A counter-example to the theorem of Hiemer and Snurnikov
Abstract
A planar polygonal billiard
¶
is said to have the finite blocking property if for every pair
(O,A)
of points in
¶
there exists a finite number of ``blocking'' points
B
1
,...,
B
n
such that every billiard trajectory from
O
to
A
meets one of the
B
i
's. As a counter-example to a theorem of Hiemer and Snurnikov, we construct a family of rational billiards that lack the finite blocking property.