Thursday, February 9, 2012

A Valentine Graph Equation

This is a fun little math trick that will give you a romantic Valentine graph!  (OK, maybe romantic isn't the right word...) Please remember to click the Like button if you like this!

Several months ago, Google added the ability to graph equations directly from their search line.  All you have to do is type in the equation instead of performing a search query, and Google will return to you a graph of your equation!  So, instead of having to pay money for a fancy math graphing calculator (such as the TI83), or doing it the long and slow way of graphing out by hand on graph paper, now you have a very easy to use graphing calculator for free whenever you are on the Internet!

Just in time for Valentine's Day, @Huckberry on Twitter has noted that if you type in the following equation into the Google search line, this is actually a Valentine graph equation and Google will return a result that shows you a nicely graphed out heart!  Try searching for this Valentine graph equation on Google and see what happens!

sqrt(cos(x))*cos(300x)+sqrt(abs(x))-0.7)*(4-x*x)^0.01, sqrt(6-x^2), -sqrt(6-x^2) from -4.5 to 4.5

This graph is composed only of standard trigonometry functions (ie. cosine), square roots, absolute values, exponents... all familiar concepts introduced in your math classes fairly early.  However, you've probably never seen them put together quite like this!  I can point out a few things about this equation though.  The absolute value is involved in creating the mirror image, and the 300x part of the cosine function actually is the part that determines the frequency of the plotted line.  If you reduce the 300 to something smaller (try 20), you can actually see that the interior of the heart (the "solid" colour) is actually just a line bouncing up and down along the domain of the equation.  The 300 makes the frequency so tight that it appears solid.  (Thanks to Samantha Murphy for pointing this out in her post!)

A Valentine graph is just one of many impressive graphs that can be created by plotting mathematical expressions.  As many of my readers will undoubtedly remember, a few months ago I posted an image of the Batman equation and Batman graph.  A lot of people have since searched for that and have really appreciated what a mathematical equation can actually represent.  Hopefully this Valentine graph equation also helps to demonstrate that math isn't just all about problem sets and tests... math can be pretty fun and cool too!

I'm going to send an email to my wife with a link to that search result page.  How's that for romantic?  :)

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