## Archive for August, 2010

### Pop Quiz

Twelve questions to get the mental math joke juices flowing. Answers will be posted tomorrow.

- How many eggs can you put in an empty basket?
- How is the moon like a dollar?
- What coin doubles in value when half is taken away?
- If you can buy 8 eggs for 26 cents, how many can you buy for a penny and a quarter?
- What occurs once in a minute, twice in a week, but only once in a year?
- What goes up but never comes down?
- Why is it impossible for a human arm to be exactly 12 inches long?
- Only DEAD people can read hexadecimal. How many people can read hexadecimal?
- How do you make 7 even?
- One is the loneliest number, two’s company, and three’s a crowd. What is four and five?
- Why do statisticians hate to shop for clothes?
- The math department organizes a raffle in which the prize is announced as an infinite amount of money paid over an infinite amount of time. With the promise of such a prize, the department is able to sell lots of tickets. How could the department offer such a prize and not go broke?

### Presentation and Booksigning: Reiter’s Bookstore (DC)

I’ll be presenting (an abridged version of) my workshop Puns and Puzzles at Reiter’s Books in Washington, DC, on Saturday, September 11.

Reiter’s Books

1900 G Street NW

Washington, DC 20006

**2:00 pm**

The presentation will combine jokes from * Math Jokes 4 Mathy Folks*, some new jokes and even a comedy sketch, as well as some of my favorite mathematical puzzles. If you happen to find yourself in the nation’s capital with nothing better to do on a Saturday afternoon, please stop by to say hello.

*Math Jokes 4 Mathy Folks*will be available for sale, and after the presentation, I’ll be happy to sign a copy for you — or for the special geek in your life!

I look forward to seeing you!

### The Girl With the Dragon Tattoo

*The Girl Who Played with Fire* is the second volume in the late Stieg Larsson‘s *The Millenium Trilogy*. (Of course, you probably already knew that, since virtually everyone in North America has read this book. I mean, *someone* had to buy those 20 million copies, right?)

In this book the heroine, Lisbeth Salander, gets absorbed in recreational mathematics. She stumbles across a theorem about perfect numbers that, surprisingly, was proved by Euclid. (This is surprising because Euclid did most of his work in geometry, and a proof of his theorem about perfect numbers would rely on algebra and number theory.) The theorem appeared as Proposition IX.36 of Euclid’s *Elements.*

Stieg Larsson writes:

…a perfect number is always a multiple of two numbers, in which one number is a power of 2, and the second consists of the difference between the next power of 2 and 1. This was a refinement of Pythagoras’ equation, and [Lisbeth] could see the endless combinations:

6 = 2

^{1}(2^{2}– 1)28 = 2

^{2}(2^{3}– 1)496 = 2

^{4}(2^{5}– 1)8128 = 2

^{6}(2^{7}– 1)She could go on indefinitely without finding any numbers that would break the rule.

What Lisbeth does not state, but what is required for Euclid’s theorem to hold, is that 2^{k}(2^{k – 1} – 1) is a perfect number if and only if 2^{k – 1} is prime. She doesn’t state this — but her list of “endless combinations” only includes examples for which this is the case.

I don’t begrudge Larsson for this omission. After all, how can you be mad at the first author to sell more than one-million e-books on Amazon, especially when his most popular works were published posthumously? Besides, adding too much math to a popular fiction novel might make it a little less popular. I’m just happy that so many readers will be exposed to a little of the mathematical beauty that makes me love numbers.

Here’s a perfect quote from Descartes:

Perfect numbers, like perfect individuals, are very rare.

And a perfect joke:

Teacher: What is 14 + 14?

Student: 28.

Teacher: That’s good!

Student: Good? It’sperfect!

### Back to School

Even though parents, teachers, and kids in Alabama aren’t happy that their summer ended several weeks ago, school has started or will be starting soon for kids across the country. **Best of luck to all those returning to the classroom, regardless which side of the desk you’re on.**

Here are a few rib-ticklers about (and appropriate for) the classroom.

Father: Did you learn a lot in math class today?

Son: Apparently not! They want me to come back again tomorrow!

Why did the student eat her homework?

Because she thought it was “a piece of cake.”

A young boy asked his grandmother for help with his math homework. “I need to find the least common denominator,” he told her.

“My goodness,” his grandmother replied. “I can’t believe theystillhaven’t found that. They were looking for that when I was in school!”

### Brief Q & A

Even Georg Cantor would have trouble counting the number of mathematician light bulb jokes…

Q: How many mathematicians does it take to change a light bulb?

A: Just one. She gives it to three physicists, thus reducing it to a problem that has already been solved.

And it’s rumored that the following joke is what caused Gottfried Leibniz to lose favor with George I…

Q: What happened in the binary race?

A: Zero won.

### Random Thoughts

The following was sent to me by my friend Pat Flynn, and it may enter my email signature soon.

The derivative of my enthusiasm for mathematics is positive for all values of the independent variable.

And here are some one-liners that don’t warrant their own posts, but they’re just too good not to share…

Heisenberg might have slept here.

Old mathematicians never die; they just lose some of their functions.

Whenever four mathematicians get together, you’ll likely find a fifth.

“Take a positive integer

n. No, wait,nis too large; take a positive integerk.”

### National Tell a Joke Day

There is no shortage of fabricated holidays. I eat popcorn on National Popcorn Day (January 19), I don’t tell lies on National Honesty Day (April 30), and I break mirrors and walk under ladders with reckless abandon on Defy Superstition Day (September 13).

But there is no fabricated holiday around which I am more able to rally than National Tell a Joke Day, celebrated annually on August 16! That’s today, so happy holiday to you.

Here’s an oldie but goodie that’s just right for a day so special:

Some engineers needed to measure the height of a flag pole. They only had a measuring tape, and were getting quite frustrated trying to slide the tape up the pole. Eventually, a mathematician happens by, listens to their problem, and says he can help. He removes the pole from the ground and measures it easily. When he leaves, one of the engineers says, “Leave it to a mathematician! We need to find the height, and he gives us the length!”

### Compound Probability

When I told my friend AJ that I had written a book of math jokes, he asked me a question that I found difficult to answer. He asked, “How many will I laugh at?” I paused for a second. Hearing my hesitation, he asked, “Are the jokes really that bad?”

“Well, no,” I explained. “I’m just not sure how many you’ll get.”

AJ is not a dumb guy. He’s quite intelligent, actually. He can hold his own in a conversation with just about anyone on nearly any topic. But some of the jokes in *Math Jokes 4 Mathy Folks* require some advanced understanding of mathematics. Thinking about his question further, I derived the following formula (though not while I was drinking… I never drink and derive):

P(L) = P(G) × P(F|G)

where…

- P(L) is the probability of laughing;
- P(G) is the probability that you get the joke; and,
- P(F|G) is the probability that you’ll think a joke is funny, if you get it.

The question, of course, is how you determine the values for P(G) and P(F|G). Based on absolutely no data whatsoever, I offer the following:

- P(G) = 0.99, if you have a degree in mathematics;
- P(G) = 0.95, if you completed a high school calculus or statistics course;
- P(G) = 0.68, if you completed the minimum high school requirements in mathematics;
- P(G) = 0.51, if you were reasonably successful in mathematics through middle school;
- P(G) = 0.32, if you were okay until your teachers started using words like
*denominator*and*irrational*; - P(G) = 0.03, if you’re a professional athlete;
- P(G) = 0.02, if you’re a member of my extended family (who hate math, aren’t good at it, and are proud to trumpet both facts to anyone willing to listen);
- P(G) = 0.01, if you’re a journalist or other member of the popular media (and possibly lower, if you write for a tabloid).

Of course, I’m egotistical enough to believe that P(F|G) = 1.

So, how many jokes will AJ laugh at? I don’t know. But with over 400 jokes in *Math Jokes 4 Mathy Folks*, there’s got to be a few that he’ll find funny, right?

Anyway, here’s a joke involving compound probability:

When a respected statistician passed through the security check at an airport, a bomb was discovered in his carry-on luggage. “Come with us,” said the security guards, and they took him to a room for interrogation.

“I can explain,” the statistician said. “You see, the probability of a bomb being on a plane is 1/1000. That’s quite high, if you think about it — so high, in fact, that I wouldn’t have any peace of mind on a flight.”

“And what does that have to do with

youcarrying a bomb on board?” asked a guard.“Well, the probability of

onebomb being on my plane is 1/1000, but the chance of there beingtwobombs on my plane is only 1/1,000,000. So if I bring a bomb, the likelihood of there being another bomb on the plane is very, very low.”

### Reap What You Sow

Yesterday, our home owner association paved and painted the parking lot behind our townhouse. My twin three-year-old sons, Alex and Eli, were fascinated by the large, white numbers that now adorn each parking spot. They counted all of the numbers out loud, which ranged from 16 to 37. “Where is 1?” Alex asked.

The lot behind our house is Parking Lot B; spaces 1‑15 are in Parking Lot A. I probably should have explained this to him, but instead I just said, “There’s no number 1 in our parking lot. This lot begins with number 16. Isn’t that an odd number with which to begin a parking lot?”

He responded, “No, daddy. Sixteen is an **even** number, actually.”

I suppose that’s what I deserve for teaching my kids about parity before their fourth birthday.

This incident reminded me of the following joke, which appears in a slightly different form in *Math Jokes 4 Mathy Folks*:

A teacher asks her class, “How can you divide 25 sugar cubes among 3 cups of coffee so there is an odd number of cubes in each cup?”

Bekkah responds, “Put one in the first cup, and put 12 in each of the other cups.”

“But 12 isn’t an odd number,” the teacher replies.

“Sure it is,” Bekkah replies. “Twelve is a very odd number of sugar cubes to put in a cup of coffee!”

This joke is typically told so that the teacher asks students to divide 14 sugar cubes into 3 cups of coffee, and the student says to divide them as 1, 1, and 12. I never liked that version, though, because the problem as posed by the teacher is unsolvable — that is, there is no way to divide 14 sugar cubes such that there is an odd number in each cup. Yes, I know it’s only a joke… but I like to think that a teacher would only ask a question that had a solution.

### In Bookstores Now

Here’s a math problem for today:

The sum of three consecutive integers is 27. What is the product of the integers?

Today is August 9, 2010, also known as 8/9/10. It’s no coincidence that today was chosen as the official publication date for ** Math Jokes 4 Math Folks**.

You can preview the first chapter on the NCTM web site.

You can also order a copy online at the following online retailers.

Thanks to those of you who purchased a pre-publication copy. To those of you who buy a copy in the future — thanks in advance!