eintr: Height of label
What height should the label be?
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The next issue is what height the label should be? Suppose the maximum
height of tallest column of the graph is seven. Should the highest
label on the Y axis be ‘5 -’, and should the graph stick up above the
label? Or should the highest label be ‘7 -’, and mark the peak of the
graph? Or should the highest label be ‘10 -’, which is a multiple of
five, and be higher than the topmost value of the graph?
The latter form is preferred. Most graphs are drawn within
rectangles whose sides are an integral number of steps long—5, 10, 15,
and so on for a step distance of five. But as soon as we decide to use
a step height for the vertical axis, we discover that the simple
expression in the varlist for computing the height is wrong. The
expression is ‘(apply 'max numbers-list)’. This returns the precise
height, not the maximum height plus whatever is necessary to round up to
the nearest multiple of five. A more complex expression is required.
As usual in cases like this, a complex problem becomes simpler if it
is divided into several smaller problems.
First, consider the case when the highest value of the graph is an
integral multiple of five—when it is 5, 10, 15, or some higher multiple
of five. We can use this value as the Y axis height.
A fairly simply way to determine whether a number is a multiple of
five is to divide it by five and see if the division results in a
remainder. If there is no remainder, the number is a multiple of five.
Thus, seven divided by five has a remainder of two, and seven is not an
integral multiple of five. Put in slightly different language, more
reminiscent of the classroom, five goes into seven once, with a
remainder of two. However, five goes into ten twice, with no remainder:
ten is an integral multiple of five.
Info Catalog
eintr: print-Y-axis in Detail
eintr: print-Y-axis
eintr: Compute a Remainder