The $1,000,000 Question

Riemann Zeta GraphThis article offers a nice introduction to the Riemann Hypothesis, one of the mathematics problems eligible for the Millennium Prize.

Solve it, and you’ll earn yourself one million dollars!  If you do solve it, I’d be happy to look it over before you submit your proposal to the committee.  Just send it my way and I’ll get back to you shortly.

If finding zeroes of the Riemann Zeta function is asking too much, the author offers up a classic problem in elementary number theory at the end of the article–something anyone with a few minutes to spare and a calculator can dive into.  It’s a surprisingly serious result, with a surprisingly easy solution!

By patrick honner, ago

Coffee and Cream – An Elegant Solution

My colleague, Scott Matthews, offered a very elegant solution to the Coffee and Cream mixture problem in response to the straight-forward solution I put forward.  As he commented:

In the end, both cups have the same amount of liquid. Therefore, by the simple law of displacement, the amount of cream in the coffee is the the same as the amount of coffee in the cream.

This is a really nice way to think about the problem.  In the end, the “coffee” cup contains the same amount of liquid as it started with.  Therefore, any cream that ends up in the “coffee” cup had to displace some coffee.

Where did that coffee go?  It ended up in the “cream” cup!  Here’s a visual interpretation.

coffee and cream -- equal displacement

 

Thanks, Scott, for the elegant solution!

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By patrick honner, ago

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!

By patrick honner, ago

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!

By patrick honner, ago
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