How To Draw A Heart On Your Graphing Calculator

Saturday

Jan222011

How To Draw A Heart On Your Graphing Calculator

Saturday, January 22, 2011 at 12:00PM

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 $\bg_white x^2+(y-\sqrt[3]{x^2})^2=1$

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 $\bg_white x^2$ to the right side and then taking the square root of both sides. Lastly, move the $\bg_white \sqrt[3]{x^2}$ over to the right side. This can also be written as $\bg_white x^{2/3}$ .

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. $\bg_white f(x)=x^{2/3}-\sqrt{1-x^2}$

2. $\bg_white f(x)=x^{2/3}+\sqrt{1-x^2}$

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.

Kristi |

31 Comments |

1 Reference |

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References (1)

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Response: chaseonline

at chaseonline on December 29, 2011

[...]Science Knitting Girl - Home - How To Draw A Heart On Your Graphing Calculator[...]

Reader Comments (31)

if you want a connected heart, press ZOOM then 4. Also you can press 2ND ZOOM (FORMAT) and turn the axes off.

January 25, 2011 |

Ben

Hi Ben, thanks for commenting! I'll post a follow-up soon about how people can make the heart connect and turn off the axes. Thanks!

January 25, 2011 |

Kristi

Add .3 to the second equation and the broken heart will close.

January 26, 2011 |

Marvin

Love this! I ordered the shirt and did this activity yesterday with my algebra 2 students. They really liked this activity. We used geogebra., a free graphing software program( http://www.geogebra.org/cms/ ) instead of graphing calculators and printed our results on hot pink paper. The kids got creative and made a few Valentines cards too. Thanks for the inspiration! PS. I brought in heart shaped cookies to make it extra special, they will always work harder for food! :)

February 10, 2011 |

Mary

I'm confused. I've entered the same equations, but i only get either the top or bottom half.

February 13, 2011 |

Bryan

Instead of graphing calculators and printed our results on hot pink paper. The kids got creative and made a few Valentines cards too. Thanks for the inspiration! PS. I brought in heart shaped cookies to make it extra special.

May 18, 2011 |

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Using Functions,

X^(2/3) ± (24 - X^2)^(1/2)
Xmin = -10
Xmax = 10
Xscl = 1
Ymin = -10
Ymax = 10
Xscl = 1
*Technically just reset the GC to obtain the original graph WINDOW*

You will get an almost perfect heart shape graph...from my GC :D

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if you resize the variables in the equasion to :
2x^(2/3)-square root(20-x^2)
2x^(2/3)+square root(20-x^2), it closes the heart and allowes you to use default window sizes

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Hey guys you can also try this, this makes a connected heart.
f(x)=sqrt(1-(|x|-1)^2
g(x)=arcos(1-|x|)-pi

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