# Thunderstorms!

It’s safe to say that thunderstorm season has officially arrived in Iowa!  The temperature and the humidity has been on a steady climb for the last couple of weeks (remember when we were making jokes about how cold it was?!?) and seasoned midwesterners can spot the ideal weather for a good thunderstorm from miles away!

I love thunderstorms!  For some reason, they always prompt me to bake a batch of chocolate chips cookies whenever they roll through!  (There’s nothing quite like watching the clouds roll in while you chow down on homemade cookie dough!)  Unfortunately, my children do not share my affinity for thunderstorms, not even the promise of warm chocolate chip cookies can calm their nerves when the thunder starts booming and the lightening flashes!

Last week a quick thunderstorm rolled up in the middle of dinner.  Instead of focusing on the scary booms and flashes I said to them “Did you know if you count the number of seconds between when you see the lightening and hear the thunder, you can estimate the distance the thunderstorm is from our house?”  (P.S. Did you know that?)

The speed of sound through the air is approximately 340 meters per second, and the speed of light is approximately 300 million meters per second.  Even though thunder claps and lightening  flashes are happening at the same time, the difference in speed makes it seem as though the lightening is flashing before the thunder.

Using the relationship between distance, rate, and time we know that D = R*t, where D is distance, R is rate, and t is time.  Since we have the rate of sound and light in meters and seconds, we’ll also report D and t in terms of meters and seconds.

Now, suppose you hear thunder approximately 5 seconds after you see a flash of lightening.  If we use the relationship between distance, rate, and time we can substitute known values into the equation, which gives us D = 340*5 = 1700 (remember this is meters).  1700 meters is approximately 1 mile.

The next time a thunderstorm rolls up in your neighborhood, see if you can track how quickly its  moving through the area.  Keep a record of the length of time between lightening flashes and thunder rumbles.  Can you tell when the storm is getting closer and farther away from you?

P.S. I got my facts and figures from two great sources: the National Weather Service and The Department of Physics at the University of Illinois Urbana Champaign.

# Boston Marathon Times

This morning thousands and thousands of people did something I can not even imagine doing . . . they ran the Boston Marathon (It was actually 35,671 entrants to be exact)!

This year the winning men’s time was 2:08:37 (Meb Keflezighi from California) . . . that’s an average speed of about 1 mile every 4.88 minutes.  (As a comparison I re-started Couch-to-5K last night . . . and I ran about 1 mile every 11 minutes).

Anyway, the whole Boston Marathon thing got me thinking . . . I wonder how Meb’s time compares to other people who have won the Boston Marathon?

The first Boston Marathon was run in 1917.  John J. McDermott (NY) won that race with a time of 2:55:10.  He was still averaging about 1 mile every almost 7 minutes.  So, is Meb just exceptionally fast?  Was John just exceptionally slow?

The graph above represents all of the Boston Marathon times–from John to Meb and all of the marathoners in between.  What do the data seem to tell you?  Was John exceptionally slow?  What about Meb?

This shows the average time for 10 year time spans of Boston Marathon winners.  What seems to be happening to marathon times-over time?

If you had to model Boston Marathon winning times, based on the number of years since the first marathon what type of model would you use?  Exponential Growth/Decay?  Linear Increase/Decrease?  Quadratic model?  Why?  Do you think there might be anything noteworthy about the graph as people continue running the marathon?  Will anyone ever run the marathon in under 2 hours?  1 hour? (if someone ran a marathon in under an hour they would be averaging 1 mile approximately every 2.25 minutes)

I’d love to know what you think!  In the meantime . . . I’ll be trying to get under the 10 minute mile mark with my Couch-to-5k app!

# In like a Lion; Out like a Lamb?

This morning as I was walking to work through whipping wind and freezing cold temps, I thought to myself “March, you’re supposed to be going out like a lamb.”  Goodness knows it sure came in like a lion!  Then, I started thinking about Groundhog’s Day and how unreliable that good old Phil actually is!  That made me wonder . . . is there really any truth to this whole lion/lamb thing?

I spent the better part of my morning trying to track down an answer!

This is what I did:

I’m only concerned with how March comes in and out, and not what happens in the middle of the month, so I thought I’d look at the first 7 days of March and the last 7 days of March.  Then, I did a quick search and found that the average March temperature in Iowa for the past 150 years is 34.5 degrees Fahrenheit.

Given this information I decided I would define “Lion” to be a 7-day span in which 4 or more of the days had an average temperature that was less than the average monthly temperature.  Then, a “Lamb” was a 7-day span in which 4 or more of the days had an average temperature that was greater than or equal to the average monthly temperature.

I obtained daily average temperature data for Des Moines from The University of Dayton Average Daily Temperature Archive dating back to 1995.  Because the month of March isn’t over yet for 2014, I didn’t use the temperature data for any of the days in March 2014.  This is what I came up with:

In the past 19 years March has followed the “In like a Lion; Out like a Lamb,” pattern in 13 different years (or 68% of the time).  It has followed an “In like a Lamb; Out like a Lamb” pattern 5 different years (or 26% of the time).  And once in the last 19 years March has come in like a Lion and gone out like a Lion . . . according to the average daily temperature in Des Moines.

This got me thinking about a few things:

1. This saying seems to be a little more accurate then the Groundhog shadow thing.

2. There weren’t any “In like a Lamb; Out like a Lion” years . . . I wonder how many times that has happened in the past 150 years (if at all)?

3. What do you think of my definition for Lion-like weather and Lamb-like weather?  Would you define it another way?  If so, how?

This is the second post in a trilogy!  Read the first post here.  And when you’re done with this post, read the last post here.

Have you been counting chocolate?

Good!

Did you eat the chocolate you counted?

Even better!

If we pick up where we left off last week, you’ll recall the M and M debacle (the debacle being the fact that my children fought, not the fact that I fed them chocolate before 8am)!

You remember the fight, don’t you?  You know, the one where my daughter said it wasn’t fair that her brother got all the colors of the M&M’s in his bag and she didn’t?

Then, I asked you to try to figure out how likely that situation was to occur?  And then . . . I asked you to buy lots and lots of M&M’s?

Well, did you?  I did!

See . . .

The question that led to all of this M&M consumption was “How likely is it that a bag of fun sized M&M’s will contain exactly two colors of M&M’s?”

I asked you to start by looking at a sample of M&Ms.

My sample contained 17 bags of fun sized M&M’s and 299 candies.    When collecting the data to answer this question, I did two things.

1) Counted the total number of M&M’s in the bag.

2) Counted the number of each color of M&M in the bag.

My piles looked like this:

And the data I collected looked like this:

If you look closely, you’ll see that many times during the data collection phase I opened a bag of M&Ms that was missing one color.  In fact, this particular event occurred approximately 35% of the time.

And when a color was missing, 33.3% of the time it was the blue or brown M&Ms that were missing and 16.67% of the time it was the orange or yellow M&Ms that were missing.

In my study, two or more colors were missing 0% of the time.

Considering this data, it seems very, very unlikely that my daughter would have opened a bag of M&M’s containing only two colors of M&M’s.  In fact, in my data collection this occurred 0% of the time.

So, here’s my next question; since the instance my daughter described happened 0% of the time during my study does it mean it will never happen?  How do you know?

Could I use this data to make an educated guess that my daughter my have just been picking a fight with my son, and that her bag of M&M’s did, in fact, contain more than just two colors of M&M’s?

To be continued . . .

# TIme Lapse Photography

This week’s math walk post got me thinking about taking pictures of math things that I encounter everyday, but don’t really think about.

You already know that I work at the Belin-Blank Center on The University of Iowa campus.  But, you probably didn’t know that my office is on the top floor of the Blank Honors Center and that I have a straight shot at the Chemistry Building right out my window.

The other morning I was looking out my window, thinking about my math walk, and feeling inspired about taking pictures when I saw a student rushing into the Chemistry Building at about 9:03 (probably late for a 9am class).

That got me thinking. . . .I wonder how many students walk into the Chemistry Building on any given day?  And, I wonder what the ebb and flow of students looks like?

So, I took my first stab at time lapse photography (TLP).  Now, the primary purpose of this TLP project wasn’t to be artistic.  In fact, if you’re looking for an artistic TLP project you should go here.  The point of this project was to answer my second question; What’s the ebb and flow of students like outside my window everyday?

I set up a camera (and by “I”, I mean I asked someone I work with to help . . .she ended up doing while I stood in her office and watched!)  and programmed it to start snapping photos at 7:45 am and stop taking photos 12 hours later.  The camera took a picture every 15 minutes.  And, this is what I got:

Next, I graphed the flow of student traffic, based on the pictures I had.  The graph looked like this:

Now, I’m wondering about quite a few things:

1. I wonder if I missed the busiest time of the day with my every 15 minute photo-shot?  It seems to me that at some point more than 18 students should be entering the Chemistry Building at one time.

2. What’s a good model for the data I collected?  Should I divide the graph into two (or more) separate parts . . .like day classes and evening classes?  Do I think these two times of day need to be modeled using two different equations?

3. Look at the shadows!  I wonder if I could try to plot the position of the sun or length of shadow vs. the time of day.

4. Given the structure of college courses I wonder how different the data would look if I collected data on a Monday or Wednesday?  Why might Friday not be a good data collection day?

What are some of the things you notice as you watch this TLP video?

Interested in creating your own?  I’d start here (actually, I did start there!).