# Are you a fair weather fan?

This past weekend my husband and I went first home football game of the season for the Iowa Hawkeyes.  I was excited about the game until I saw the forecast for this past Saturday . . . every day on the news it seemed like the high temperature for the day kept creeping higher and higher.  Finally, on Thursday of last week the air temperature was forecast to reach 94 degrees and the University of Iowa athletic department began posting tips on now to start hydrating now for the game on Saturday.

I called my husband and work and our conversation went something like this:

Me: Did you see the forecast for Saturday?  I think its supposed to be dangerously hot . . .

Husband: Are you trying to bail?

Me: No!  I’m just worried about the heat . . . they said to start hydrating today.

Husband: You’re a fair weather fan!

Really?!? A fair weather fan?

We went.  We had a great time.  The Hawkeyes won.  I didn’t melt.  All in all it was a successful Saturday.

But my experience on Saturday got me thinking about a little thing called the heat index . . . I always thought it of it as the wind chill of really, really hot temperatures.  So, I decided to do a little digging to

1. Find out about the heat index.
2. Prove to my husband that I am not a fair weather fan.

According to the National Weather Service, the calculation of the heat index is a regression equation . . .which quite frankly seemed a little complicated for this blog (but if you’d like to see it, look here).

But, I did think that it was interesting that there was an important note when reading the heat index table . . . the NWS warns that the heat index can only be accurately calculated when the humidity and air temperature are represented on the chart.  In other words, this is a domain and range issue.

There are many situations in mathematics when we’d like to model a particular phenomenon. . .  (heat index, racing times, time-lapse modeling) just to name a few.  And in those situations it does not make sense to have the domain and range be all real number.  Sometimes it doesn’t make sense because the situation represented doesn’t make sense (i.e. negative time) and sometimes it doesn’t make sense because the function will not fit the data as closely if we allow the domain to be all real numbers (as in the case of the racing times).

This past Saturday the temperature at game time was 90 degrees with about 60% humidity . . . we stayed until the end of the third quarter when the Hawkeyes were winning 31-0.  So, what say you . . . am I a fair weather fan?

P.S. If you’re new here, let me let you in on a little secret . . .I love to think about the weather.  Don’t all midwesterners?  Check out a few more weather related posts here and here and here.

# Moving right along . . .

I’m two weeks in to my new job at St. Ambrose University in Davenport, IA.  I’m the newest tenure-track faculty member in the School of Education.  This semester I’m teaching the Theory of Arithmetic (Elementary Mathematics Methods/Content course) and Pre-Calculus.  It seems as though the last few weeks many people in my life have been talking about money . . . my husband talking about the lack of my paycheck (a slight annoyance when starting a new job . . . the one month lag in pay!), my students talking about the cost of textbooks, and everyone else at the University talking about the rising cost of tuition and the shrinking amount of state aid/student scholarships.  With money on the mind, I thought it’d be nice to check in with my stellar mathematics student from a few years ago who started a reverse savings plan during the first week of 2014.  (Remember her?)  If not, check out the posts here and here.  I’m checking in to see how she’s been doing and I’ll update you soon!

# Two times Pi = Tau

2π = τ, which means that tomorrow is Tau Day! (Remember 3/14 is Pi Day, since Pi ≈ 3.14).  Since tomorrow is 6/28 (or 2(3.14)) tomorrow, June 28 is Tau Day!  How will  you celebrate?  Might I suggest you celebrate with 2 pies?

For more Tau Day fun check out my Pi Day activities . . . just do them twice!

# Don’t worry the groundhog isn’t right anyway . . .

This year my two oldest children really got in to the whole Groundhog Day thing . . . so much so that when they heard on the Today Show that Punxsutawney Phil saw his shadow, signaling 6 more weeks of winter the oldest insisted that there be a “redo,” because he was not going to endure 6 more weeks of winter.

See? They still have fun in the winter!

“You guys,” I said.  “Just relax.  The groundhog can’t really predict the weather.  It’s just something fun to do on February 2 every year.  It’s just folklore.”  (My son is currently learning about folk stories in 2nd grade, so I thought this might sell my explanation!)

“How do you know mom?”  (that was my kindergartener, not convinced and not happy about the groundhog’s prediction).  “Maybe he’s right and you’re just saying its folklore so we won’t be sad.”

I don’t really remember how the rest of the conversation went, mostly because there wasn’t any use in arguing with either of them and also because by then, they had completely lost interest in the conversation.  But that kindergartener, she got me thinking.  How often is the groundhog right?  Does he predict the end of winter enough that there might actually be something to this whole “groundhog sees his shadow” thing?

U.S.A. Today wrote an article about the groundhog’s predictions and the National Weather Center also has a thing or two to say about how accurate the groundhog actually is; they report the groundhog has been wrong 15 times and right 10 times.  But here’s the thing . . . according to both websites the groundhog either predicts 6 more weeks of winter or an “early spring.”

Who decides if spring has come early?  How do we know if winter has lasted for 6 weeks?  Is this measured by the air temperature?  The amount of snow on the ground?  The vernal equinox is the “official” start of spring, but clearly that’s not what people are talking about when they refer to the groundhog’s prediction . . . otherwise, no prediction would be needed!

I suggest we get a little more precise about what we mean by the groundhog’s prediction, before we decide whether his predictions are accurate or not.  I propose that if the temperature for half or more than half of 6 weeks after February 2 (so that’s the week of 2/2, 2/9, 2/16, 2/23, 3/2, 3/9, 3/16) has an air temperature at or below the national average for the last 100 years that counts as 6 more weeks of winter; otherwise, spring.  According to this definition of an “early spring” Phil has correctly predicted the weather for the next 6 weeks, 11 times over the course of the last 26 years.

But, I agree spring is much, much better!

If we recognize this as an example of binomial probably, we know that about 30% of the time we would have been able to be just as accurate as Phil by flipping a coin where “heads” is early spring and “tails” is 6 more weeks of winter.  I’d say that qualifies as a folktale to me, wouldn’t you?