On Pinned Billiard Balls and Foldings

Jayadev S. Athreya, Krzysztof Burdzy, Mauricio Duarte

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We consider systems of “pinned balls,” that is, balls that have fixed positions and pseudo-velocities. Pseudo-velocities change according to the same rules as those for velocities of totally elastic collisions between moving balls. The times of possible pseudo-collisions for different pairs of pinned balls are chosen in an exogenous way. We give an explicit upper bound for the maximum number of pseudo-collisions for a system of n pinned balls in a d-dimensional space, in terms of n, d, and the locations of ball centers. We also study foldings, that is, mappings that formalize the idea of folding a piece of paper along a crease. We prove a theorem on foldings that implies the number of pseudo-collisions of a finite number of pinned balls must be finite.

Original languageEnglish
Pages (from-to)897-925
Number of pages29
JournalIndiana University Mathematics Journal
Issue number3
Publication statusPublished - 2023

ASJC Scopus subject areas

  • Mathematics(all)


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