Holding off on evaluating variables

There is a difference between performing a calculation and solving a problem.

I’ve been considering the equation of a circle, x^2 + y^2 = r^2. Except, you see, that’s not the entire thing. There’s a bit that we’ve dropped because it’s  zeroes (and therefore doesn’t affect our equation):

(x-h)^2 + (y-k)^2 = r^2.

This equation contains the full information–everything that is necessary to draw and position a circle on a cartesian graph. You see, the and k move the circle around the graph. When the circle is on the origin, they are both zero and often dropped from the formula. When figuring something quickly with a circle, the shortened form is more than adequate. However, without them, part of the story is lost.

Similarly, if we have the task of working a problem it is tempting to perform the arithmetic along the way. If we resist, however, at the end we produce a general solution that may be used for other similar problems.

Programming can work the same way. We may write a program to perform a calculation. This would involve lots of hardcoding, many assumptions making it analogous to our “arithmetic along the way”.

Alternatively, try leaving the variables in, or not doing the arithmetic along the way, and preserve the information in the equation which would otherwise be lost.