Unsolved_problems_in_plane_geometry.pdf

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Two Dozen
Unsolved Problems
in Plane Geometry
Erich Friedman
Stetson University
Stetson University
3/27/04
efriedma@stetson e
efriedma@stetson.e
du
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Polygons
Polygons
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1. Polygonal Illumination Problem
• Given a polygon S constructed with
i
mirrors as sides, and given a point P
in the interior of S,
ithi id fS
id
d
i
i t P
is the inside of S
completely
illuminated by a
illuminated by a
light source at P?
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1. Polygonal Illumination Problem
• It is conjectured that for every S and P
that the answer is yes but this is not
that the answer is yes, but this is not
known.
• Even this easier problem is open: Does
every polygon S have some point P
where a light source would illuminate
the interior?
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1. Polygonal Illumination Problem
• For non-polygonal regions, the
conjecture is false as shown by the
conjecture is false, as shown by the
example below.
Th
• The top and
bottom are
lli ti
t
d
elliptical arcs with
foci shown,
td th
l
ith
connected with
some circular
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