Susquehanna Mathematics Colloquium

Susquehanna Mathematics Colloquium

March 27 – Iwan Praton, Franklin and Marshall College,

Dissections with Equal-Area Triangles

ABSTRACT: Is it possible to cut a square into an odd number of nonoverlapping

equal-area triangles? (The triangles don't have to be the same shape.) It's not hard to convince yourself that it's impossible to cut a square into three or five triangles of equal area. (Try it!) But perhaps it is possible to cut a square into a large odd number of equal-area triangles. Is it? This question seems purely geometric, but the answer involves an unexpected appearance from abstract algebra. We will investigate this unusual geometry-algebra connection, then branch out to consider other shapes besides the square.

(Talks begin at 4:15 in Seibert 017. Refreshments at 4:00.)