Scattered Popularity in Baseball

I enjoyed reading through this marketing document from Harris Interactive about the popularity of Major League Baseball.  Lots of interesting facts about who watches baseball (higher percentage of people in the East versus other regions; percentages rise with income), and a nice ranking of the league’s most popular teams.

Putting the popularity rankings together with team salary information, I made myself a nice little scatter plot.

MLB Popularity Regression

Team payroll along the horizontal is in millions, and the popularity is out of 30 teams, with 30 being “most popular”.

Not too hard to guess the red triangle in the upper right:  first in popularity and team payroll, your New York Yankees!  The World Series Champion San Francisco Giants are the big red circle around (93,23).  And kudos to the Atlanta Braves, the nice red square in the top middle, as they seem to be getting the best popularity return for their payroll dollars.  The sad yellow diamond in the bottom left is for one particular reader:  maybe next year!

There does seem to be a positive relationshp between the amount spent on salary and the team’s overall popularity, but there are probably a lot of reasons for that.

Lots of other interesting ways to slice and dice this data.  Take a look at the document and try it yourself!

Daylight Saving Time is Mathematically Illogical

I’ve always found daylight saving time confusing, and now I know why:  mathematically, it doesn’t make sense.

As summer turns to winter and our part of the Earth spends less time in the sun, the length of the day contracts.  This kind of transformation is known as a dilation–a shrinking or stretching of something.

The yellow part of the graph represents the amount of sunlight per day.  This part dilates, while the times-of-day on the clock stay fixed.

In order to increase the amount of productive daylight, we translate the times-of-day.  Naturally, this doesn’t change the amount of available sunlight; it simply shifts the clock-times so that more of that sunlight occurs during preferred times-of-day .

Thus, the new day looks like this.

Essentially, daylight saving time tries to counteract a dilation with a translation.  But mathematically, the way to truly counteract a dilation is with another dilation!  Thus, the mathematical logic of daylight saving time is faulty.

Now that I fully understand the source of my confusion, I can rest easier.  And for an extra hour!

Geometry Photography Competition

geometry photoThe New Scientist magazine has a monthly photo contest, and the theme this month is Geometry!

I’m thinking of submitting my picture of Parabolas in Nature, but probably not my picture of my imperfect division of a squash.

The contest ends November 30th, at midnight.  The winner and select runners-up will be posted on the New Scientist website.  All the details can be found here:

http://www.newscientist.com/article/dn19684-photo-competition-geometry.html

So keep your eyes open and your camera at hand–there’s a lot of Geometry out there!

Shocking Mathematical Results

 

Welectroshock therapyhen it comes out that I’m a math person, the most common response from people I meet is “I was never very good at math“.  After a lifetime of struggling to find the appropriate response, I finally have something positive and proactive to say:  go get yourself some electroshock therapy.

According to a recent study, running a mild electric current through the brain seems to temporarily increase mathematical ability.   Apparently the study involved teaching the subjects a new numeration system (could it have been octomatics?) and testing their ability to organize those symbols before and after electrical stimulation of the parietal lobe.

In addition to slightly increasing mathematical ability and potentially treating dyscalculia, there is hope that such electrical stimulation could improve other brain function, as well.

Now, how can I bring this revolutionary technique into my classroom?

Twirling Tori

This is a mind-blowing animation of arms circulating around a torus, created by Emilio Gomariz.  I definitely became entranced for a bit, trying to follow a single hand all the way around the donut.  (Click the image or this link if you can’t see the animation).

emiliogomariz

Apart from being visually amaazing, this puts me in mind of a result about fluid flows on surfaces.  This animation demonstrates that a liquid, for example, can flow over the surface of a torus in such a way that every point movesnothing appears stationary here, and everything is moving in a smooth (i.e., continuous) fashion.

The remarkable result is that this same can not be done on the surface of a sphere!  There will always (at least) one point on the surface of the sphere that doesn’t move.  A popular interpretation of this result is that however windy it might be outside, there is always at least one point on the Earth that is perfectly calm.

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