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# The Equation for a Happy Mother's Day

What's the most important holiday in May? Obviously it's Mother's Day. But did you know there's an equation that can help you celebrate Mom? Keep on reading to find out what it is!

By
Jason Marshall, PhD
May 9, 2014
Episode #198

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## What Are Parametric Equations?

Instead of relating x and y directly, we can just as well relate each of them to some additional thing, which we call a parameter (usually represented by the letter t). So instead of the single equation yx + 2, we can instead write the pair of equations:

• y​ = t
• x + 2 = t, or turning this around we get x = t - 2

If you think about it, you'll see that you can plug-in any value for the parameter, t, that you'd like, and you'll get back x and y values that match what you'd get back using our previous ("normal") equation. This new way of writing our relationship is called a "parametric equation" because it relies on an extra parameter.

Why are parametric equations useful? In truth, that's a big topic that we're going to save for another day. For today, suffice it to say that writing certain equations parametrically makes them much easier to work with. Among these equations is a certain special little one that I've been hinting just might ensure you have a happy Mother's Day. What does it look like?

## The Equation for a Happy Mother's Day

The equation I'm referring to belongs to a class of equations whose graphs are called heart curves. Of particular importance for us today is a heart curve which can be represented with the parametric equation:

• x = 16 sin3(t)
• y = 13 cos(t) - 5 cos(2t) - 2 cos(3t) - cos(4t)

Looks crazy, right? Well, it kind of is. But the amazing thing is that if you plug-in a bunch of values for t ranging between -π and π, get the x and y values, and then plot them all on the same set of axes, you'll get a graph that looks like a beautifully drawn heart. Alternatively, if you don't want to make the plot yourself (which given the complexity of the parametric equation is indeed a lot of work), you can let WolframAlpha do it for you!

Go ahead, click that link—pretty amazing, right?And if you plot that up and give it to your mom for Mother's Day, it just might help make your Mother's Day that much happier.

## Wrap Up

OK, that's all the math we have time for today.

Please be sure to check out my book The Math Dude’s Quick and Dirty Guide to Algebra. And 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.

Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

Mother's Day image from Shutterstock.

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