Greenwood press

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REFLECTIONS
A mirror needs to be only one-half your
height in order to see your entire body.
A reflection of the final destination
is used to determine the shortest
path for a ship when a fuel stop is
needed on a journey.

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2001 Nobel prize in chemistry was awarded to scientists who developed catalysts
that would determine the twists in the molecules and either remove the malignant
forms or change their orientation to the beneficial version.
online sources for further exploration
The billiards simulation

Diamond design

Frieze patterns

Mathematical art of M. C. Escher

Measurement microphones

Reflection of light

Reflectors
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Road coatings

Seismic reflection

Total internal reflection


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ROTATIONS
Rotations allow the same object to reappear along a circular path. For exam-
ple, in a tiling pattern, lizards can be rotated so that they tessellate, or fit neatly
into each others’ grooves, as shown in the following figure. Since there are three
congruent lizards in a circle centered around the intersection of the lizard’s
knees, the angle of rotation must be one-third of the degree measure of a circle,
which is 120 degrees.
Rotations are used in circular motion, such as the rotation of a wheel caused