2020
DOI: 10.1142/s0218216520500716
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Knot diagrams on a punctured sphere as a model of string figures

Abstract: A string figure is topologically a trivial knot lying on an imaginary plane orthogonal to the fingers with some crossings. The fingers prevent cancellation of these crossings. As a mathematical model of string figure, we consider a knot diagram on the [Formula: see text]-plane in [Formula: see text]-space missing some straight lines parallel to the [Formula: see text]-axis. These straight lines correspond to fingers. We study minimal number of crossings of these knot diagrams under Reidemeister moves missing t… Show more

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Cited by 2 publications
(2 citation statements)
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“…Our analysis reveals patterns indicative of innovation and guided variation 33 within certain regions, while the global distribution of certain string figures strongly suggests a temporally deep shared ancestry reaching back, we suggest, into the Pleistocene. The making of string figures has also been related to the development of mathematical thinking 30,[34][35][36][37][38] .…”
Section: Mainmentioning
confidence: 99%
See 1 more Smart Citation
“…Our analysis reveals patterns indicative of innovation and guided variation 33 within certain regions, while the global distribution of certain string figures strongly suggests a temporally deep shared ancestry reaching back, we suggest, into the Pleistocene. The making of string figures has also been related to the development of mathematical thinking 30,[34][35][36][37][38] .…”
Section: Mainmentioning
confidence: 99%
“…Described by Waugh and Sherman 35 . This method is seemingly also used by the Mapuche, described in Spanish 36 .…”
Section: Data Availabilitymentioning
confidence: 99%