patrick honner

Math teacher in Brooklyn, New York

Football Inequality

The 2010 NFL season is off to a mathematically interesting start.

The Jets, Patriots, Bengals, and Ravens each have played two games against other teams in that group of four.  The results can be organized like this (for example, the Bengals lost to the Patriots but beat the Ravens)

AFC East InequalityNow, if we interpret “wins the game” to mean something like “is better than”, and if we believe that “is better than” is a transitive relationship (i.e. “If A is better than B and B is better than C, then A is better than C”), then the Jets are better than every team in their division, including themselves!  Some might prefer to say that they are even worse than themselves.

It’s not easy producing mathematically consistent ranking systems, but it’s an interesting and useful problem, and the field is quite rich.

By patrick honner, ago

Insignificant Digits

No U TurnsAs someone with an affinity for numbers, I’m always conscious of how they appear around us.  And I’m always trying to decode the numbers I see:  what do they mean?  Why are they here?

It didn’t take much to figure out these numbers below these No U-Turns signs along the highway.  (It’s a bit blurry, but if you squint you can make out the 55.39 in yellow.)

After a couple of miles of confirmation, it was clear that the 55 corresponds to the highway’s mile marker.  So the 55.39 tells emergency vehicles the exact location of the U-Turn, 55.39 miles up the highway.

But is the .39 really necessary?  How much accuracy do we need in these measurements?  I can see wanting to avoid the confusion of naming it 55 (is it between 54 and 55, or 55 and 56?), but couldn’t we just call it 55.5 and save ourselves the trouble of the .39?

If the Highway Department has extra money to spend, how about new speed limit signs?  Rounded the nearest integer, please!

Related Posts

By patrick honner, ago

Meet the Egg-Bot

egg-botThis is pretty awesome:  an assemble-yourself perhipheral that allows you to draw on spherical/ellipsoidal/other objects:  the egg-bot!

http://egg-bot.com/

Plug it in to your USB port, render your drawing in a freeware illustration program, and voila!  And it’s open-source:  both hardware and software.

There are so many interesting things that could be done with the egg-bot:  sketching grid lines on ellipsoids to illustrate parametric surfaces, investigating how projection affects map-making, graphing closed-curves on golf balls, or maybe just creating the greatest Easter Eggs in human history.

By patrick honner, ago

Cold Oceans and Newton’s Law of Cooling

feet in oceanWhen in Maine, I thought it would be fun to go swimming in the ocean.  I’d driven all that way, right?  I knew it would be cold when I noticed that of the 200 or so people at the beach, only 5 were actually in the water, and only one of them was in past their knees.  And he was Canadian.

After I swam for a few minutes, lost much sensation in most of my body, and stumbled back to the beach feeling slightly burned all over, I asked around and discovered that the water temperature was around 55 degrees Fahrenheit.  Which made me wonder, “How long could I have swim in such water before suffering severe consequences?”

Normal body temperature is around 98.6 degrees.  Hypothermia sets in when one’s body temperature falls to 95 degrees, and apparently things seem to get very bad at around 92 degrees.  Now, Newton’s Law of Cooling states that the rate of change of the temperature of an object is proportional to the difference between the temperature of that object (in this case, my body) and the ambient temperature (the 55-degree ocean).  The difference in those two temps–about 34 degrees–seems [relatively] high, so I imagine that my body would cool pretty rapidly to the danger zone.

I was very excited to calculate how much time I theoretically had, but unfortunately I didn’t know how to determine the value of the constant in the Newton’s equation.  Can anyone suggest an appropriate value of k? It probably depends on properties of salt-water and the human body.  I asked the lifeguard, but he didn’t know.

By patrick honner, ago

Math Quiz: NYT Learning Network

Through Math for America, I am part of an on-going collaboration with the New York Times Learning Network.  My latest contribution, a Test Yourself quiz-question, can be found here:

http://learning.blogs.nytimes.com/2010/09/15/test-yourself-mathseptember-15-2010/

This question was based on a recent study regarding New York’s trains, how often they run on time, and how that measures up with the perception that they run on time; click here to read more.

By patrick honner, ago
Follow

Get every new post delivered to your Inbox

Join other followers: