Monsky's theorem: Difference between revisions

Rescuing 1 sources and tagging 0 as dead. #IABot (v1.6.2)
m (link directly to p-adic norm (which redirects to a section under p-adic order))
(Rescuing 1 sources and tagging 0 as dead. #IABot (v1.6.2))
#Conclude from the straight-line property that a tricolored triangle must also exist in every dissection of the square into triangles, not necessarily meeting edge-to-edge.
#Use Cartesian geometry to show that the 2-adic valuation of the area of a triangle whose vertices have three different colours is greater than 1. So every dissection of the square into triangles must contain at least one triangle whose area has a 2-adic valuation greater than 1.
#If ''n'' is odd then the 2-adic valuation of 1/''n'' is 1, so it is impossible to dissect the square into triangles all of which have area 1/''n''.<ref>{{webarchivecite web |url=http://www.math.lsu.edu/~verrill/teaching/math7280/triangles.pdf |title=Dissecting a square into triangles |accessdate=2010-08-18 |deadurl=bot: unknown |archiveurl=https://web.archive.org/web/20100818142143/http://www.math.lsu.edu/~verrill/teaching/math7280/triangles.pdf |datearchivedate=August 18, 2010 |titledf=Dissecting a square into triangles }}</ref>
 
==Generalizations==