Application

Folding Steel

This is an amazing application of origami:  a steel grocery bag that can fold flat!

http://news.sciencemag.org/sciencenow/2011/03/paper-plastic-or-steel.html

Although you probably wouldn’t want to carry these to the store with you, this result could have real applications in industrial packaging.  In addition, it’s another step towards the mathematical-origamist’s dream:  designing building that can rearrange and rebuild itself as needed!

A great talk by Erik Demaine on mathematical origami opened my eyes have this amazing application of mathematics, and my students and I have been having a lot of fun with folding ever since!

By patrick honner, ago

The Other Line Always Moves Faster

This is a nice introductory video on elementary queuing theory from Bill Hammack, the engineer guy.

http://www.youtube.com/watch?v=F5Ri_HhziI0

Hammack poses a classic queuing theory conundrum:  people in a town use phone lines at an average rate of two per hour; how many phone lines should the town have?  The naive answer of two lines is far from optimal, because of bunching.

In addition to exploring this basic idea, Hammack also discusses the efficiency of the single-line system (everyone waits in one line for the next available cashier) versus the multiple-line system (each cashier has a separate line).  Assuming that delays are distributed randomly among the cashiers, the single-line system minimizes the overall impact of a delay at any one cashier, and so, is more efficient.

And if every individual line has an equal chance of experiencing a delay, it stands to reason that every line has an equal chance of being the fastest.  This explains why the other line always seems to move faster:  if there are ten lines, you’ve got a 1 in 10 chance of choosing the fastest one, which means 9 times out of 10 a different line is moving faster!

By patrick honner, ago

The Shape of the Moon’s Orbit

This is a short and readable exploration of the question “What is the shape of the Moon’s orbit around the Sun?”

http://www.math.nus.edu.sg/aslaksen/teaching/convex.html

The Moon makes circles (ellipses, really) around the Earth while the Earth makes circles around the Sun, so what does the path of the Moon look like?

It’s a fun problem to think about, and I encourage you to do just that before you click through and see the discussion.

This simply posed problem touches on polar and parametric curves, 3-dimensional geometry, and of course, astronomy.  And naturally there are lots of extensions, like “What if something were orbiting the Moon?”

By patrick honner, ago

More Quantitative Confusion

I’m pretty sure printer ink is a huge scam to begin with, and stuff like this doesn’t help.

I went to purchase some ink and looking to minimize my time spent in office supplies stores, I thought I’d buy a two-pack.  “We’re out of the two-pack,” the helpful employee said, “but this is the XL.  It’s the same price as the two-pack, and it has 3 times as much ink as the single cartridge.”

So after my purchase, I felt compelled to perform a side-by-side comparison.

I’d estimate the XL cartridge to be about 120% the size of the original.  But its ink capacity is 350% of the original?  That doesn’t seem to add up.

By patrick honner, ago

Math and Computer Animation

This is a clear, concise, and fascinating overview of how some very advanced mathematical ideas are making their way into 3-D animation.

http://www1.ams.org/samplings/feature-column/fcarc-harmonic

Here’s the basic setup.   In order to efficiently model a character, you approximate it with a frame that is built around a few important points.  To move the character, you focus on moving just those points that define the frame.  Thus, moving the character from point A to point B boils down to understanding where those handful of crucial points go.

The tricky part is figuring out a way to smoothly bring all those in-between points along for the ride, and that’s where the math comes in.  The secret is to think of those in-between points as averages of the points that define the frame.  The article explains how barycentric coordinates, harmonic functions. and a surprising amount of calculus are being used to pull off this movie magic!

By patrick honner, ago
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