Leírás
Abstract:
In 1970, Paul Monsky proved that a square cannot be dissected into an odd number of triangles of equal area. This theorem raises the more general question of what other restrictions there might be on the areas of the triangles in a dissection of a square. It turns out that if one fixes the combinatorics of the dissection, then there is a single irreducible polynomial that must be satisfied by the areas of the triangles in the dissection. Further, the area of any triangle of the dissection turns out to be integral over the ring generated by the areas of the other triangles in the dissection. Similar relations exist for dissections of trapezoids and general 4-gons. These integrality relations and the mysteries surrounding them will be the focus of this talk.
This is joint work with Aaron Abrams.
Zoom link: https://us06web.zoom.us/j/89449663486?pwd=MjF5SE5IMXZ3Smg5MEhSdSt5YlRiUT09
Meeting ID: 894 4966 3486
Passcode: 809782