Archive for March, 2015

What If?

My favorite question is, “Why?” (And my favorite answer is, “Because.”) But not far behind is the question, “What if?”

What if a baseball player swings a bat with the proper speed, but starts swinging 0.01 seconds too late? What if I could earn 6.3% on a real estate investment instead of 1.4% in a Roth IRA, but had to pay capital gains taxes? What if I tried to walk through a revolving door with a pair of skis on my shoulder?

“What if…?” questions don’t always have to be mathy, ya know.

The beauty of Excel is that you can repeatedly ask “What if…?” questions and then explore to your heart’s content.

Overheard in math class:

“It’s not that I don’t want to do all those math problems,” Julia said to her teacher. “I’m just saying, if we put them into a spreadsheet and let Excel do its thing, we can have an extra 20 minutes for recess.”

Sure, one of the powers of Excel is reducing the tedium associated with calculations, but a much greater power is its ability to allow for deep exploration of math topics in a short period of time.

Art Bardige and Peter Mili agree. That’s why they’re giving away spreadsheets that allow students to explore mathematics.

Their What If Labs allow students to investigate questions like:

  • What if you used Excel to design a house?
  • Is the world population growing at a faster or slower rate than 50 years ago?
  • Instead of wood, nails, and string, what if you used a graph and coordinates to create string art?

The spreadsheets are useful, fun, educational and — dare I say — beautiful. Not to mention, free.

Art believes that teaching math with Excel has two benefits. First, it fosters business skills by having students learn the basics of the most ubiquitous business application on the planet. Second, it empowers students by giving them complete control to explore on their own.

I concur with Art’s philosophy.

Excel is one of my best friends. I use it to test conjectures, especially for probability problems about which I don’t have any intuition — or, more often, when my intuition is wrong!

One of my favorite problems, which was discussed in the post Fair and Square in 2011, is the following:

Three points are randomly chosen along the perimeter of a square. What is the probability that the center of the square will be contained within the triangle formed by these three points?

Unsure how to attack this problem, the answer was estimated using an Excel simulation. From the insights gained by that simulation, a solution eventually revealed itself.

Would I have solved that problem without Excel? Maybe. Probably. But without Excel, it would have taken longer, and I might not have had the same deep understanding of the underlying structure.

Kudos to Art and Peter for providing a free resource that will let other students benefit from that same type of insight.

March 30, 2015 at 7:33 am 2 comments

The Game of POP

No one knows how to live a funky life more than Prince:

Life, it ain’t real funky
Unless it’s got that pop

Need a little extra pop in your life? Here’s a game you can play.

Create a game board consisting of n adjacent squares. Here’s a board for n = 10:

POP Board

Still with me? Good.

The rules of POP are rather straightforward.

  1. Players alternate turns, placing either an O or a P in any unoccupied square.
  2. The winner is the first player to spell the word POP in three consecutive squares.

I first learned this game using O’s and S’s and trying to spell SOS, but for young kids, O’s and P’s are much better… the accidental occurrences of POO and POOP add a certain je ne sais quoi. (But not as much as foreign phrases add to a sentence about feces.)

Alex and Eli played this game tonight on the board shown above. After six turns, the game was decided. (As you can see, an accidental POO occurred in squares 6‑8. I mean an accidental occurrence of the word POO, not an actual occurrence of POO itself. If the latter had happened, the game would have ended immediately, and I wouldn’t be writing about it now.) It was Alex’s turn, and he realized that he lost: playing either an O or a P in squares 3‑4 would give Eli the win, and playing either an O or P in squares 9‑10 would just delay the inevitable.

POP - Losing Position

“So, what’re you gonna do?” I asked.

Alex added an O to the third square, shrugged, and handed the pencil to Eli.

POP - Alex's Loss

A coward dies a thousand deaths; the valiant die but once.

In that game, Alex went first and lost. So an immediate question:

  • Will the second player always win when n = 10?

This then leads to follow-up questions:

  • Are there other values of n such that the second player has a winning strategy?
  • Are there any values of n such that the first player has a winning strategy?
  • Are there values of n for which neither player has a winning strategy?

If you’d like to play a game of POP, then head over to The Game of POP spreadsheet on Google Drive, email the link to your friend, and start adding O’s and P’s. Feel free to change the size of the game board, too! Just please be a sweetie — when you finish, clear all your letters, reset the size of the game board to 10 squares, and be sure all the directions are retained at the top of the page.

Enjoy!

March 24, 2015 at 7:28 pm 1 comment

P (NFL ∪ Math) > 0

John UrschelJohn Urschel is an offensive lineman for the Baltimore Ravens and admits, “I love hitting people.” As it turns out, he loves hitting the books, too. He earned a masters degree in mathematics from Penn State, and he recently published a paper with the impressive title A Cascadic Multigrid Algorithm for Computing the Fiedler Vector of Graph Laplacians in the Journal for Computational Mathematics.

Note that Urschel was the lead author, even though his three co-authors were an associate math professor from Tufts and two math professors from Penn State.

I have to wonder if the paper was fairly refereed. I mean, honestly, who in the math community is gonna tell a 6’3″, 308‑pound football player that he made an error?

A la Paul Erdös, Urschel doesn’t need much to be happy. In an essay published March 18, he wrote:

I drive a used hatchback Nissan Versa and live on less than $25k a year. It’s not because I’m frugal or trying to save for some big purchase, it’s because the things I love the most in this world (reading math, doing research, playing chess) are very, very inexpensive.

I was thinking about how Urschel has superior talent in two fields, when I saw this comment on an article on Deadspin:
Comments - Sports or Math

Here’s the thing.

There are 1,596 players in the National Football League at any given time (32 teams with 53 players each). Throw in a few more who serve on practice squads and occasionally get a chance when someone else gets hurt, so maybe that number climbs to 2,000. Still, the chance of making it to the NFL is unbelievably remote. Recruit 757 claims that only 0.008% of all high school athletes get drafted by the NFL.

And if you can believe Wolfram Alpha, there are 2,770 mathematicians in the United States, or approximately 1/47,165 of the U.S. workforce.

Point is, the probability of becoming either a professional football player or a mathematician is ridiculously small. Becoming both is smaller still. Though John Urschel proved it’s greater than 0. The saving grace is that he seems like a down-to-earth guy who realizes how lucky he is.

To read a math article written by John Urschel, check out 1 in 600 Billion.

March 22, 2015 at 6:25 am 1 comment

Will the Real Steve Reinhart Please Stand Up?

I met Steve Reinhart when he was a presenter at a 2001 NCTM Academy in Branson, MO. I only met him that one time, yet he had a profound effect on my teaching philosophy. Read his article “Never Say Anything a Kid Can Say!” and you’ll see why.

Last week, I met a second Steve Reinhart who works for an educational publisher. I asked the second one if he knew the first one, and he told me a funny story about how he was in his hotel room at a conference, and the door to his room opened. He looked at the guy standing there, realized what happened and asked, “Steve Reinhart?” And the first Steve Reinhart said, “Yep,” paused for a second, then asked, “Are you Steve Reinhart, too?” And the second one said, “Yep.” With the same name, when the first one showed up but there was already one checked in, the hotel receptionist gave the first a key to a room already occupied by the second.

Now, that’s a funny coincidence.

What does a mathematician do when it starts to rain?
Coincide.

At the end of my senior year of college, I finished my last final on Friday afternoon. I then worked 8 hours, headed home and pulled an all-nighter cleaning our apartment before returning the key on Saturday morning, and then headed to work for another 12-hour shift. After work, I trekked to the on-campus hotel where my best friend and I would stay the night before going our separate ways. After nearly 50 hours awake and a 3-mile walk, I was delirious when I arrived at the hotel. I told the hotel clerk my name, and he handed me a key. I walked wearily to the elevator, exited at the second floor, looked at the key to check the room number (it was the olden days — the room number was etched on the brass key that I was given), and proceeded to Room 222.

When I opened the door, a naked, middle-aged woman lying in the bed quickly pulled the sheets over herself, and a naked, middle-aged man sitting on the toilet with the bathroom door ajar gave me a look I’ll never forget. I said, “Oh, my gosh! I’m so sorry,” then quickly exited and closed the door. I heard some indecipherable yelling come from the room as I made my way down the hall.

I returned to the lobby, explained that I must have been given the wrong key, and told the receptionist what I had seen. “I’m very sorry, Mr. Vennebush,” he told me.

“No apology necessary,” I said. “But I don’t think I’m the one you need to be worried about.”

And then, as if on queue, the elevator door opened across the lobby, and an irate-but-now-clothed guest yelled, “What the f**k kind of place is this?”

That was not a funny coincidence.

This is just a funny mathematical coincidence:

\text{liters in a gallon} \approx 3 + \frac{\pi}{4}

And the crazy part? It’s accurate to within 0.00002.

But as far as coincidences go, this is good advice:

It’s far more likely for something to seem suspicious and turn out to be nothing, than for something to seem like nothing and wake up to a smoking crater where your city used to be.

March 12, 2015 at 8:30 am 2 comments

Shoestring Probability

March 15 is Shoe the World Day. And April 5 is One Day Without Shoes Day.

Shoes and math have a lot in common.

A shoe salesman consults a mathematician on what size shoes to keep in stock. The mathematician tells him, “There is a simple equation for that,” and shows him the Gaussian normal distribution.

The shoe salesman stares at the equation for a while, then asks, “What’s that symbol?”

“That’s the Greek letter π.”

“What is π?”

“The ratio between the circumference and the diameter of a circle.”

The shoe salesperson thinks for a minute. “What the hell does a circle have to do with shoes?”

As it turns out, there are at least 43 different ways to arrange the laces on your shoes. My favorite is the hexagram method:

But there are some fun things to do with your shoelaces other than lacing up your kicks. Here’s one.

Take the shoelaces out of your shoes. Fold the shoelaces in half and hold them in one hand so that the four aglets are exposed but the rest of the shoelaces are hidden in your palm. Like this:

Shoelaces

Have a friend select two of the aglets and tie those ends together (I recommend a square knot). Then, have your friend tie the other two ends together. Finally, offer your friend the following wager:

You give me $1 if you formed one large loop.
I’ll give you $1 if you didn’t.

Is it a fair bet?

Too easy? Then try this. Take your shoelaces and your friend’s shoelaces, fold them in half, and then expose the eight aglets. Choose two at a time and tie them together. The wager remains the same.

Now is it fair?

Is it possible to create a fair wager with any number of shoelaces? If so, how many?

March 7, 2015 at 10:30 am Leave a comment

Passwords, Age Restrictions, and Computer Silliness

My computer has been a bad boy recently.

First, it told me that my password is going to expire approximately 11 months before I was born

Password ExpirationInterestingly, the folks at www.timeanddate.com disagree with the number of days between March 31, 1970, and the date that screen capture was snapped (March 1, 2015). So much for the truism that, “Computers make very fast, very accurate mistakes.” I thought the difference could be explained by excluding the end dates, but that doesn’t seem to be the case, so I’m not sure what ADPassMon is doing. (Then again, I’m not sure why I’m wasting my time checking the calculations of a piece of software whose warning messages suggest the existence of time travel.)

Then, when attempting to register my sons for ski camp, it gave one of the craziest age restrictions I’ve ever seen…

Ski Camp Math

check out the valid ages…

An age of 5.925 corresponds to 5 years, 11 months, 7 days, and 15 hours, which seems quite an arbitrary cut-off for a ski camp. Further, an age of 7.999 years means that kids are eligible for ski camp so long as they are not within 15 hours, 14 minutes, and 24 seconds of their eighth birthday. The framers of the Common Core would be happy with the consideration paid to MP.6: Attend to Precision. Where else have you seen ages expressed to the nearest thousandth? Not even parents of newborns use this many decimal places.

Both of these issues remind me of a childhood friend who wanted to be a writer. He said he wanted to write stuff that would be widely read, cause an emotional reaction, and make people scream and cry. He now writes error messages for Microsoft.

Here’s wishing you an error-free day!

March 2, 2015 at 7:46 am Leave a comment


About MJ4MF

The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

MJ4MF (offline version)

Math Jokes 4 Mathy Folks is available from Amazon, Borders, Barnes & Noble, NCTM, Robert D. Reed Publishers, and other purveyors of exceptional literature.

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