Archive for the ‘Representation’ Category

Averia: The Average Font

This is a clever and interesting idea:  creating a new font by taking the average of all existing fonts.

By overlaying all the small letter a‘s, say, from all the different fonts, one can take a visual average and create a new letter a.  Repeat for the whole alphabet, numerals, and punctuation marks, and voila!, you’ve got Averia.

The idea of taking a visual average may be a bit mysterious, but the author describes a few different approaches in how to combine the images.  Essentially all of the instances of a particular symbol are placed on top of each other, and the the darkest parts of the new image are where the instances intersect the most.  The result is then smoothed over to create a readable letter.

And the font looks pretty nice, if not too exciting.  Just what you might expect from the average font.

Click here to see more in Application.

Combinatorial Bracelets

This is another wonderful visual demonstration from Jason Davies:  a combinatorial bracelet generator.

Combinatorics is the mathematics of counting things, and one of the classic “advanced” counting problems is this:  given a certain number of beads of various colors, how many different bracelets can you make?

The problem may seem easy enough, but it becomes quite difficult when you start to understand what “different” really means.

For example, if you turn one bracelet into another by rotating it, then those two bracelets aren’t different.  Even more complicating is that if you can obtain one bracelet from another by flipping it over, then they are also the same!

This visualization can really help develop a sense of the complicated symmetries at work here.

Click here to see more in Representation.

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!

Click here to see more in Art.

Visualizing Ocean Currents

April 23, 2012 1 comment

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.

Click here to see more in Representation.

Wind Map

April 6, 2012 2 comments

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!

Click here to see more in Representation.

GIF Animations of Simple Machines

February 11, 2012 Leave a comment

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

January 13, 2012 Leave a comment

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.

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