## Posts tagged ‘pi’

### Σ Π :: The Sum and Product Game

This joke, or a close facsimile, has been taking a tour of email servers recently, and it’s now showing up on t-shirts, too:

…and it was delicious!

Appropriate for Pi Day, I suppose, as is the game my sons have been playing…

Eli said to Alex, “18 and 126.”

Alex thought for a second, then replied, “2, 7, and 9.”

“Yes!” Eli exclaimed.

I was confused. “What are you guys doing?” I asked.

“We invented a game,” Eli said. “We give each other **the sum and product of three numbers**, and the other person has to figure out what the numbers are.”

After further inquisition, I learned that it wasn’t just any three numbers but **positive integers** only, that **none can be larger than 15**, and that they must be **distinct**.

Hearing about this game made me immediately think about the famous Ages of Three Children problem:

A woman asks her neighbor the ages of his three children.

“Well,” he says, “the product of their ages is 72.”

“That’s not enough information,” the woman replies.

“The sum of their ages is your house number,” he explains further.

“I still don’t know,” she says.

“I’m sorry,” says the man. “I can’t stay and talk any longer. My eldest child is sick in bed.” He turns to leave.

“Now I know how old they are,” she says.

What are the ages of his children?

You should be able to solve that one on your own. But if you’re not so inclined, you can resort to Wikipedia.

But back to Alex and Eli’s game. It immediately occurred to me that there would likely be some ordered pairs of (sum, product) that wouldn’t correspond to a unique set of numbers. Upon inspection, I found eight of them:

(19, 144)

(20, 90)

(21, 168)

(21, 240)

(23, 360)

(25, 360)

(28, 630)

(30, 840)

My two favorite ordered pairs were:

(24, 240)

(26, 286)

I particularly like the latter one. If you think about it the right way (divisibility rules, anyone?), you’ll solve it in milliseconds.

And the Excel spreadsheet that I created to analyze this game led me to the following problem:

Three distinct positive integers, each less than or equal to 15, are selected at random. What is the most likely product?

Creating that problem was rather satisfying. It was only through looking at the spreadsheet that I would’ve even thought to ask the question. But once I did, I realized that solving it isn’t that tough — there are some likely culprits to be considered, many of which can be eliminated quickly. (The solution is left as an exercise for the reader.)

So, yeah. These are the things that happen in our geeky household. Sure, we bake cookies, play board games, and watch cartoons, but we also listen to the NPR Sunday Puzzle and create math games. You got a problem with that?

### Can I Get Your Digits?

Saw this on a t-shirt recently:

It made me think about this problem involving digits.

Consider the number

1234567891011121314151617181920obtained by writing the numbers from 1 to 20 in order side-by-side.

What’s the greatest number that can be obtained by crossing out 20 digits?

If a fetching lady or handsome gent catches your fancy by solving that problem, you might want to ask her or him…

How can I know so many digits of π and so few digits of your phone number?

And if he or she still hasn’t taken leave of you, then you could really press your luck with the following:

- Ask your new friend to write down a number with four or more digits.

459,163

- Then, have your friend add the digits.

4 + 5 + 9 + 1 + 6 + 3 = 28

- Subtract the sum from the original number.

459,163 – 28 = 459,135

- Have your friend cross out one of the digits, and then read the remaining number aloud to you.

45,935

- Then, miraculously announce the missing digit.

**1**

The secret to the trick? Simple. Just add the digits of the number that your friend reads aloud, and then figure out what number must be added to get the sum to a multiple of 9. Above, the digits of the number 45,935 have a sum of 26, which is 1 less than a multiple of 9, so the removed digit is 1.

### Happy Pie Day!

Yes, I know you probably think I’m jumping the gun by 50 days, and you probably think I spelled *pie* wrong, too.

But you’re wrong on both counts. The American Pie Council (who knew there was a pie council?) has declared that January 23 is National Pie Day.

So let’s celebrate!

Grab a fork!

Grab a friend!

And grab a slice of life!

As for hokey-ness, National Pie Day outdoes Pi Day in its choice of date. The APC chose 1/23 for National Pie Day because the phrase

Easy as pie!

is synonymous with

Easy as 1-2-3!

And here’s a crazy fact about pies: In 1644, Oliver Cromwell banned pies as a pagan form of pleasure, and the ban lasted for 16 years. Which means that Oliver Cromwell nudges out the Anti-Saloon League as the winner of the stupidest prohibition in history.

But you didn’t come here for pie facts, you came here for pie jokes, right? So let’s get on with it.

Why did the pie go to the dentist?

Because it needed a filling.Who led mathematicians out of Hamelin?

The π-ed π-per!An infinity of mathematicians walked into a bakery. The first one ordered a slice. The second one ordered half a slice. The third one ordered a quarter slice. And so on. The baker said, “You’re all idiots,” and gave them two slices.

The police were waiting for me when I got home. “I’m sorry,” said one of the officers. “Your wife went to the bakery, bought two pies, ate one of them, and dropped dead on the sidewalk.”

I said, “That’s terrible. What happened to the other pie?”The boss was upset at my co-worker for making a math error in a report. Trying to belittle him at a meeting, the boss asked my co-worker, “If you had four apple pies, and I asked for one of them, how many would you have left?”

“I’d have four pies,” he answered.

The boss said, “See, those are the kinds of mistakes that are ruining our business!”

My co-worker said, “It wasn’t a mistake. You’re an a**hole, and you’re not getting any of my pies!”

### A Life of Pi

I fell asleep on the couch last night while watching *Modern Family*. At 3:14 a.m., I woke up, left the couch, and stumbled to bed.

Several hours later, my son Eli came into our room and woke me. That was at 6:28 a.m. My wife agreed to take the morning shift, so I fell back asleep.

When I woke again, it was 9:42 a.m.

Then, at 12:56 p.m., I received an email from my friend Pat Flynn, and I was cheered by the silliness of the subject line: “My new favorite quadratic formula song.” I smiled thinking about the possibility that anyone would have a favorites list containing more than one song about the quadratic formula.

This was a rather uneventful sequence… except that the times were π, 2π, 3π, and 4π. Sort of. To two decimal places, 4π = 12.57, not 12.56. So my theory that my life is ruled by π was discredited.

All was not lost, however. The link in Pat Flynn’s email made me smile. It featured two teachers singing a song about the quadratic formula to the tune of Adele’s *Rolling in the Deep*. The lyrics are decent, and the teachers are pretty good vocalists. Here, give it a listen yourself…

And here are a few quotes about π you might enjoy.

If equations are trains threading the landscape of numbers, then no train stops at π. – Richard Preston

The primary purpose of the DATA statement is to give names to constants; instead of referring to π as 3.141592653589793 at every appearance, the variable PI can be given that value with a DATA statement and used instead of the longer form of the constant. This also simplifies modifying the program, should the value of π change. – FORTRAN manual for Xerox Computers

So here we have π

^{2}, which an engineer would call 10. – Frank King

### What Dates are Mathier than Pi Day?

While I am grateful that Pi Day gives some much-needed publicity to math, it’s a contrivance like textbook problems about two trains approaching from opposite directions. (Honestly, rather than spend your time determining how long until two trains on the same track collide, why not use that time to inform someone about the imminent collision?) Other than containing the same digits that appear in 3.14, there’s nothing terribly special about 3/14. And it propagates the widely held belief that π is only known to two decimal places.

That said, the cultural significance of Pi Day cannot be overstated. (Or maybe it just was?) Consequently, there are **six cool Pi Day cards at Illuminations** for you to share with friends via Facebook, Twitter, and Pinterest, or download them and include them in an email, on your website, or in a blog post. This one is my favorite:

Recently, there has been a movement to replace π with τ = 2π. (See The Tau Manifesto.) That would suit me just fine, and then we could celebrate Tau Day, which occurs on the more mathematical date 6/28. In addition to 6.28 representing the value of 2π (to two decimal places, anyway), it is also the case that both 6 and 28 are perfect numbers (the sum of their proper factors is equal to the number itself), and this year the value of the month, date and year of 6/28/12 are all even.

Please understand, my disdain for 3/14/12 is not personal. It’s just that other dates this year are, well, *mathier*.

Christmas Eve is one of those mathier dates…

- When written as 12/24/12, all of
*mm*,*dd*and*yy*are even. *mm*+*yy*=*dd*- Each of the digits within the date (1, 2, and 4) are powers of 2.
- The sum of the digits is 1 + 2 + 2 + 4 + 1 + 2 = 12, and 122412 ÷ 12 = 10,201 = 101
^{2}.

…as is the ninth of June…

- The numbers 6, 9, 12 form an arithmetic sequence.
- All three numbers are multiples of 3.
- The month (6) is a perfect number, the date (9) is a square number, and the year (12) is the smallest abundant number.

What do you think is the mathiest date of 2012? And what criteria do you use to determine if a date is mathy?

### Memorable Math Mnemonics

I recently read a conference proposal in which the potential presenter declared, “PEMDAS must die!” Upon reading this, I thought, “Hear, hear!” But then the potential presenter claimed, “We should use GEMDAS instead!” Really? Does this presenter honestly believe that changing P (parentheses) to G (grouping) is sufficient to eliminate all the problems students have with order of operations?

I have heard that some teachers use GEMS, where M stands for both multiplication and division and S stands for both subtraction and addition. That eliminates the problem some students have, thinking that multiplication has to happen before division or that addition has to happen before subtraction.

Whatever. From my experience, most of the trouble students have with PEMDAS, GEMDAS, or GEMS typically results from a failure to consider it at all when working with a complex expression. It isn’t the mnemonic.

Here’s a mnemonic for remembering what a mnemonic is: Think about a person with a terrible memory who previously suffered an inflammatory lung condition. Imagine that he often makes up catchy little phrases to help him remember things. Then you can make the association of *pneumonic* with *mnemonic*, and you won’t have any more trouble. There, now… isn’t that simple?

The following are some of my favorite mnemonics.

**Feet in a Mile**

Five Tomatoes → 5 2 M8 0’s → 5,280 feet per mile

**Tough Multiplication Fact**

5, 6, 7, 8 → 56 = 7 × 8

**Arithmetic**

A Rat In The House May Eat The Ice Cream

**Multiplying Signed Numbers**

My **friend’s friend** is my **friend** (pos × pos = pos)

My **friend’s enemy** is my **enemy** (pos × neg = neg)

My **enemy’s friend** is my **enemy** (neg × pos = neg)

My **enemy’s enemy** is my **friend** (neg× neg = pos)

**Interest Formula**

**I** am **pr**e**t**ty → *I* = *prt*

**Distance Formula**

DiRT → *d* = *rt*

**Metric System**

King Henry Died By Drinking Chocolate Milk

Kilo, Hecto, Deca, Base, Deci, Centi, Milli

**Trig Formulas**

(sung to the tune of *Yankee Doodle*)

Oscar had a heap of apples, sine and cosine tangent

**Angle Sum Formulas**

Sine Cosine, Cosine Sine;

Cosine Cosine, Sign Sine Sine!

sin (*a* + *b*) = sin *a* cos *b* + cos *a* sin *b*

cos (*a* + *b*) = cos *a* cos *b* – sin *a* sin *b*

** e** (6 digits)

By omnibus I traveled to Brooklyn.

**π** (7 digits)

May I have a large container of coffee?

**π** (3,835 digits)

In 1995, Mike Keith wrote a poem called *Poe, E., Near A Raven*, which gave the first 740 digits of π (the number of letters in each word indicates the value for that digit of π). It was based on Edgar Allan Poe’s poem *The Raven*. But some people are never satisfied, so he later wrote the *Cadaeic Cadenza*, which gives the first 3,835 digits of π.

### Interview: Colin Adams, Williams College

Colin Adams likes to set up his students with jokes like this:

What do you get when cross a mosquito with a fishmonger?

Nothing. You can’t cross a vector (disease) with a scalar (fish scaler).

He tells several more jokes of the same ilk, then delivers the following:

What do you get when you cross a mathematician with a movie star?

Dream on. It’ll never happen.

Jokes are only one way that Colin tries to capture student interest. He also uses stories, plays, and fictional characters. “The trick is to get people’s attention long enough for them to see the beauty of the mathematics in front of them,” he explained. “I get a huge kick out of trying to come up with unusual ways to do that.”

One of his unusual ways is teaching class under the guise of Mel Slugbate, a sleazy real estate agent who sells property in hyperbolic space. Despite popular belief, Colin says that Mel is not a close personal friend. “He is my brother-in-law, and I am forced to spend time with him at family events. The worst real estate advice he ever gave me was, ‘Buy this house I have for sale.’”

While his humor may pique students’ curiosity, it certainly doesn’t hurt that Colin loves mathematics, too. In fact, it’s the primary reason he chose to become a professor. “The first time I proved something that no one else had ever proved, it was a rush. I really enjoyed that,” he said. “I still do.” He also loves that mathematics is free of personality issues when it comes to a proof. “You are either right or wrong,” he said.

In 1998, Colin was honored with the Haimo Distinguished Teaching Award, the highest teaching award given by the Math Association of America. Impressively, four of the 61 recipients of this award have been from Williams College. If you want to follow in Adams’s footsteps, an online masters degree in education can help you improve your math teaching skills.

I recently interviewed Colin to find out why he loves teaching and, hopefully, to learn a little about how to be mathematically funny.

**What’s your favorite thing about teaching?**

I love to come up with different ways to teach. The trick is to get people’s attention long enough for them to see the beauty of the mathematics in front of them. So I get a huge kick out of trying to come up with unusual ways to do that. Stories, jokes, plays, characters.

**What’s the funniest thing you’ve ever said during a lecture?**

I honestly don’t know. The ones that are unplanned are the funniest, and then afterward I forget what it was that I said. I just remember there was a big laugh.

**With you, Ed Burger, and Tom Garrity on the faculty, Williams College arguably has the funniest math department in America. Who would your students say is the funniest?**

We all have very different styles. They would say Tom is the wackiest. Ed is the one who would be the most likely to succeed in the real comedy world. He is a natural stand-up comic. I am the one who plays a part, and I’m funniest when I’m not myself but am playing someone else. So, depending on the student’s taste, they might give a different answer.

**Who is the funniest mathematician or professor you know? What’s the funniest thing that he or she ever said?**

I would say Ed Burger. He is *always* on. I remember when he was giving a talk to parents during Parent’s Weekend at Williams. He was demonstrating how you can tie your feet together, then turn your pants inside out and put them back on while keeping your feet tied together the whole time, a topological demonstration. When he dropped his trousers with his feet tied together, he had on boxers with purple cows (the Williams mascot) all over them. He waited a second, and then said, “All junior faculty at Williams are required to wear these.” I couldn’t stop laughing.

**Tell us about yourself. In particular, what things would you like my audience (a bunch of silly folks who like math jokes) to know about you?**

Let’s see. Before I wanted to be a mathematician, I wanted to be a writer. But then I fell in love with mathematics. It has been a joy to be able to go back to my previous interest and write math humor.

**Your list of math humor titles is impressive: the Streetwise Guides to Calculus, Riot at the Calc Exam, all of your “Mathematically Bent” columns. Which is your favorite, and why?**

I love writing the “Mathematically Bent” column. It comes out four times a year, so I know I have about three months per column. Other than the constraint that it should be funny and involve mathematics, there are no constraints. So, I love the freedom that gives me. Every time I read a story, see a movie, hear an interesting anecdote, or follow the news, I think, “Is there a way to do this from a mathematical point of view? Can you write a funny math story based on that idea?”

**If folks are only able to read one item that you’re written, which one would you want them to read?**

How about *Mangum, PI*? It was a piece in the *Mathematical Intelligencer* that also appears in the book *Riot at the Calc Exam and Other Mathematically Bent Stories*. (Ed. Note: Colin was kind enough to share a copy of this story for readers of the *MJ4MF* blog. You can download it here.)

**In addition to your writing, you also starred in a film, The Great Pi/e Debate with Tom Garrity, and you have several plays to your credit. Where is it hardest to be funny — on screen, in print, or on stage?**

For me, screen and stage are the same, in that all of my videos are based on stage productions. But the same production on video is never quite as funny as it was live. I spend a lot of time writing my material before I perform it. I am not an extemporaneous performer. When I do come up with something on the fly and it’s funny, and it goes over well, that is the best feeling.

**When not writing math books, which books do you like to read? Any favorite authors?**

I like to read lots of different books. Some science writers (John McPhee), some novels (Dave Eggers), some stories (Stephen King), some nonfiction (Christopher Hitchens).