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# Some mathematical results on guarding art galleries

by

Joan P. Hutchinson
Macalester College

January 26, 2009
4:30 pm
Bailey Hall 207

Refreshments will be served at 4:15 in Bailey 204

## Abstract:

What is the minimum number of "guards" needed to guard the interior of the "art gallery," shown below in Figure 1?

Rules: a guard stands in one place, a guard can look and see in 360 degrees, and every point inside and on the boundary of the gallery must be visible to some guard.

What is the minimum number of guards needed to guard the exterior of this art gallery? Same rules except that every point outside and on the boundary of the gallery must be visible to some guard.

And what is the minimum number of guards needed to guard the interior of this art gallery with interior walls, as in Figure 2?

Same rules except that (guards cannot see through walls, but can see through the small doorways in each interior wall and) a guard placed in a doorway can see in 180 degrees in both rooms.

Finally suppose you only know that an art gallery has 25 walls. Then how many guards might you need in the worst case? And what if there are four interior walls, arbitrarily placed, each with a small door opening?

For additional information, send e-mail to math@union.edu or call (518) 388-6246.
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