# Valentine Heart

This post came through on my reading earlier this week and I decided to comment on it just in time for Valentine’s Day.  The post was called "This Valentine, Send your Loved One a Google Search Query".  The whole point of the post was to remind us that a Google Search could be used to draw a graph.  In this example, the search query

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

would draw a heart for you.  All that you have to do is copy the above equation and past it into a Google search and the result would be a heart.  It looks like this.

The resulting graph is actually interactive if you move your cursor along the x-axis to generate the corresponding point on the y-axis.  The adventurous will go into the equation and adjust some of the calculations to see what effect it might have on the image.  It’s pretty interesting in a mathematical way.

It’s one of the purest joys of mathematics that you can create an equation that will draw a graph or image and visualize things for you.  In that respect, it is such an art.

Do we show "real world" applications though?  This is a silly little example that hit home recently with my university class.  A group of students was demonstrating a piece of graphic software and was showing off their new-found knowledge of the file types that it would save/export to.  JPG, GIF, PNG, EPS, AI, CDR, … we got them all.  The class was impressed with the variety of formats.  But did they know why or what the significance was?  Where would you use these different formats?

I pushed the conversation by asking if anyone could explain the different between vector based and raster based graphics.

chirp, chirp

You’ve got to love those teachable moments.  So, we did a little digging and everyone understood the dangers of just dragging the corner of a photo that they were going to upload to Facebook.  They understood the concept of bitmapped images but that’s where the understanding stopped.  The concept that an image could be generated by a series of equations rather than a bunch of dots was really foreign.  So, we dug a little deeper and found this excellent article describing the differences.

Now chances are these folks will not be creating the next roadside billboard or drafting diagram but clearly this concept had eluded them in their education.  We didn’t have time to do the topic justice.  I wonder, though.  Do you only learn this if you’re taking a drafting or graphic design course?  Is this a concept that everyone should at least know about or is it a niche piece of learning that’s only necessary if it directly applies to a task at hand?

But if you don’t understand that an image can be created by a mathematical equation, where will the inspiration for the next Valentine Heart of St. Patrick’s Day Shamrock come from?

Happy Valentine’s Day.