## Archive for November, 2010

### Warning Labels

Don’t you wish there were more truth in advertising? I applaud the efforts of the surgeon general, the FDA, the EPA, and others in their recent attempts to make consumers aware of the potential dangers of products. But the current warnings merely scratch the surface of the imminent dangers posed.

It might also be wise to include mention of the following danger, in light of discoveries during the past century:

There is an extremely small but non-zero chance that, through a process known as “tunneling,” this product may spontaneously disappear from its present location and reappear at some random place in the Universe, including your neighbor’s medicine chest. The manufacturer is not reponsible for any damage or inconvenience that this may cause.

In fact, there are inherent dangers in the labels that currently appear on products…

How do you keep a programmer in the shower for hours?

Give him a bottle of shampoo that says, “Lather, Rinse, Repeat.”

### Thanksgiving Jokes

So, maybe they’re not mathy… but the following jokes are appropriate for today…

The young turkey graduated high honors with a math degree, but he returned home and seemed reluctant to look for work. His mother was distraught. Arriving home one day, she found him on the couch again, watching reruns of Mystery Science Theater 3000. “Jesus, look at you,” she said. “If your father could see you, he’d be rolling over in his gravy!”

Why don’t turkeys get invited to high society parties?

Because the hosts are worried they’ll use fowl language.An octogenarian calls his daughter a few days before Thanksgiving and tells her that he and her mother are getting a divorce. “But, daddy,” she says, “you can’t do that!” He explains that even though they’ve been together 50 years, they’re miserable and it’s for the best. “Please tell your brother and sister,” he says, “because I just don’t want to talk about it anymore.” The daughter immediately calls her siblings; they agree that they will not allow their parents to divorce. The daughter calls her father back. “There’s no way you’re getting a divorce,” she says. “We’re coming there tomorrow to sort this out. Don’t say anything to mom before we get there.” As she hangs up, her father turns to his wife and says, “It’s all taken care of, honey — they’re all coming for Thanksgiving, and it isn’t costing us a dime!”

### One-Liners

I asked God for a good grade in math class, but I know God doesn’t work that way. So I cheated on my test and asked for forgiveness.

If you get depressed when you think about how dumb the average person is… then you’re probably horrified to realize that half the population is even dumber.

Light travels faster than sound, which is why some people appear bright until you hear them speak.

People who take a long time computing the ratio of rise to run are slope pokes.

Having gone to school doesn’t make you a teacher any more than standing in a garage makes you a car.

To steal ideas from one person is plagiarism. To steal from many is research.

I should’ve known things weren’t going to work out with my ex‑wife. After all, I’m an introverted mathematician, and she’s a lying, cheating, good‑for‑nothing whore.

Mathematicians don’t suffer from insanity. They enjoy every minute of it!

If Bill Gates had a penny for every time I had to reboot my computer — oh wait, he does.

### Investigating National Pi Day

American Express is running ads for Small Business Saturday (November 27). It’s a good idea, but I was taken aback by one of their radio spots, which says:

There’s a day for everything — Thesaurus Day, Groundhog Day, National Pi Day…

That last one caught my ear. I’ve celebrated Pi Day for years, but *National* Pi Day? At first, I was sure the copywriters for American Express had screwed the pooch on this one. Pi Day cannot be a national holiday, because π is a universal constant. And the United States is not the only country that writes dates in the mm/dd format — so do Canada, Greece, Kenya, China, and the Phillipines, among others.

I did a little investigating. Sure enough, there is a National Pi Day. On March 12, 2009, the U.S. House of Representatives passed HRES 224, a non‑binding resolution that declares:

Whereas Pi can be approximated as 3.14, and thus March 14, 2009, is an appropriate day for “National Pi Day…”

The resolution continues:

The House of Representatives supports the designation of a “Pi Day” and its celebration around the world.

Doesn’t it seem a bit incongruous to declare a National Pi Day but then support its celebration around the world?

At least HRES 224 correctly states that π can be approximated as 3.14. This is in stark contrast to House Bill 246, passed by the Indiana State Legislature in 1897, which stated, among other things:

that the ratio of the diameter and circumference is as five-fourths to four

thereby implying that π = 16/5 = 3.2.

What a difference 113 years make, huh?

A geometry teacher hands a cylindrical metal container to a student and asks her to find the ratio of the circumference to the diameter. She thinks for a moment, then offers, “Um… pot pi?”

### Working at NCTM

I am the Online Projects Manager at the National Council of Teachers of Mathematics. I love my job — I’ve been here for 6 years, and I’ll stay here another 60, if they’ll let me; I love my organization — I’m not yet 40 years old, but I’ve been a member almost half my life; and I love my colleagues. But working at NCTM has its share of, um, *challenges*.

Take the equipment we have in the building, for instance. Today, I selected “single‑sided” on the photocopier, and all of my copies were printed on Möbius strips.

Of course, my mathy colleagues cause problems, too. There are three types of people who work at NCTM: those who can count, and those who can’t.

About a year ago, a small fire started in one of the hallways. An engineer, a scientist, and a statistician — who were at NCTM headquarters attending a summit about the merits of always including three related professions in the set-up of a joke — began debating the best way to extinguish the blaze.

“Dump some water on it!” the engineer suggested.

“No! Remove the oxygen!” said the scientist.

The statistician, however, started running around the building, starting fires in other locations. “What the heck are you doing?” the other two asked.

“Trying to create a decent sample size,” he said.

To put out the fires, a mathematician on staff brought them several buckets of water. The fires were extinguished one by one, but when they finished, there was an unused bucket of water. The statistician said to the mathematician, “Can you please get rid of that water?”

The mathematician proceeded to start another fire, and then he dumped the bucket of water on it.

“What’d you do that for?” the statistician asked.

“I reduced it to a previously solved problem,” said the mathematician.

More seriously, the following is a **true** story about NCTM.

The James D. Gates Building in Reston, VA, serves as the national headquarters for NCTM. In 1993, an addition to the building nearly doubled its size. In the area between the original structure and the addition, a courtyard was created, and a geometric design of circles and triangles was constructed on the floor of the courtyard with bricks and drainage pipes:

Long‑time members of NCTM might recognize the old NCTM logo:

Shortly after the building was expanded, however, it was learned that a number of publishing companies, eager to align themselves with NCTM after the release of *Principles and Standards for School Mathematics*, began placing the NCTM logo directly on their products. Cease‑and‑desist letters were sent to the publishers asking them to kindly remove the logo from their materials — and NCTM was shocked when they said, “No!” As it turns out, the publishers’ lawyers had done their homework, and they learned that the NCTM logo had never been trademarked. As a result, there was nothing that NCTM could do to prevent them from using it.

Consequently, the NCTM logo was revised to the version we have today:

In the courtyard, we have a constant reminder of a bureaucratic blunder. As you’ll notice, the current logo has the ® symbol — and no one’s taken this one away from us, baby! Personally, I think the new one is better, anyway, with allusions to the infinity symbol; the letter *x*, as an algebraic variable; and a small child, which is a constant reminder that our profession is not just about numbers and shapes but about the lives we touch.

### Notable and Quotable

Some of my favorite quotes by and about mathematicians:

I like your results. Let’s make it a joint paper, and I’ll write the next one. – *Stefan Bergman*

Someone told me that each equation that I included in the book would halve the sales. – *Stephen Hawking*

Amusement is one of the fields of applied mathematics. – *W. F. White*

The total number of Dirichlet’s publications is not large; jewels are not weighed in a grocery scale. – *C. F. Gauss*

Any astronomer can predict with absolute accuracy just where every star in the heavens will be at 11:30 tonight. He can make no such prediction about his teenage daughter. – *J. T. Adams*

### Joy in Repetition

Today is 11/11, a day of repeated digits, which makes it a good day to share an email with you that I recently received. My coworker Julia blows me out of the water when it comes to being a number geek, and that’s saying something. Of course, her love of mathematics may be destiny — her name is Julia, and her brother’s name is Vitali. This is the message she sent me:

This Thursday, my dad will be 55 years old. On that same day, I’ll be 11,111 days old. It’s a day of repeated digits for [my] family.

I don’t know what compelled her to do the calculations that allowed her to figure that out, but it reminded me of some repdigit problems. I’ll share those in a minute. But first, a question about Julia:

How old was Julia’s dad when she was born?

Okay, that one was pretty easy. Here’s my favorite repdigit problem, which is a little tougher but can still be attempted by most anyone:

What is the smallest positive integer that, when multiplied by 7, gives a positive integer result in which every digit is a 5?

Of course, there’s the really cool repdigit number pattern:

1 × 1 = 1

11 × 11 = 121

111 × 111 = 12,321

1,111 × 1,111 = 1,234,321

Which leads to the question:

What is the value of the product 1,111,111,111 × 1,111,111,111?

And to end all this silliness, just some facts about repdigit polygonal numbers — numbers that repeat the same digit that are also polygonal numbers. Define *P*(*k*,*n*) to be the *n*th polygonal number with *k* objects on a side. For instance, P(3,4) = 10, because *P*(3,4) is the notation for the 4th triangular number (*k* = 3). Then *P*(5,4) = 22 is a repdigit polygonal number, and so is *P*(8,925,662,618,878,671; 387) = 666,666,666,666,666,666,666. Wow.

As it turns out, there’s a formula for these beasts:

*P*(*k,n*) = (*n*/2)(*k* – 2)(*n* – 1) + *n* (for *n*, *k* > 1)

Over and over,

she said the words

’til he could take no more…

– Prince, *Joy in Repetition*

### Theorems Without Thought

Conceptual understanding is overrated. It’s clearly better to teach rote algorithms without comprehension, so long as they can be repeated with minimal effort. Right?

I learned this poem a long time ago…

Ours is not to reason why;

Just invert and multiply!

But this one was new to me…

Minus times minus is equal to plus.

The reasons for this we need not discuss.

Here’s a limerick that provides the formula for a sphere without explanation…

A great circle inside a sphere

Has an area, it would appear,

Exactly one quarter —

Not longer or shorter —

Of that of the sphere. Is that clear?

And I really like this poem of a woman who doesn’t believe everything she’s told…

“Since day follows night,” they told Fawn,

“It is darkness that causes the dawn.”

But Fawn said her cat

Followed her, too, and that

Didn’t prove that the cat’s caused by Fawn.

### Race Results

In a race between two electric cars, one developed by a United States company, the other developed by a British firm, the American car prevailed. It was a friendly, unpublicized race, mainly giving each company a chance to test their cars on a closed course. Taking a page from Darrell Huff’s *How to Lie with Statistics*, however, a French newspaper ran the following headline:

In Race Between Electric Cars, British Car Loses,

and American Car Finishes Next‑to‑Last