Dimensionality
November 14, 1985
A review of "Dimensionality" by Arthur F. Smith.
Copyright © 1997 Property of Deborah K. Fletcher. All rights reserved.
Dimensionality is a concept dealing with length, width, and depth, and the
relationship among them. It is the concept which permits us to know the difference among the
formulae for perimeter, area, and volume. The concept involves ratios, or proportions.
One example given for dimensionality was this: "If a man is twice as tall as his son,
how much should he weigh compared with his son (assuming they are similarly proportioned)?"
The logic used for this problem under dimensionality is as follows: "the 2:1 ratio for linera
dimensions becomes an 8:1 ratio for volume." This is true because three dimensions (length,
width, and depth, or thickness) were increased. The three dimensions indicxate that the
numbers in the ratio should be cubed, or raised to the third power.
In my opinion, the concept of dimensionality is one which bears further study. I feel
that it could be an effective means of teaching math, particularly if the concept was taught from
early in elementary school. I, personally, have often found myself applying the dimensionality
logic to geometry and proportion problems, though I never before knew what to call the method.
It is comforting to know that this is a legitimate procedure, and heartening to consider that this
might one day be taught as a topic for its own merit. I hope that I shall see that day.
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