Greenwood press

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online sources for further exploration
Consumer price index (CPI) 

The P/E ratio and other stock ratios are discussed at the Motley Fool page

Musical scales

FAA instructions on making a scale drawing of an F-16 

Compute gear ratios for a bicycle


U. S. Census Bureau QuickFacts on States (Rates and Ratios)

Body-mass calculator


Cooking by numbers

Density lab


How to compute baseball standings

Scale models



Screen ratios

Tuning in

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REFLECTIONS
A reflection is a transformation that produces an image of equal size by flip-
ping an object over a line. For example, you will see a reflection of yourself
when you look in the mirror. Your size in the mirror will be the same as your
actual size, but all of your features will be reversed. So if your hair is parted to
the left, it will appear to be parted to the right in a reflection. Using two mirrors
can create double reflections, allowing someone such as a hair stylist to show
you the back of your head after a haircut while you look straight ahead.
Reflections of objects are naturally visible in water. If you walk up to a pond
on a still, sunny day, you will see an image of yourself on the surface of the
water. In the picture below, buildings and boats on a Holland canal are reflected
in the surface of the canal. The reflection is so good that when you turn the pic-
ture upside down, it looks almost the same.
Reflections are sometimes used to create illusions or expand the size of an
object. Many restaurants have large mirrors on one wall so that the room will
appear twice as large. In an amusement park, a house of mirrors creates multiple
images of anyone walking through, making it difficult to determine the correct
pathway to the exit. Another example of using reflections to replicate an object is
to create designs with a kaleidoscope. A kaleidoscope is a cylindrical toy that cre-
ates colorful patterns by using tiny objects situated at its base and in between two
intersecting mirrors. The reflections at the base repeat themselves as a function of
the angle 
n between the mirrors. Since there are 360 degrees in a circle, then 
there will be 
360
n
repetitions of the object caused by reflections. Each time the 
kaleidoscope rotates, the tiny objects inside it move around and consequently
change the symmetrical pattern one sees when looking through the cylinder.