No Stupid Questions

It is not about actual use when they calculate pi to tthese numbers.

It is about finding out if pi is actually irrational or is it recurring on some level.ie: does it start repeating at some point.

For the sheer unadulterated thrill of calculating pi.

In addition to what @Pons_Aelius replied, it is also used as a benchmark/flex for computers, as to who can build a beefy enough machine or good enough card to calculate more digits of pi.

Why do most records exist?

For those still in the dark, I'm referencing the bible in 1 Kings 7, 23-26:

And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about. And under the brim of it round about there were knops compassing it, ten in a cubit, compassing the sea round about: the knops were cast in two rows, when it was cast. It stood upon twelve oxen, three looking toward the north, and three looking toward the west, and three looking toward the south, and three looking toward the east: and the sea was set above upon them, and all their hinder parts were inward. And it was an hand breadth thick, and the brim thereof was wrought like the brim of a cup, with flowers of lilies: it contained two thousand baths.

Those measurements would only work if either the cauldron were not actually circular, or if Pi were equal to 3.

There are infinitely many. Any sequence of rational numbers converging to pi contains infinitely many. 22/7 and 355/113 are just particularly good ones for their small denominators. You can find such good approximations ("the best rational approximations of a given size") by truncating the continued fraction representation of pi:

pi = [3;7,15,1,292,1,1,1,2,1,3,1,14,2,1,1,2,2,2,2,…]
pi = 3  + 1/(7 + 1/(15 + 1/(1 + ... )))

These approximations yield:

pi ~ 3
pi ~ 3 + 1/7 = 22/7
pi ~ 3 + 1/(7 + 1/15) = 333/106
pi ~ 3 + 1/(7 + 1/(15 + 1)) = 355/113
pi ~ 3 + 1/(7 + 1/(15 + 1/(1 + 1/292))) = 97591/31065

and so on. Note that by pure coincidence one of the first few terms is quite large (292), so the difference between the corresponding partial expansions is small (1 + 1/292 is close to 1). That's why 355/113 is an unusually good approximation for such a small denominator.

you have to remember 11 33 55 and put the bar in the middle. It is mainly small MCU like ATMEGA and co. lacking FPU, and yes old stuff like Z80 ,6502, etc.

That may not have been a wise thing to say on the internet.

Does she bake pies?

Accurate(closer to the real answer), is not equal to precise(consistent measurements). I think… right?

It is kind of weird that real world measurements always have error to them so you only really know something to a few digits of precision… but mathematical constants like pi can have effectively have unlimited significant figures (but it’s kind of pointless to have more because any real world applications only need a rather small amount of them). I feel kind of similarly about integration. It’s nice to find a closed form solution for an integral, which can make certain calculations a lot faster and more accurate… but in reality if you’re just solving an integral or two for an engineering project you’re probably better off just computing it numerically to the correct number of sig figs. There’s something a little sad about that to me.