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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Rotation and winding numbers for planar polygons and curves


Authors: Branko Grünbaum and G. C. Shephard
Journal: Trans. Amer. Math. Soc. 322 (1990), 169-187
MSC: Primary 52A99; Secondary 26B15, 51M99, 57M99
MathSciNet review: 1024774
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Abstract: The winding and rotation numbers for closed plane polygons and curves appear in various contexts. Here alternative definitions are presented, and relations between these characteristics and several other integer-valued functions are investigated. In particular, a point-dependent "tangent number" is defined, and it is shown that the sum of the winding and tangent numbers is independent of the point with respect to which they are taken, and equals the rotation number.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1990-1024774-2
PII: S 0002-9947(1990)1024774-2
Keywords: polygon, curve, winding number, rotation number
Article copyright: © Copyright 1990 American Mathematical Society