Rectangles attached to sides of a triangle

Forum Geometricorum Volume 01/2003; 3:145-159.


We study the figure of a triangle with a rectangle attached to each side. In line with recent publications on special cases we find concurrencies and study homothetic triangles. Special attention is given to the cases in which the attached rectangles are similar, have equal areas and have equal perimeters, respectively.

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    ABSTRACT: Classroom Capsules are short (1–3 page) notes that contain new mathematical insights on a topic from undergraduate mathematics, preferably something that can be directly introduced into a college classroom as an effective teaching strategy or tool. Classroom Capsules should be prepared according to the guidelines on the inside front cover and sent to any of the above editors. Rock-paper-scissors (RPS) is a popular way to settle simple disputes because it is can be played quickly, can accommodate multiple players, and is presumably fair. (We as-sume that the reader is familiar with the rules of RPS. If not, consult [7].) Game theory confirms that RPS between two players is fair, provided that at least one of the two players follows the optimal strategy of choosing rock, paper, and scissors uniformly at random. This note discusses experimental results that show that people do not fol-low the optimal strategy in practice, and suggests two strategies for defeating human opponents in RPS.
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