Does pi really go on forever?

Dee put this question to mathematician Bobby Seagull...

Bobby - Yeah so people have historically tried to come up with an answer, what is pi? So think, Archimedes used geometry, drew I think a 96 sided shape inside a circle, and outside, and try to come up with an approximation. And then in the seventeen hundreds a mathematician called Lambert proved it's irrational, so you can't write pi as a ratio of two whole numbers. And then in the 1880s, a mathematician proved it’s transcendental, showing that actually, you can’t determine its exact values, so actually it does go on forever and never repeats, and one of the cool things about pi is technically, all of our birthdays are there, all our date of death, all our date of engagement, our favourite number, our recipes, sort of our favourite mathematical recipes for cakes, everything is inside pi because it goes on forever.

Chris - So if you give enough monkeys enough calculators, eventually they'll reproduce pi.

Bobby - Exactly.

Fran - The monkeys would always be reproducing a part of pi right? Whatever they type, very intelligent really! 

Eleanor - If one of your students writes down the wrong number for pi then I guess they could claim that they got it right!

Bobby - They could! I hope none of my students are listening to this!

Chris - But more seriously for a second Bobby, what actually is pi used for and how is it derived? How did they actually get to this magic number, which is incredibly powerful.

Bobby - So pi essentially, is the ratio between the circumference and diameter of a circle. So no matter how small or big a circle, that is approximately again roughly three times, a bit larger than three times, and in school we've seen people use approximation 22 over 7, that's 3.142857 recurring or three point one four. But again that ratio, it never ends, and we use it for I guess in physics, in areas of your life, but it's something which I think mathematicians currently, there's one mathematician, a computer scientist in Japan that I think earlier in 2019, used 25 computers over 121 days and came with 31 trillion digits to pi...

Chris - And is this really useful, because don't NASA just for the purposes of their calculations, stop at something like five or seven decimal places that they're satisfied that that's good enough.

Bobby - Yes and I think I've read somewhere that with 32 digits of pi you can then estimate the size of the universe to like, one protons width.

Chris Is that right Fran? Just to put you on the spot.

Fran - It sounds plausible.

Bobby - So we don't need that 31 trillion digits I'm sorry for the person who set that world record.