## Posts tagged ‘numbers’

### Can’t We All Just Get Along?

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Some numbers really like other numbers. Like 220 and 284, which are *amicable (or friendly) numbers*, so called because the sum of the factors of 220 is equal to 284, and the sum of the factors of 284 is equal to 220. That is,

1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 = 284

and

1 + 2 + 4 + 71 + 142 = 220.

On the other hand, other numbers despise one another, eying them suspiciously at the grocery store, frequenting different restaurants to avoid awkward conversations, and cutting them off on the freeway. The reasons for this disdain varies widely…

Why doesn’t 3 like to hang out with 4?

Because he’s a square.Why doesn’t 4 like 5?

Because he’s odd.Why is 5 annoyed by 6?

Because she thinks she’s perfect.Why is 6 afraid of 7?

Because 7 8 9.Why does

edislikepi?

He’s more of a cake person.Why doesn’t 144 like 288?

Because he’s two gross.

### Math Dreams

“I can’t get the numbers to stop.”

That’s what Eli told my wife tonight when he woke from a bad dream.

I once had a dream where I was afraid of numbers, too. During the week leading up to my midterm in Linear Algebra, I was reviewing problems from old exams. Though I thoroughly understood all that had been covered in class, and though I was able to complete all the exercises from the textbook with aplomb, I was only getting about 25% of the questions on the old exams correct.

It was freaking me out, and the night before the exam, I went to sleep very nervous.

My sleep was broken by a nightmare in which numbers were flying past my head like cannonballs from a numerical howitzer. They were coming from every direction. To make matters worse, my head was being squeezed by the brackets of a matrix as if it were in a vice.

I woke in a cold sweat. It was 5 a.m. Too anxious to sleep any more, I went to a study carrel in the library where I read and re-read the textbook and continually tried the problems from the old exams. I skipped my morning classes and studied for five straight hours. Yet I was still only able to get a quarter of the problems correct.

The midterm was at 12:30 p.m. At 11:55 a.m., I saw a woman from my class. Though I had never spoken to her before, I approached her and said, “Excuse me, aren’t you in Dr. Sibley’s linear algebra course?”

“Yes,” she replied skeptically.

“Would you mind helping me?” I asked, embarassed by the question.

“Uh… sure,” she said.

I asked her a few questions about the topics we had covered. She confirmed that I understood the material correctly. “So why am I missing so many of the questions from the old exams?” I asked rhetorically.

She took a look at my work and confirmed that it, too, was correct. Then she revealed the punch line: The professor had given us a packet of six exams, and the answer keys for all six exams were copied onto a seventh sheet. But the answer keys and the exams were **not** in the same order — each answer key had to be matched to an exam by noting the semester and date on each.

Arrgh.

I was relieved. Yet frustrated. I managed an 85 on the midterm… yet I’m certain I would have aced it had I gotten a good night’s sleep.

Mark Jason Dominus has much better math dreams than I. He posted the following problem to the mattababy listserv. He claimed that it came to him in a dream; when he woke, he thought it was still a good problem, so he decided to share it.

The volume of a 3 × 3 × 3 cube is 27 cubic units, and the volume of a 2 × 2 × 1 prism is 4 cubic units. Theoretically, six prisms should be able to fit inside the cube, with three cubic units empty. But can you arrange six 2 × 2 × 1 prisms so they fit inside a 3 × 3 × 3 cube?

Friends of mine who taught at the Center for Talented Youth claim that M. J. Dominus would often arrive late to the evening study sessions. As the story goes, he would take naps after dinner… if his alarm sounded while he was in the middle of a math dream, he would shut off the alarm and return to sleep so he could finish whatever mathematical proof his subconscience had been working on.

Wow.

**What’s the scariest or coolest math dream you’ve ever had?**

### Book Review: The Joy of *x*

Steven Strogatz says that by arranging things in the right way, we can make a surprising link seem obvious — the hallmark of an elegant proof.

In particular, he’s talking about arranging a group of rocks — several groups of rocks, actually, each containing an odd number — to show that when you add all of the consecutive odd numbers, starting with 1, the sum is a square number:

1 + 3 = 4

1 + 3 + 5 = 9

1 + 3 + 5 + 7 = 16

1 + 3 + 5 + 7 + 9 = 25

I didn’t have to read *The Joy of x* to know that 1 + 3 + 5 + 7 + … + (2*n* + 1) = *n*^{2}, and of course I’ve seen the visual proof that Strogatz demonstrated with a group of rocks:

But I don’t think that I had ever heard a definition for the concept of an elegant proof. Therein lies the beauty of Strogatz’s new book: while most of the concepts he covers will be familiar territory for the mathy folks who read this blog, each of the 30 chapters contains a pearl of wisdom, or an interesting factoid, or an eloquent sentence that makes you realize he’s as good with words as he is with numbers.

For instance, you probably didn’t know this about the distribution of heights on the online dating site OkCupid:

…the heights reported by both sexes follow bell curves, as expected. What’s surprising, however, is that both distributions are shifted about two inches to the right of where they should be. So either the people who join OkCupid are unusually tall, or they exaggerate their heights by a couple of inches when describing themselves online.

The chapters within the book are short and, as Strogatz admits, are not dependent on one another. You could start at Chapter 10, “Working Your Quads,” and it wouldn’t matter if you had read any of the nine chapters that precede it.

All in all, *The Joy of x* is breezy and fun, and while it won’t significantly further the education of a mathematician, it will provide some entertainment. And for the non-mathematician, it provides a nice overview of mathematics “from one to infinity,” covering everything from numbers to geometry to calculus, giving adults a second chance at the subject.

### Garrison Keillor Reads Math Poem

As Garrison Keillor said, “Here’s a poem for today by Mary Cornish, entitled *Numbers*.” (Or maybe you’d prefer to hear GK read the poem on The Writer’s Almanac.)

**Numbers**, by *Mary Cornish*

I like the generosity of numbers.

The way, for example,

they are willing to count

anything or anyone:

two pickles, one door to the room,

eight dancers dressed as swans.

I like the domesticity of addition—

*add two cups of milk and stir*—

the sense of plenty: six plums

on the ground, three more

falling from the tree.

And multiplication’s school

of fish times fish,

whose silver bodies breed

beneath the shadow

of a boat.

Even subtraction is never loss,

just addition somewhere else:

five sparrows take away two,

the two in someone else’s

garden now.

There’s an amplitude to long division,

as it opens Chinese take-out

box by paper box,

inside every folded cookie

a new fortune.

And I never fail to be surprised

by the gift of an odd remainder,

footloose at the end:

forty-seven divided by eleven equals four,

with three remaining.

Three boys beyond their mothers’ call,

two Italians off to the sea,

one sock that isn’t anywhere you look.

### If You’re Happy and You Know It…

Some neighbors recently told me that childless adults are happier than parents. When I mentioned this to a different friend (who is currently trying to become a parent), his response was, “Yeah, but the graph shows that parents don’t become really unhappy *until the third child*.”

A quick search did not yield the graph he mentioned, but it did provide a lot of contradictory information:

- A blog post by Philip Cohen claims that “children beget happiness, eventually.”
- A report from the Pew Research Center claims, “married people with children are about as happy as married people without children. And unmarried people with children are about as happy as unmarried people without children.” (This chart shows that marriage is a better predictor of happiness than children.)
- A Global Perspective on Happiness and Fertility by Margolis and Myrskyla indicates that people over 50 are happier than younger folks, regardless of the number of children; but among parents, those with 4+ kids are less happy than others.

So, I don’t know what to believe. All I know is that when my four-year-old son Eli created the following math joke last night, I was pretty happy.

What did the table say to the counter?

“Give me some numbers!”

Get it? *Counters*? They count!

Then today, while riding in the car, Eli’s twin brother Alex asked what language people speak in Europe. “I think they speak European,” he posited, “but Eli thinks they speak Urine.”

Who couldn’t be happy with wonderful moments like that?

For tolerating (another) story about my kids, here are a few funny quotes about happiness.

I didn’t know true happiness until I got married; but then it was too late.

Whoever said that money can’t buy happiness didn’t know where to shop. – Gertrude Stein

Happiness is good health and a bad memory. – Ingrid Bergmann