jednotkové kouli; gaussovský trojúhelník; Gaussian triangle; random triangle; triangle in rectangle; náhodný trojúhelník; triangle in unit ball; trojúhelník v obdélníku
    arxiv: Computer Science::Computational Geometry

The author summarizes some previous results concerning random triangles. He describes the Gaussian triangle and random triangles whose vertices lie in a unit n-dimensional ball, in a rectangle or in a general bounded convex set. In the second part, the author deals with an inscribed triangle in a triangle - let ABC be an equilateral triangle and let M, N, O be three points, each laying on one side of the ABC. We call MNO inscribed triangle (in an equi- laterral triangle). The median triangle is a special case of that triangle. Author starts with the median triangle and one by one replaces it's vertices by random points with uniform distribution on the corresponding sides. He proves that propability of such inscribed triangle to be an obtuse triangle increases with number of randomly chosen points while the expected area reminds constant. The whole thesis is concluded with a simulation study. 1
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