4.3. WHAT ABOUT REFLECTIONS?
225
also asked to find a formula for the reflection through a plane that does not
pass through the origin.
A reflection that sends a geometric figure onto itself is a type of sym
metry of the figure. It is not an actual motion that you could perform on a
physical model of the figure, but it is an ideal motion.
Let’s see how we can bring reflection symmetry into our account of
the symmetries of some simple geometric figures. Consider a thickened
version of our rectangular card: a rectangular brick. Place the brick with
its faces parallel to the coordinate planes and with its centroid at the origin
of coordinates. See Figure
4.3.2
.
r
2
r
1
r
3
Figure 4.3.2.
Rotations and reflections of a brick.
The rotational symmetries of the brick are the same as those of the
rectangular card. There are four rotational symmetries: the nonmotion
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 Fall '08
 EVERAGE
 Algebra, Geometry, Ji, rotational symmetries, rectangular card, diagonal matrix Ji

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