## Saturday, March 7, 2009

### More Fun with Dates!

Birth dates, actually. Ages, to be exact.

So, here's the thing. When people have a birthday I often tell them why their new age is a cool number. (I know, I know, the nerditude. It consumes.) I'm already planning a 33 1/3 birthday party. For myself. Also, when kids ask me how old I am, I just give them a mathematical clue. They find this very annoying.

My favorite is students turning 16, because we sing them a special little song (originally written in honor of my friend Denisse) -

Happy birthday to you!
You're a power of two!
The next time that happens,
You'll be 32!

I've lately been trying to compile a list. I left out all the primes - they're more interesting as people get older. Can you fill in any holes? And no cheating - everyone older than 3 is the sum of two primes!

If your age is _____, you are a(n) ________

6 - a perfect number
7 - the only single digit number spoken with two syllables
8 - a perfect cube
9 - a perfect square
10 - a triangular number
11 - the first three-syllable counting number
12 - an abundant number
15 - a triangular number
16 - a power of two, and a perfect square
24 - a factorial
25 - a perfect square
27 - a perfect cube
28 - a perfect number
32 - a power of two

Anything else I come up with is either "prime" or a big stretch! I could really use good ones for 17 and 18.

update: 13, 19, 23 and 31 are happy numbers.
17 is a hungry number.
17 is also a Fermat Prime.
65 is the least number that can be written as the sum of two squares in more than one way.

Sarah Cannon said...

Being lazy (or resourceful) I went to Number Gossip. I'm not sure how you work them into a song, but it's good for random number facts. (Didn't notate how I discovered it. Half thought it might have been through you.)

For example, we learn that 17 is a hungry number and with another click begin to figure out what that means.

jd2718 said...

I intended a 33 and 1/3, but didn't carry through. Do you have lots of vinyl?

I was thinking for a reprise for 45, but I never owned very many at all.

17 is odd. And that's just the right age for that to get a reaction. 18 used to be legal, but those days are long gone. The third number of the form n^3 - n^2 is not so impressive. If you start a Fibonacci-like sequence with 1, 3, then you reach 18... Hmm. I guess 18 is just a little bit grown up.

Kate said...

I'd never seen that before, Sarah, thanks! Neat!

Oh there's plenty to hype about 18 - they can buy a lottery ticket, vote, buy cigarettes (not that the little angels would, or that I'd mention it), um.... enlist in the army? Is it 18 for R-rated movies, or is that 17?

Number gossip informs us that 18 is the only number that's twice the sum of its digits. That's kind of cute.

I don't think I have any vinyl. I will have to be on the lookout at garage sales.

jd2718 said...

And I have stacks of LP and no turn table. 60s jazz. Late 60s early 70s rock. Late 70s early 80s Rock and New Wave (we really called it that)

Hmm. Maybe I will buy a turntable and some speakers....

David said...

I don't have one for 17 or 18 but for 13, 19, 23, 31 are all happy numbers.

Matt said...

17 is one of only four known Fermat primes, and therefore the regular heptadecagon is one of only four known regular polygons with a prime number of sides that is constructible with compass and straightedge!

That's kind of a mouthful, though.

There are a bunch that are the sum of two squares. (I am currently the sum of two squares.) I don't know how often you run into someone who's 65, but it's the least positive integer that can be written as the sum of two squares in more than one way.

mrfollett said...

http://www.stetson.edu/~efriedma/numbers.html

H. said...

Love the birthday song :D Can't wait for a chance to show it to the students, together with the Number Gossip site.

Sarah Cannon said...

Glad to share Number Gossip. It's a perfect website for times like this. (Honestly, it was hard not to copy/paste the entirety of the descriptions for each number while I was writing earlier.)

Went back to Delicious. Jackie B tagged it a week before I did. I needed to figure out that puzzle.

17 for R-rated movies.

Sean Henderson said...

17 is expressible as the sum of two 1st powers (obviously), the sum of two 4th powers (the first to do such) and, to finish off the whole 1 to 4 thing, is the sum of a square and a cube ( interestingly enough it is 2^3 + 3^2).