Geodesic
Retroreflecting curves in nonstandard analysis
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 5 (2009) no. 1, pp. 12-24 Cet article a éte moissonné depuis la source Math-Net.Ru

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We present a direct construction of retroreecting curves by means of Nonstandard Analysis. We construct non self-intersecting curves which are of class $C^1$, except for a hyper-nite set of values, such that the probability of a particle being reected from the curve with the velocity opposite to the velocity of incidence, is innitely close to 1. The constructed curves are of two kinds: a curve innitely close to a straight line and a curve innitely close to the boundary of a bounded convex set. We shall see that the latter curve is a solution of the problem: nd the curve of maximum resistance innitely close to a given curve. 
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R. Almeida; V. Neves; A. Plakhov. Retroreflecting curves in nonstandard analysis. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 5 (2009) no. 1, pp. 12-24. http://geodesic.mathdoc.fr/item/JMAG_2009_5_1_a1/

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