Monsky's theorem: Difference between revisions

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#Take the square to be the unit square with vertices at (0,0), (0,1), (1,0) and (1,1). If there is a dissection into ''n'' triangles of equal area then the area of each triangle is 1/''n''.
#Colour each point in the square with one of three colours, depending on the [[p-adic numbernorm|2-adic valuation]] of its coordinates.
#Show that a straight line can contain points of only two colours.
#Use [[Sperner's lemma]] to show that every [[Triangulation (geometry)|triangulation]] of the square into triangles meeting edge-to-edge must contain at least one triangle whose vertices have three different colours.