π...pi?

[user789653241]

What is it?
I know it is 3.14159.... and the ratio of a circle's circumference to its diameter, etc.

But what is it really?
My ds asked me, and I couldn't really answer that properly. Is there any resources that explains what it is?

YouTube is your friend.

22/7

The ratio of a circle's circumference to its diameter is what defines pi.

If you take any circle, no matter how big (solar system sized!) or small (atom sized!) and divide its circumference by its diameter, you will always get 3.141592653..... which is pretty astounding.

Pi crops up in lots of formulae involving circles or curves.

One of my pupils asked about pi recently and we cut string to the length of the diameter of a circle and then used that to measure the circumference. Did that with lots of different circles to show that we always needed 3.14 x the diameter length.

It is the ratio of a circle's circumference to its diameter. That is how it is defined. That is what it really is.

It happens to be an irrational number which means it cannot be expressed precisely as a decimal or as a fraction. 22/7 is close but is not bang on. Many people find it hard to get to grips with the idea that irrational numbers exist but there is a simple proof.

It's a never-ending number with no pattern.

Thank you, I've watched few you tube and found good one.(why didn't I think about that...)

I'll do what Cagliostro did as well. Great idea.

Thanks everyone!

It is what it is, what you've said in your OP.

Not sure what else you're looking for?

pincha, I know!
But what I needed was something like Cagliostro's suggestion.
So, I might sound really thick, but glad I asked!

Oh I can't take credit for it BTW I think I saw it on Facebook :o

Yes, Wheredid, that's what I really wanted to explain to my ds.
He knows what it is, he knows how to use it, but that's all.
But he started questioning what it really was, so I really wanted to give him some answers.
I will keep researching!

Long way to go, but thank you.
It makes me happy that he gets interested in something, but sad at the same time I can't really help him.
I guess he need to pursue it himself in the future.

Pi, you say....

Yes, my ds is a geeky and quirky child, but fortunately, he has friends!

I think this is a really interesting question and, if nothing else, shows he is thinking about what he is taught, not just taking it as given.

I would like to know the answer, but have not the time to take a Cambridge Masters degree, even if I could pass the entrance test!

Numberphiles usually has some quite good youtube videos.

I would love also to know about the number e. Again, I sort of get the idea of a function with a gradient at any point being whatever the value of y is, but do not quite see why it works. Also why does e crop up again in binomial expansion?

Thank you Richmal, Numberphiles looks great.
We will have lot's of fun watching them!