Why Is Algebra Useful?
Is algebra actually useful to anybody? Might it even be useful in your daily life? Absolutely! Keep on reading to find out how.
In the last episode, we began talking about how to solve equations. We’re certainly not finished with that topic yet—and we’ll come back to it soon enough—but today I want to tackle a different but related question: Is algebra actually useful in the real world? It probably won’t surprise you that my eventual answer is going to be: Absolutely—algebra is super useful! But why exactly? Stay tuned because that’s precisely the question we’ll be answering today.
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The Story of Knot Dude
To get things started, let’s jump into our algebraic time machines and travel back about 4,500 years…back to the time when the Great Pyramid of Giza was being built in Egypt. Imagine if you will—since no, this isn’t a true story—that at that time there was a young guy who loved to tie knots in rope…tons and tons and tons of knots. Not surprisingly, everybody thought this guy—we’ll call him Knot Dude—was kinda strange, but he really didn’t care because he was absolutely fascinated by his knots.
Now, it turns out that Knot Dude’s dad—aka, Papa Knot—was a prominent member of Egyptian society. In fact, Papa Knot was the person in charge of figuring out how to build the foundation for the Great Pyramid. And that was not a job to be taken lightly since this is a big pyramid—about 750 feet long on each side and 450 feet high!
Not having much of a social life, Knot Dude spent a lot of time in the evenings listening to his father complain about the difficulty of his job. In particular, one problem was proving quite vexing: how to line up the four walls of the foundation of the pyramid so they all would meet to form a giant perfect square. After all, without a perfectly square base, the pyramid wouldn’t be a pyramid—it’d just be a mess.
What’s the key to getting the foundation to come out right? Well, Papa Knot knew that if he could come up with a way to make sure that each of the four walls came together and formed perfect corners known as right angles—the kind you see in the corners of a perfect square—then his foundation would also be perfect. But for the life of him, he couldn’t figure out how to do it.
How to Make a Right Angle
When Knot Dude heard his father describe this problem, he got extremely excited because he realized that he had made a discovery several months earlier during one of his knot-tying frenzies that solved it.
All Papa Knot needed to do was get a single piece of rope and tie 13 evenly spaced knots in it—one at each end, and then eleven more spaced evenly between the two ends. If he stretched the rope out and folded one end up after 3 even segments and the other end up after 5 even segments to form a triangle, he’d end up with a very special triangle in which two of the resulting sides always form a perfect right angle.
Knot Dude also discovered that the rope doesn’t have to have 13 evenly spaced knots in it for this to work. It also works if the rope has 25 or 37 evenly spaced knots. In fact, he found that any number of knots would work so long as the lengths of the resulting three sides of the triangle—which we’ll call lengths a, b, and c—satisfy the equation
a^2 + b^2 = c^2
In other words, Knot Dude found an algebraic way to look at this problem, too! To Papa Knot’s great joy, this bit of mathematical insight was exactly what he needed. It gave him a way to form a right angle that he could use to lay out the four corners of the pyramid’s foundation. Afterwards, huge celebrations ensued and a merry time was had by all since the great dilemma had been resolved…with math, I might add.
Is Algebra Useful in Real Life?
And that’s the story of Knot Dude. What’s the point of this tale? It’s definitely not to suggest that this is how things actually went down 4,500 years ago. The real point is that something happened in this story that also happens in the real world. And that is that some creative person spent time thinking about seemingly abstract and crazy things. Things like: How many ways are there to tie knots in a piece of rope? What interesting arrangements can I make from this? Is there some way to use algebra or some other kind of math to write down and share what I’ve discovered?
In other words, some creative person starts by spending time thinking about abstract math. And sometimes these abstract thoughts end up having important real-world uses. In fact, the algebraic equation that Knot Dude discovered, a^2 + b^2 = c^2, has so many important uses that it’s now quite famous—you probably know it as the Pythagorean Theorem.
How does it work? Where does it show up in real life? And what does it have to do with our larger story of learning how to solve equations? Check back next time to find out.
Wrap Up
Okay, that’s all the math we have time for today. If you want to learn more about algebra, please check out my book The Math Dude’s Quick and Dirty Guide to Algebra.
Remember to become a fan of the Math Dude on Facebook where you’ll find lots of great math posted throughout the week. If you’re on Twitter, please follow me there, too. Finally, please send your math questions my way via Facebook, Twitter, or email at mathdude@quickanddirtytips.comcreate new email.
Until next time, this is Jason Marshall with . Thanks for reading, math fans!
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About the Author
Jason Marshall is the author of The Math Dude’s Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.
