## Posts tagged ‘birthday’

### You Say It’s Your Birthday

*It’s my birthday, too.*

Okay, not really, but it wouldn’t be surprising if it were. Today (September 17) is the fourth most common date on which to be born. Or at least it had been from 1973 to 1999 in the United States, according to an analysis by Amitabh Chandra, a professor of social policy at Harvard who compiled 28 years of birth date data.

Yesterday (September 16) was the overall most common birth date, and tomorrow (September 18) was the tenth most common.

In fact, all of the top ten most common birth dates occur in September, and even the lowest-ranking date of the month is still in the top third of the most common dates (September 5, #125). Apparently November and December are busy times for gettin’ busy.

It’s a busy birthday time elsewhere, too. Statistics New Zealand issued a warning about the excessive number of birthdays that will occur near the end of September.

How common is your birth date? Take a gander at the image below. Or, for an interactive experience, click around on **Andy Kriebel’s version that uses Tableau**.

This information (which is not new, btw — an initial analysis was completed by Chandra for a paper published in the Journal of Political Economy in 1999; a table with Chandra’s full data appeared in a column by David Leonhardt in 2006; and, various versions of the image above have been floating around the internet for several years) throws a wrench into the famous Birthday Problem, which asks, **“At a party of n people, what is the probability that two of them share a birthday?”**

The solution to the Birthday Problem assumes that birth dates are evenly distributed across the calendar. But clearly they’re not. How much does real data affect the solution, though? As it turns out, not much.

Using real birth date data from 1985-88 pulled from the CDC, Joe Rickert completed an analysis using Revelation R Enterprise 6. The results look like this:

On the other hand, the theoretical probability of two people sharing a birth date in a group of *n* people is given by the formula:

And if you try to graph that formula, you get something like the following:

Admittedly, I was lazy. The scatterplot above only includes *n*-values from 2‑10 and multiples of 5 from 15‑100. That’s because Excel can’t handle factorials larger than 170!, so I had to use a large number calculator online and enter the values into an Excel sheet by hand. Still, it gives a pretty good idea of what the shape of the curve.

A typical benchmark for the Birthday Problem is *n* = 23, when the probability of a pair sharing the same birth date first exceeds 50%. Using real data, P(23) = 0.5087, and using the theoretical model, P(23) = 0.5073. Good enough for government work. By visual inspection, you can see that the other values match up rather well, too.

Finally, here are some math jokes about birthdays.

Statistics show that those who celebrate the most birthdays live longest.

I only drink twice a year: when it’s my birthday, and when it’s not.

Happy integer number of arbitrary units of time since the day of your birth!

You don’t need calculus to figure out your age.

They don’t make birthday cards for people who are 85 years old. So I almost bought you a card for an 80-year old and a 5-year old. But they I figured no one wants to do math on their birthday.

### You Say It’s Your Birthday…

Well, no, actually it’s not my birthday. And it’s not my friend Jacqui’s birthday, either, but she did just celebrate a milestone with us that she wanted to share. Via email, she announced,

I’ve been alive for two billion seconds, a milestone I passed this morning.

This reminded me of a problem from Steve Leinwand’s book, *Accessible Mathematics*, in which he tells kids his age as a unitless number, then asks them to identify what units he must be using. Along those lines, here are some questions for you.

- How old (in years) is my friend Jacqui?
- What is her date of birth?
- If I tell you that my age is 22,333,444, what units must I be using? Assuming I’m not telling a fib, of course. And what is my age in years and my date of birth?

This reminds me of two math jokes about birthdays.

Statistics show that those who celebrate the most birthdays live longest.

A algebraist remembers that his wife’s birthday is on the (

n– 1)^{st}of the month. Unfortunately, he only remembers this when he is reminded on then^{th}.

### Can’t Argue with That

My momma always told me:

Don’t break a person’s heart; they only have one. Break their bones; they have 206.

Who can argue with that logic? Here are some other logical statements with which you won’t want to argue, either.

I asked my wife what she wanted for her birthday. She said, “Nothing would make me happier than diamond earrings.” So, I got her nothing.

I find it strange that my advisor always begins conversations with me by saying, “You haven’t heard a word I’ve said, have you?”

It doesn’t matter if the glass is half empty or half full; either way, there is room for more alcohol.

I only drink twice a year: when it’s my birthday, and when it’s not.

My math teacher just fell in a wishing well. Go figure! I never knew they worked.

My advisor says I’ll never graduate because I’m lazy. But I just can’t take that kind of criticism. I was going to kill myself… but the gun’s, like, way over there.

Don’t judge a book by its cover… my math book has a picture of someone enjoying himself.

A grad student told his friend, “My girlfriend hates it when I sneak up behind her and kiss her on the cheek. But according to her lawyer, she also hates it when I call her my girlfriend.”

I got a tattoo of Chinese symbols on my arm that reads, “I don’t know. I don’t speak Chinese.” So when someone asks what it says…

Boy: I hate my math professor. He’s a terrible lecturer, he has bad breath, and he laughs at his own jokes.

Girl: Who’s your professor?

Boy: Dr. Jacoby.

Girl: Do you know who I am?

Boy: No.

Girl: I’m Dr. Jacoby’s daughter.

Boy: Do you know who I am?

Girl: No.

Boy: Good.

### How Many Share Your Birthday?

This afternoon, we celebrated Alex and Eli’s sixth birthday with a Disney-themed Cinco de Mayo party. The kids all wore Mickey Mouse ears, while the parents drank lots of margaritas. Tonight’s “bedtime math” question for my sons was the following:

You celebrated your birthday on May 2. How many other people in the world do you think celebrated their birthday on May 2?

It’s a simple estimation problem for most of us, but ratio is a tough concept for six-year-olds. I wasn’t sure they’d make much progress… especially since the good folks at about.com make this claim:

You currently share your birthday with about 859,178 people who reside in the United States.

This estimate appears to have used 313,600,000 as the U.S. population, which is reasonable, and then divided by 365. My frustration is that they then display the result to six significant figures. That’s problematic for two reasons — first, because their population estimate has only four significant figures, but also because it’s not the case that exactly 1/365 of the population celebrates their birthday on a given day.

But I digress. Sure, I’m frustrated with about.com’s negligence, but I started this post to tell you about our bedtime math problem, and it highlighted why I hate traditional textbook problems even more than I hate bad math in the media.

Alex first suggested that maybe the number of people who have the same birthday could be found by calculating 1/14 of 7 billion. When I asked why he wanted to divide by 14, his response was, “Because it’s a multiple of 7.” When I asked a few more questions to probe his thinking, he changed his mind. “No, wait, maybe it’s 1/35.” This time, he said he wanted to divide by 35 because it was a multiple of 7 *and* a multiple of 5, and he knew that 7 billion was also a multiple of both 7 and 5.

Then it hit me. He wasn’t trying to solve the problem. He was just trying to make sure the answer was a “nice number,” that is, an integer that preferably would end in a couple of zeroes.

A few more questions, and he finally admitted he knew an estimate could be found by dividing 7 billion by 365. “But that doesn’t work when you divide,” he told me.

Arrgh.

I believe this is what happens when kids see too many traditional textbook problems where the answers are neat and clean. They get conditioned to thinking that math is never messy.

**[Update: 5/8/13]** Just read this on the About page at the Let’s Play Math blog and thought it was worth including here: “Math is like ice cream, with more flavors than you can imagine — and if all your children ever do is textbook math, that’s like feeding them broccoli-flavored ice cream.”

And that couldn’t be further from the truth. Math is unbelievably messy. At least, real math is. Solving real-world problems often means getting a little dirty. You’ll have to roll around in fractions, dig through some decimals, and — Heaven help us! — occasionally tangle with some irrational numbers and extraneous results.

Eli then offered, “If you divide 7 billion by 365, you won’t get an integer.” (He smiled, proud of himself for using the term *integer*.) “That’s the answer, but I don’t know how to do that.” What he meant is that he couldn’t compute the result in his head; nor would I expect him to. We then found an estimate by building on Alex’s idea — instead of dividing by 35, we divided by 350 to approximate the number of people who celebrated a birthday on May 2, since 350 is close to 365 but gives a much nicer answer.

Wow. There are roughly 20 million people who will celebrate their birthday on the same date as you. Crazy, huh?

All of this reminds me of a few jokes.

Recent research shows that those who celebrate more birthdays live longer.

And all the time, I tell my wife:

Honey, you’re one in a million. Which means that there are 7,000 people on Earth exactly like you, so just remember that it wouldn’t be that hard to replace you.

### Mathy Birthday Problems

Last week, I turned 42. Here’s a math problem related to that number.

Take 27 cubes, numbered consecutively from 1 to 27. Arrange them into a magic cube so that every row, column, corridor, and space diagonal has a sum of 42.

If that’s too much for ya, try this problem instead. It’s a slight modification of a math problem that appeared on the birthday card given to me by colleagues.

Two men my age go out for drinks at 10 o’clock on a Saturday night. One of them drinks six 12-ounce beers, each of which is 8% ABV. The other drinks four Lynchburg lemonades, each of which contains one ounce of 80-proof Jack Daniels and one ounce of 60-proof triple sec. Assuming the men are the same size, which one gets more drunk?

The answer to the first question can be found at Math Palette.

The answer to the second one? Trick question. Men my age don’t go out after 10 o’clock.

### Live Longer: Have More Birthdays

Satchel Paige asked, “How old would you be if you didn’t know how old you were?”

There are lots of quotes about aging. Age is an issue of mind over matter, they say — if you don’t mind, it doesn’t matter. Or, you’re only as old as you feel. But the following is my favorite quote about age:

Anyone who stops learning is old, whether at twenty or eighty. Anyone who keeps learning stays young. The greatest thing in life is to keep your mind young.

With each passing year, I learn more and more things. But I also learn more about how much I’ll never know.

The number of years on Earth is not an accurate measurement of a life. Many people fill their entire lives with trivial matters.

A graduate student saw a professor working on a proof of the Riemann hypothesis. On the professor’s desk were thousands of papers with various notes about the problem.

“My goodness,” said the student. “Have you been working on this problem your whole life?”

“Not yet,” said the professor.

And what is age, anyway? It’s just a number. For instance, Paul Erdös claimed to be two and a half billion years old.

“When I was a child, the Earth was said to be two billion years old,” he said. “Now scientists say it’s four and a half billion. So that makes me two and a half billion.”

Now in the computer age, it seems that no matter how much we know, machines may know more than we do.

A computer manufacturer unveils a new computer that supposedly knows everything.

A skeptical man asks, “How old is my father?”

The computer thinks, then says, “Your father is 57 years old.”

“See?” says the man. “This is nonsense. My father has been dead for 20 years, and if he were alive, he’d be 71.”

“No,” replies the computer. “Your mother’s husband has been dead for 20 years. Your father is only 57, he’s currently fishing on Lake Michigan, and he just landed a three-pound trout.”

### It’s Back to Prime Time

On Saturday, I turned 41 years old. I’ve been looking forward to this for a while. It’s a prime year, and its twin prime is two years away. In between, I’ll be a number of years that is “the answer to life, the universe, and everything.”

Forty-one is also cool because *f*(*x*) = *x*^{2} + *x* + 41 is a prime-generating function. That is, *f*(1) = 43, *f*(2) = 47, *f*(3) = 53, and so on.

What is the first value of

xfor whichx^{2}+x+ 41 isnotprime?

The following image might help you answer that question. The number 41 appears in the center, and consecutive positive integers then proceed in a spiral. Notice that all of the numbers highlighted in yellow are prime. A pattern of primes continues along the diagonal — at least for a little while.

It also turns out that 41 is the smallest number whose cube is the sum of three cube numbers in two different ways:

41

^{3}= 2^{3}+ 17^{3}+ 40^{3}= 6^{3 }+ 32^{3}+ 33^{3}= 68,921

And 41 is the sum of the first six prime numbers:

2 + 3 + 5 + 7 + 11 + 13 = 41

At 41, I still feel young. But you know you’re an old mathematician when…

- You report your age in hexadecimal. (I’m only 29!)
- You’re not dead, but you’ve lost most of your functions.
- The distance you walked to school as a kid is directly proportional to your age.
- Your age can be described as “countably infinite.”
- You regularly go off on tangents.
- The phrase “pulling an all nighter” means not getting up to pee.
- When asked your age, you reply, “I’m in the 99th percentile.”
- You use the term
*surd*, and you know how to calculate its value on a slide rule.