Algebra vs. Geometry: The Battle for “Real World”

If you’re not really a math person, this is for you.

And based on my life experience, there’s a pretty good chance you don’t like math. There’s an even better chance you don’t like algebra, specifically. I’ve often heard statements like, “I don’t really like math, but at least geometry is useful, unlike algebra.” and I’m ashamed to say I was also one of those voices when I was in my teens. I wish someone had told me better (or I wish I had listened better).

The title Algebra vs. Geometry is a bit misleading, because I’m not going to play out that battle here and name a winner. Because there is no battle.

The Angle on Geometry

Geometry gives us tools to organize and understand the physical world (even if only hypothetically). Distances, angles, volumes, you’ll be good to go. This is where geometry gets its reputation for practicality: its “real world” application. And that’s accurate, I’m not going to argue that. It really does work (obviously), and I’m glad most people seem to strongly associate geometry with fields like engineering, construction, or design.

But what about geometry’s ineffectual cousin, algebra?

A Variation on Algebra

First of all, I’m talking about basic algebra here, not advanced stuff. That’s an entirely different discussion (and one in which I couldn’t intelligently participate).

Let’s start with the basics: algebra is the basic adding of one or more variable to an equation. For example, a normal math equation could be 10+5=15.  Basic addition. Now, if we algebrize (yes, I made that up) that same equation, we get: 10+X=15. Then of course, we have to solve for X. So what, right? You already know that, and now you hate me as much as you still hate your high school algebra teacher.

The problem is, no one ever walks up to you at your job and asks you what the value of X is. That’s what creates the disconnect between algebra education and the “real world.” But there’s two great uses of algebra I want to suggest.

1. You Use Algebra Already

The fact that so many people say things like, “I’ve never used algebra since high school” indicates nothing more than their lack of understanding of what algebra really is.

Time when I use Algebra

I’ll venture to say 90% of people use algebra at least once every day, and that guess is quite conservative. People are doing it in their heads, but they don’t recognize it as algebra.

I have half a tank of gas. My car gets 30 miles per gallon. How far can I go?

14(0.5) * 30 = Y

The tank of gas is 14 gallons (multiplied by 1/2 because it’s a half tank), multiplied by 30 miles per each gallon, and that equals the distance before you’re walking.

We figure out basic equations like this on a regular basis.

We have 11 people in our group. How many vehicles do we need to take to the concert?

We need to start recognizing that algebra is the tool we use to solve for variables. Need to figure out how many hotdogs you need for the picnic? How much did your office parties cost last year, on average? If your boss gives you a percent raise equal to the number of new clients you get this week, how many new clients do you need to earn that vacation you want to go on?

Any time you find yourself saying things like, “Well, it depends on…” or “If that…then this…” you are most likely doing algebra in your head, even if only on a subconscious level. So, give it a fair chance; try jotting down your predicament as an equation. The results might surprise you.

But wait. If you’re about to give up because “this is still really mathy,” don’t stop yet.

2. It’s Not About the Variables

Well, it is and it isn’t. I’m about to tell you something about algebra that I don’t think most people have considered.

What if I told you the numbers don't have to be numbers

The numbers don’t have to be numbers. What unleashed the real power of algebra for me is not what I plug into the variables, but what I use in place of the numbers. I understand this may be an extraneous use of algebra, but I’ve found it to be helpful nonetheless.

What I’m talking about is using situational information as parts of an equation. Pieces of your life become the constants (and the variables) of the equation. Let’s look at a real example I use in my life.

I try to live by the following rule-of-thumb: when going on a leisure trip, I must spend two or more times the amount of time (awake) at the destination than the amount of travel time. In other words, if a place is two hours away, I should spend at least eight hours actively enjoying the destination in order to justify the trip. Admittedly, I have compromised on this, but this is my goal. It’s also algebraic.

T ≤ H/2

The travel time (T) is less than or equal to the waking hours (H) divided by two.

This algebraic equation now gives me a perfectly consistent barometer with which to make decisions about road trips. I’m not suggesting you completely systematize your life to remove subjectivity and human judgement. What I’m saying is that algebra can be used to help organize and understand life from another perspective.

Maybe you don’t care about travel time, but maybe you care about fuel usage instead. Plug it in. Quite frankly, sometimes the equation doesn’t even have to be solvable to be helpful. Just taking the time to organize the pieces of a situation and lay them out in relationship to one another is all you need to gain a deeper understanding. That’s what it’s really about anyway.

X = “Real World”

So there you have it. That’s my plea to you: give algebra another chance in your life. We navigate variables and constants all around us every day, but have been fooled into thinking algebra isn’t “real world.”

Geometry represents the physical world; algebra represents everything else.

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