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Technically, either of them could be deemed equivalent. The right side is angled
at 14.4 degrees from vertical, or 4 percent of 360 degrees, and the middle is
angled 3.6 degrees, or 4 percent of 90 degrees. As it turns out, most people,
whether due to training in school or a natural proclivity, tend to perceive the
middle figure—represented as a percentage of the difference between vertical
and horizontal—as closer in difference to the change in height.
A change in area in a column, as shown in these
figures, is harder to read. The area in each of the
three columns in Figure 2-5 are equivalent, and can
be perceived as such after a little mental ninjitsu.
At first glance, though, your eye rebels at seeing
them as the same.
This difficulty comes in trying to equate change in
two different dimensions with each other. A rect-
angular shape is by far the easiest to do this with.
Attempt to determine the relationships between
the circular shapes in Figure 2-6 using area and
not radius.
FIguRe 2-5
Doubling and
halving widths and heights
to keep the areas the same
FIguRe 2-6
Evaluating the area of circles
The answer may be surprising: the radii are 20, 28, 34, and 40. The areas, based
on
>
* (radius squared) are 1256.63, 2463, 3631.38, and 5026.55.
Not an even stepping, but that is hard to pick up.
This problem is compounded with pie charts. Attempting to dissect a circle
and determine the constituent percentages is even more difficult. You might
be saying, “But we can use the angles to tell the difference!” Alas, although the
human eye is skilled at judging the angle from vertical or horizontal, judging
intermediate angles is something at which humans are not so skilled, as you
can see from the examples in the figures. Read more on this issue in Chapter
12 about comparison visuals.
Use lengths and
heights rather than
area. Use straight
lines and slopes
rather than circles,
except as markers.
