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Archive of posts filed under the Representation category.

Wind Art

This sculpture by Charles Sowers functions simultaneously as a stimulating piece of art, a representation of data, and an illustration of vector fields.

Windswept is a giant billboard covered in little aluminum arrows that twist and turn in the wind.  The arrows can be thought of as bits of data, namely, the direction of the wind that point.  Taken together, and dynamically, they give a sense of the complicated nature of swirling and changing winds.

Just like this wonderful wind map, this sculpture represents mathematical ideas in a beautiful and thought-provoking way!

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Visualizing Ocean Currents

This is a beautiful representation of ocean currents around the world:

Put together by the NASA/Goddard Space Flight Center Scientific Visualization Studio, this short video circles the digital globe, showing the relative strengths and directions of ocean movement.

Watching this allows one to see some of the basic mathematics of fluid flow, like tendency toward rotation and how fluid behaves at boundaries.  In addition, global phenomena like the jet stream and trade winds can also be perceived.

This dynamic representation of data is similar to this wind map in how it brings to life the ideas of vector fields and flow lines.

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Wind Map

This is a stunningly beautiful visualization of wind patterns in the US:

Not only is this a functional and immediately accessible representation of data, but it also brings to life the mathematical concepts of vector fields and flow lines.

Apart from atmospheric science questions like “Why is this area windier than others?” are purely mathematical questions like “Which location is the calmest?” and “Which location is most volatile?”

And if you enjoy this, be sure to check out this visualization of the world’s ocean currents!

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GIF Animations of Simple Machines

World of Technology has several great GIF animations demonstrating some fundamental mechanics:

Seen at right is the radial engine.  The constant velocity joint is my favorite, but it’s also great to learn how a sewing machine really works!

Some great visualizations of interesting and intricate 3D geometry and engineering.

Click here to see more in Technology.

Kitchen Counting

I was making lemonade the other day, and this happened.

which of course, equals, the following:

There you have it:  the sum of the first three triangle numbers is the third tetrahedral number!  Proof by lemons.

Click here to see more in Appreciation.