  We prove that the Poisson Boolean model, also known as the Gilbert disc
model, is noise sensitive at criticality. This is the first such result for a
Continuum Percolation model, and the first for which the critical probability
p_c \ne 1/2. Our proof uses a version of the Benjamini-Kalai-Schramm Theorem
for biased product measures. A quantitative version of this result was recently
proved by Keller and Kindler. We give a simple deduction of the
non-quantitative result from the unbiased version. We also develop a quite
general method of approximating Continuum Percolation models by discrete models
with p_c bounded away from zero; this method is based on an extremal result on
non-uniform hypergraphs.
