A Fire Fighter's Problem

Rolf Klein, Elmar Langetepe, Christos Levcopoulos
Suppose that a circular fire spreads in the plane at unit speed. A fire fighter can build a barrier at speed v > 1. How large must v be to ensure that the fire can be contained, and how should the fire fighter proceed? We provide two results. First, we analyze the natural strategy where the fighter keeps building a barrier along the frontier of the expanding fire. We prove that this approach contains the fire if v > v c = 2.6144. .. holds. Second, we show that any "spiralling" strategy must
more » ... " strategy must have speed v > 1.618, the golden ratio, in order to succeed.