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Dynamizing elementary geometry: an introduction to the work of Richard Schwartz. (Dynamiser la géométrié élémentaire: introduction à des travaux de Richard Schwartz.) (French. English summary)
Rend. Accad. Naz. Sci. XL, Mem. Mat. Appl. (5) 31, No. 1, 1-24 (2009).
Let us consider a certain geometric figure $P$ to which we apply a geometric transformation $f$. Thus, we obtain a new figure $f(P)$. If we repeat this process, we obtain a sequence of figures $\{f^n(P)\}$ whose properties we might study (its limit, density, etc.). This idea resembles that of dynamical systems. This paper develops the above idea in some particular cases, namely, that of barycentric subdivisions, Pappus’ theorem and the so-called “pentagram” transformation. Editorial remark: This is a republication, commissioned by the Accad. Naz. Sci., of the paper [Zbl 1092.51500].
Reviewer: Antonio M. Oller (Zaragoza)
Classification: G15 A30
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