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I want to learn more about de Rham's trisection method in

  • De Rham, Georges, Un peu de mathématiques à propos d'une courbe plane, Elemente der Mathematik 2 (1947): 73-76. http://eudml.org/doc/140463.

Specifically, if there exists a general formula for the limit of a polygon. I have the French version of his article, but I don't have the English version - could anyone provide a link?

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    $\begingroup$ Why do you think there is an English version? $\endgroup$
    – David Roberts ♦
    Commented Jan 7, 2023 at 12:05
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    $\begingroup$ I just assumed that there would be an English version, please correct me if I'm mistaken somehow $\endgroup$
    – FakeNTAccount
    Commented Jan 7, 2023 at 12:54
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    $\begingroup$ What might be reasonable to ask is if there is a modern treatment or review of this material that's in English. Google Scholar finds many citations of the original article. $\endgroup$
    – David Roberts ♦
    Commented Jan 8, 2023 at 8:43
  • $\begingroup$ Protasov's paper says that the limit curve is nowhere smooth, so not given by any analytic formula. But maybe there is some other way to write a formula. $\endgroup$
    – Ben McKay
    Commented Jan 8, 2023 at 9:14
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    $\begingroup$ @DavidRoberts: MR2069197 (2005c:37175) Protasov, V. Yu. (RS-MOSCM) On the smoothness of de Rham curves. Izv. Ross. Akad. Nauk Ser. Mat. 68 (2004), no. 3, 139–180; translation in Izv. Math. 68 (2004), no. 3, 567–606. $\endgroup$
    – Ben McKay
    Commented Jan 8, 2023 at 12:28

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A popular English-language treatment

de Boor, Carl, Cutting corners always works, Comput. Aided Geom. Des. 4, 125-131 (1987). ZBL0637.41014.

For this subsequent de Rham paper

MR0095227 de Rham, Georges. Sur quelques courbes definies par des equations fonctionnelles. (French) Univ. e Politec. Torino Rend. Sem. Mat. 16 (1956/57), 101–113.

there is a translation in

Edgar, Gerald A. (ed.), Classics on fractals, Studies in Nonlinearity. Boulder, CO: Westview Press (ISBN 0-8133-4153-1/pbk). xii, 366 p. (2004). ZBL1062.28007.

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