Editing Winding number (section)

===Alexander numbering===

A simple [[combinatorial]] rule for defining the winding number was proposed by [[August Ferdinand Möbius]] in 1865<ref>{{cite journal
| last=Möbius
| first=August
| author-link=August Ferdinand Möbius
| title=Über die Bestimmung des Inhaltes eines Polyëders
| journal=Berichte über die Verhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften, Mathematisch-Physische Klasse
| date=1865
| volume=17 |url=https://gallica.bnf.fr/ark:/12148/bpt6k994243/f482
| pages=31–68}}</ref>
and again independently by [[James Waddell Alexander II]] in 1928.<ref>{{cite journal
| last=Alexander
| first=J. W.
| author-link=James Waddell Alexander II
| title=Topological Invariants of Knots and Links
| journal=Transactions of the American Mathematical Society
| date=April 1928
| volume=30
| issue=2
| pages=275–306
| doi=10.2307/1989123| jstor=1989123
| doi-access=free
}}</ref>
Any curve partitions the plane into several connected regions, one of which is unbounded.  The winding numbers of the curve around two points in the same region are equal.  The winding number around (any point in) the unbounded region is zero.  Finally, the winding numbers for any two adjacent regions differ by exactly 1; the region with the larger winding number appears on the left side of the curve (with respect to motion down the curve).