Variable vs. Constant: Using Letters to Represent Numbers

If you are far along enough in your math education that you have encountered letters, then this post is for you.

There are cases in math where we want to work with a more abstract form than a number. See, to us, a number represents only one single quantity. We don't look at the number 4 and say "well that's the number of toes I have." (Assuming that we are human beings that have all of our appendages in the proper places…otherwise, we might say that.) A number to us is a concrete, undeniable amount.

But what if we want to talk about many different numbers? There are times in math when we want to think about a single number without knowing exactly what that number is. Or maybe we need to be able to think abstractly about a whole bunch of numbers at once. That's where letters come in.

We don't have to use letters. We could draw little pictures of elephants if we wanted to, and have the pink ones represent even numbers while the green ones represent odd numbers. The reason we use letters is simply convenience: they are right there, quickly accessible in our minds and we already know how to draw them.

There are two different uses for these letters, which I mentioned above. Now I will go into detail.

Geometry of a Line

This is a post based on a question.

In the diagram, points, V, W, X, Y, and Z are collinear, VZ= 52, XZ= 20, and WX= XY = YZ. Find the indicated length: WX