## Does pi follow a pattern?

…no, but maybe mathematicians do. I recently met someone, and when he asked me what I did my Ph.D. in (math),

he said “math…like just straight numbers, huh?”

“yup” (Not really. Low dimensional topology actually, but I wasn’t about to bring that up.)

He followed up quickly with “How many digits of pi do you know?”

Here’s the embarassing thing: my reply, “3.141592653589793”

That’s about as far as I can get these days. But he stopped me anyway. He was convinced. I was a bonified mathematician.

Contrast this story with one a friend in grad school told me. He met a man on a train in Switzerland, who happened to also be a mathematician. What did the Swiss man ask my friend to verify that he was a mathematician?

“Prove that if p is a prime number, then either p+1 or p-1 is a multiple of 6.”

One of my points is that becoming a mathematician is more about developing a thought process than learning facts.

My other point is that I’m embarrassed to have so many digits of pi memorized. Which brings me to how and when I memorized it in the first place: the 11th grade, precalculus. (Hey, there was nothing else interesting going on in the class.) The text book had pi written out to several hundred places. I memorized maybe 40 or 50.

Later that school year in a health class we answered a questionnaire that categorized us according to some color scheme. I was a green. I was the green, the only one in the class! Then we divided up into our groups (hah) and collaborated (hah hah) to make posters describing characteristics shared by the group (hah hah hah).

One thing that I put on my poster (besides that I prefer to walk rather than drive) was as many digits of pi as I could remember off the top of my head (which was probably at least 30).

I should have put on the poster why either p+1 of p-1 is a multiple of 6, but I didn’t know any better at the time.

The teacher asked whether pi follows any pattern.

I said “no.”

Of course it does, actually. It follows the pattern that it is pi: the circumferance of a circle divided by it’s diameter. But I wasn’t about to bring that up. That’s not really what he meant any way.

But what did he mean?

Maybe he meant this: “OK, I know that pi goes on forever (the decimal expansion does, anyway). But does it repeat itself?”

The answer to that is “no,” which is the same as saying that pi is irrational.

But I don’t think that he meant exactly “does it repeat?” I thought that was what he meant at the time, but not anymore.

Here is an example of an irrational number (I’ll call it y) that does follow a pattern:

y=.2202002000200002000002000000200…

See what I mean? It doesn’t repeat itself, but it does follow a pattern.

I once had a professor who called this irrational number y “stupid,” which almost offended me (the context was that my friend who met the Swiss man gave the professor y as an example of an irrational number in the Cantor set if you interpret y as being written here in base 3, but I”m not about to bring that up here).

I prefer to call irrationals that follow a nice easy pattern like this “fun.”

I’ll have more to say about fun irrationals in another post, or at least irrationals that toe the line of being fun (I haven’t given “fun irrationals” any kind of hard and fast definition).

How about you? Are you a mathematician?

Even if you don’t think you are, can you think of any fun irrationals?

Can you tell me why p+1 or p-1 is a multiple of 6?

Try it, and let me know, especially if you think of any interesting (and/or) fun irrationals.

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### 13 Responses to Does pi follow a pattern?

1. Magnus says:

Sure, they are three numbers in sequence, so one of them must be divisible by 3, and it is not p :), and the other numbers (thow two which are not p) are both divisible by 2, since p is not. So one of them will be divisible by both 2 and 3, thus by 6.

And by the way, appart from liking math, I am right now trying to memorize Pi to 10,000 decimals, with random access.

Yeah, I agree, learning to think in math is the key. I do that too, I rarely memorize formulas for example, I rather try to understand how to derive them.

But I find the memorization process as such interesting, more from a psychological point of view, so I developed a method which I am not testing. Take a look http://bigparadox.wordpress.com/

Regards,
Magnus

2. Tami says:

Wait- isn’t 2 a prime numer. 2-1=1 which is not divisible by 6 and 2+1=3, also not divisible by 6. So, the question needs to have an additional limitation that p does not equal 2.

• Jenny L. (sixth grader) says:

Yes, two is a prime number. (It’s ok, my mom can never remember the difference between prime and composite) 🙂

3. toomai says:

You’re right, p=2 and p=3 don’t work. Somehow I forgot to put that in. Thanks for pointing it out 🙂

4. Jenny L. (sixth grader) says:

Yes, “Pi Day” is coming up at my school and there is going to be a competition to see who can remember the most digits of pi. Here is what I have memorized so far: 3.141592653587939. 16 digits. Pathetic. Another girl in my grade has memorized 60! But I am with you and do not know how to memorize all of those numbers for long periods of time!

• TonyLec says:

3.141592653589793238462643383279… and so on

5. Helena Paice says:

This is how much i know of pi 3.1415926535 8979323846 2643383279 5028841971
which is 50 digits of pi and i am 11

• toomai says:

Good job! More than I knew at age 11.

• Anon says:

Or you know how to cut and paste.

6. rab says:

if p = 3 then p is prime but neither (p+1) nor (p – 1) is a multiple of 6

7. Meh says: