Greenwood press

REFLECTIONS
109
A failed attempt to obtain a hole-in-
one on a miniature golf course using
reflections, because the ball will be
blocked by the left wall.
A strategy to obtain a hole-in-one on
a miniature golf course that uses
reflections for a ball to hit two walls. 

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to the angle of reflection. That way, looking at the bottom of a mirror that is half
your size will allow you to look directly at your feet.
The concepts behind reflections can also be used to optimize fuel consump-
tion in water travel. Suppose a cruise liner was departing a port and headed
towards a series of remote islands. Along the way, it may need to refuel near a
mainland to ensure that it can travel the entire distance. The ship will be most
fuel efficient if it angles its navigation towards the shore to refuel, so that its
angle of incidence is equal to its angle of reflection. Even though the ship will
not use a reflection, moving along this path allows it to travel the smallest dis-
tance, as shown in the figure below. This path will be equivalent in distance to a
direct route between the starting point and destination, because the ship will be
directed towards the reflection of the destination. Since reflections preserve con-
gruence, the ship will still be traveling along a line, which is the shortest path
between two points.
Most molecules come in two forms, mirror images of each other. This would
be merely a chemical curiosity were it not that the reflection images of molecules
in medications can produce catastrophically different results. During the 1960s,
the drug thalidomide was given to pregnant women to reduce nausea. One of the
forms of the thalidomide molecule worked well for that task. Unfortunately, the
other form of thalidomide, the mirror image of the good molecule, caused limb
deformities in thousands of infants before its effects were recognized. The drug
L-dopa counteracts symptoms of Parkinson’s disease such as tremors and mus-
cle rigidity. The mirror image of the L-dopa molecule, D-dopa, is toxic. The pro-
duction of thalidomide and L-dopa produces both forms in equal amounts. A sig-
nificant task for scientists was to determine how to remove the toxic form of the
molecules from medications, leaving only the beneficial mirror images. The