For more information about this meeting, contact Sergei Tabachnikov.

Title: | Cutting a square into triangles |

Seminar: | MASS Colloquium |

Speaker: | Aaron Abrams, MSRI/Emory University |

Abstract: |

Suppose you want to cut the unit square into triangles. What are the possibilities for the set of areas of the triangles? It turns out there are some restrictions: for instance, a theorem of P. Monsky says that if the number of triangles is odd, it is impossible for them all to have the same area.
In general, what happens is that once you decide on the combinatorics of the triangulation, there will always be a polynomial relation that the areas are guaranteed to satisfy. This polynomial is different for different combinatorial triangulations, and it tends to be quite complicated; in particular the polynomial will have one variable for each triangle in the triangulation. The degree of the polynomial, however, is an integer invariant of the underlying triangulation. In this talk we will discuss this polynomial and an algorithm for computing its degree. |

### Room Reservation Information

Room Number: | MB113 |

Date: | 10 / 06 / 2011 |

Time: | 02:30pm - 03:20pm |