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UID:www.tcs.tifr.res.in/event/1449
DTSTAMP:20240710T110123Z
SUMMARY:Sperner's lemma and the equidissection of regular polygons
DESCRIPTION:Speaker: Pranshu Gaba (TIFR)\n\nAbstract: \nEquidissection of a
regular polygon is the problem of dissecting the polygon into triangles o
f equal area. Given a regular n-gon and a positive integer m\, we ask if i
t is possible to equidissect the n-gon into m triangles. To answer this qu
estion\, we make use of Sperner's lemma along with some elementary number
theory. Sperner's lemma is a major combinatorial result that has found app
lications in topics such as fixed-point computation and fair division.We s
hall see Sperner's lemma and its proof\, and use it to solve the equidisse
ction problem for regular polygons. We will also look at some polygons tha
t cannot be equidissected into m triangles for any positive m. Finally\, w
e will go over the equidissection problem for higher-dimensional hypercube
s.References:- Monsky\, P. (1970). On Dividing A Square Into Triangles. Th
e American Mathematical Monthly\, 77(2)\, 161–164. https://doi.org/10.1
080/00029890.1970.11992441- Stein\, S. (2004). Cutting a Polygon into Tria
ngles of Equal Areas. The Mathematical Intelligencer 26\, 17–21. https:
//doi.org/10.1007/BF02985395\n
URL:https://www.tcs.tifr.res.in/web/events/1449
DTSTART;TZID=Asia/Kolkata:20240712T143000
DTEND;TZID=Asia/Kolkata:20240712T153000
LOCATION:A-201 (STCS Seminar Room)
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