Things to do with a broken stick

We use the idea of the broken stick problem (which goes back to Poincare) and calculate the corresponding probabilities for the cases in which the three broken part are: the medians in a triangle, the altitudes, radii of excircles, angle bisectors, distances from I or O to the vertices, respectively...

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Bibliographic Details
Published in:arXiv.org 2013-04
Main Authors: Ionascu, Eugen J, Prajitura, Gabriel
Format: Article
Language:English
Subjects:
Apexes
Triangles
Online Access:Get full text
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Summary:We use the idea of the broken stick problem (which goes back to Poincare) and calculate the corresponding probabilities for the cases in which the three broken part are: the medians in a triangle, the altitudes, radii of excircles, angle bisectors, distances from I or O to the vertices, respectively sides, and some other three elements in a triangle which determine (more or less uniquely) the triangle. For each case we also look at the probability that the triangle that is (more or less uniquely) defined by the elements, being acute and compare to that of being obtuse.
ISSN:2331-8422