How To Draw A Heart On Your Graphing Calculator

As Valentine's Day approaches, we are bombarded with hearts, candy, and fluffy stuffed animals.  A slightly more geeky approach to Valentine's Day is this shirt with a heart plotted on the Cartesian coordinate plane. When I see something like this, I can't make myself think, 'Oh, cute!' and move on.  I need to know how it works and that means being able to recreate it myself.

Unable to let this go, I immediately messaged my friend who has a master's degree in mathematics.  We shall call him Mr. Mathematic.  The short answer is that, yes, it works.  However, the equation given needs to be manipulated so that it can be entered into a graphing calculator.

The equation on the shirt is

There are two variables on one side of the equation, but y must be by itself on one side so that it can be correctly entered into a graphing calculator.  This requires moving  to the right side and then taking the square root of both sides.  Lastly, move the  over to the right side.  This can also be written as .

What's important here is that when you take the square root of something, you must consider both positive and negative values.  For example, the square root of 4 can be both 2 and -2.  As a result, our equation manipulation has left us with two separate equations.

1.  

2.  

The first equation will plot the bottom of the heart and the second equation will plot the top.  Grab your graphing calculator and follow these steps to draw your own.  I'm going with the assumption that you know how to use the graphing feature on your graphing calculator of choice.

1.  In the 'Y=' screen, enter in the first equation like so:

 2.  This is what the graph should look like for this equation. Don't forget to resize your graph!  The standard graph on my calculator is when the x and y axis are displaying -10 to 10.  This makes the heart look very small.  I change it so that they both display -2 to 2.

3.  Enter in the second equation like so:

4.  This is what the graph should look like with both equations!  Congratulations!

I know that the heart appears to be broken (hah..?), but that is just a limitation of the graphing calculator.  They can't seem to make circular objects seamless.  If you zoom in, you'll see the lines are pretty close.

So, there you have it!  Show your significant other how much of a geek you really are by expressing your love on your graphing calculator!  Or, keep it simple and more stylish and get the shirt.

Thanks to ThinkGeek, R. Becker (who brought the shirt to my attention), and Mr. Mathematic.