@inproceedings{5a4aa1a80acf43efb78d1dcbc096af53,
title = "Matchstick games: On removing a matchstick without disturbing the others",
abstract = "It is shown that given any configuration of n ≥ 3 line segments (matchsticks) in the plane, there exist at least three segments that can each be translated to infinity, without colliding with the other n − 1 segments. In addition, if n ≥ 4, and the line segments are restricted to be parallel to the axes, at least four segments can be moved without disturbing the others. Furthermore, both lower bounds are best possible. The proofs are elementary and suitable for teaching in lower-level undergraduate courses on discrete mathematics.",
keywords = "Artificial intelligence, Collision avoidance, Computational geometry, Discrete mathematics, Line segments, Robotics, Spatial planning, Translation",
author = "Toussaint, {Godfried T.}",
note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2019.; 2nd International conference on Europe Middle East and North Africa Information Systems and Technologies to support Learning, EMENA-ISTL 2018 ; Conference date: 25-10-2018 Through 27-10-2018",
year = "2019",
doi = "10.1007/978-3-030-03577-8_63",
language = "English (US)",
isbn = "9783030035761",
series = "Smart Innovation, Systems and Technologies",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "580--587",
editor = "Alvaro Rocha and Mohammed Serrhini",
booktitle = "Information Systems and Technologies to Support Learning - Proceedings of EMENA-ISTL 2018",
address = "Germany",
}