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Friday, July 29, 2016

For the Love of Gifs

How many times have you been sitting in a classroom, trying to wrap your head around some unbelievably abstract concept, and no matter what the professor says or how many times the professor explains herself, you just know that you’re missing some essential piece of the puzzle. Then your professor sketches a basic picture on the blackboard and suddenly it clicks and there is a collective sigh of relief among you and your classmates.

There have been countless studies which show that multimedia enhances learning and can enrich a student’s understanding of a concept. For the most part, when talking about educational multimedia, only pictures, slideshows, and videos come to mind; but lets take a look at what gifs bring to the table.

Gifs, or the Graphics Interchange Format, are small animations or a quick, couple-second video that constantly repeat. They are commonly found cluttering up a article on Buzzfeed, or being shared on Facebook or Twitter, but there are some great math gifs roaming around on the internet.

Take this one for example: 

A lot of people in high school learn how to use the trigonometric functions, but never fully understand where they come from. Seeing this gif becomes an “Aha!” moment for some people and they finally see why the unit circle is important and why trigonometric functions are periodic.
Circle cos sin 
Gram-Schmidt orthonormalization process

Or how about this one:

We’ve all sat in a linear algebra class, been given this behemoth algorithm of calculations to perform for the Gram-Schmidt process and tried our best to memorize it. Doesn’t seeing it in action clear things up a little bit?

Remember line integrals?

Line integral of scalar field.gif

Line integral of vector field.gif

Or how about Fourier Series?

Continuous Fourier transform of rect and sinc functions
Fourier transform time and frequency domains (small)
(Speaking from experience, I took a whole class on Fourier Analysis, and it only ‘clicked’ after seeing these)

The great thing about gifs, is that they are short enough that they do not become boring, they will endlessly repeat until you understand, and are aesthetically pleasing. So, do yourself a favor and check out some math gifs. They don’t even have to be serious. Here are some of our favorites that are just fun to watch:

Rolling Hypocycloids Nested Rotating Hypocycloids

by Dan Craig via Wikimedia Commons
                Inside-Out Torus                                          

                       by Surot via Wikimedia Commons
Inside-out torus (animated, small).gif
Circle radians Relationship between Radius and Radians

by Lucas V. Barbosa via Wikimedia Commons  
          Construction of Hypotrochoid              

             by Sam Derbyshire via Wikimedia Commons
Cylinder - hyperboloid - cone Hyperboloid Constructed of Straight Lines

by Cmapm via Wikimedia Commons
  Homotopy between a Torus and a Mug
   by Lucas V. Barbosa via Wikimedia Commons
Mug and Torus morph.gif

Special thanks to Lucas V. Barbosa for creating all the public domain gifs in the main post. See more of his work here.

Do you have any good gifs of your own? Post them in the comments and we might add them to our list of favorites!

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