The Art Gallery Theorem
Thursday, Jan. 27, 2000
- Geometric software.
- Textbook, Chapter 1.1, pages 1-11: The Art Gallery Theorem, cont'd.
- Points, lines, polygons. Convex and non-convex polygons.
Simple closed curves and polygons.
Mod n counting.
Jordan Curve Theorem.
- Visibility. Klee's Art Gallery problem. Max over min formulation.
Experimentation. Chvatal's comb example: necessity of n/3 guards.
- Triangulation of a polygon.
- Graphs. Planar graphs.
- Graph coloring. 3-coloring of triangulation graphs.
- The pigeonhole principle.
- Fisk's proof of Chvatal's Theorem: n/3 guards are sufficient.
- First problem set posted on web.
Last modified January 23, 2000.