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eh yes but I think you are mixing up planck contant and planck length here.
planck constant is about energy not length
I did say scale fascinates me. Gotta allow me to talk about the Planck constant instead. We're just taking about interesting sh!t.
Did you know quarks comprise only 1% of the mass of protons and neutrons and that 99% of the mass comes from the interaction between the quarks themselves?
Hey, did you why you were banned? Trying to figure out your transgression.
Well, no.. anyone who uses pi quite often, is well aware of the rounding errors and dangers of not using enough figures for accuracy calculations. People are not blind, or else you would have very many more critical failures in dangerous machinery lol.
to answer the rest of the 'why is it accepted' question:
-all circles are the same. the only difference being the size. radius, diameter, circumference or area.
-since they're the same apart from size, the three measurements are all related in the same way for every circle.
- the radius is half the diameter, the circumference is pi times the diameter, the area is pi times the radius squared.
so pi is a common ground that you can use to express any circle, or chunk of a circle that can fit into a different geometric shape.
yes, it is unfortunate and a nuisance that pi is irrational, and is approximated.
but, until you find a better way to relate them, in pi we trust.
so, i'll be waiting for your elegant system of mathematics to provide exacting answers to many inaccuracies we currently have, which may catapult our civilization into the future. exciting.
5 digits = 3.14285 x 456789 = 1435,495 km
6 digits = 3.142856 x 456789 = 1435,622 km
If NASA used 5 digits, they shrink the planet by 127km.
The measurement rule is wrong. - Be it to increase or decrease the digits, NASA will only be further away from the truth...
The push up count is fixed. The circumference length is fixed. There is no infinite digit. People just don't know the right way to measure it.
Err.. so your answer to topic "Why is π accepted" is "We accept the wrong as a rule because we can't find the right answer"? : x
Imagine this, the planet is colonized. You bought a house there. A week later they call you up and say opps your house disappeared because we round up the surface length and now we can't find it. It's less than 2 km (2000m) but it still hits your 50m house. You might go "what nonsense, where did you guys hide my house?
and that is π. All the wrong guessing. Infinite digits of guessing.
well, mathematics doesn't work like that, but you keep on doing what you want. lol.
It's stuff like that that makes us have to use pi in calculations, otherwise after enough math, you're left with a really bad answer that makes less sense
Pi is irrational, though it is also real. Real in the sense of being in the category known as "real numbers", which includes literally any number you can fit in a single dimension -- i.e. if you draw a straight line that's infinitely long, you can find any such number as a distance between two points on it.
Irrational just means you can't express it as a ratio. There are an infinite number of numbers that can't be expressed as ratios. For example, this includes all the square roots of positive numbers that aren't perfect squares. You can draw a right triangle with legs that are one inch long each, and you can measure the length of the hypotenuse, even though it's the square root of 2, which is irrational. So it's still a real number.
As for exactly what number pi is:
* yes, it does have an exact value.
* it just can't be written down exactly using our base ten number system.
In a way, it's like how we can't write one-third exactly without using a fraction symbol or something to indicate a repeating decimal. Except in the case of pi, it just happens that it doesn't repeat.
Not all decimals (i.e. numbers with nonzero digits past the decimal) repeat. For example, consider the number implied by the following pattern:
0.1101001000100001000001000000...
This won't ever repeat. In fact, because it's a non-repeating decimal, it's irrational, like pi. But it's still a number.
That said, how do we use an irrational number? Why do we have 22/7?
That's because the numbers we actually need in real life are often approximations anyway. If you need to cut 2 inches off a piece of wood, you're not measuring down to the atom and making a straight line of atoms where the cut is. You're probably just gonna use a pencil and then saw it off. It's not exactly 2 inches you've cut off, it's a good enough estimate of 2 inches, as you can measure from a ruler on hand and mark with a pencil. And it's probably good enough for pretty much anything you'd use that wood for; you don't actually need to know if it's exactly 2.0000000000000000000000 inches.
22/7 isn't pi. 355/113 isn't pi. 3.14 isn't pi. 3 isn't pi. But depending on what you're using pi for, it might be good enough. If I need to know what length to cut a sheet of plastic to make a ring around a circular cake, I can probably get away with 3.14 for pi. If I'm planning to deposit a very thing layer of chemical coating onto a smoothly polished metal cylinder, I might need more digits. Different situations require different levels of precision.
Heck, a lot of the time when I headmath I just use 3 and run on "pi is a little more than this". So 2 pi is a little more than 6, 3 pi is a little more than 9, and so on.
In math, if you need the exact value of pi, chances are you're working in some context where writing down lots of digits doesn't even matter. So you can just use the pi symbol (technically the lowercase Greek letter pi) for it and literally just leave it there. If you need to get a numeric value, you can then decide -- based on what you're using it for -- how much precision you need, or in other words, how many digits or how complicated of a fraction you want to use.
For example, what's the period of the basic sine function? 2 pi. You don't even need to approximate it unless you're, say, building or measuring something that makes use of it. Plus, it's way faster to write symbols like that than to try to get their decimal approximations. It's just better all around if you don't need the approximations.
I havent watched this in years, but Ill drop it for anyone interested. This guy has a very different approach to mathematics and I remember he calculates that ratio slightly differently. He also has a lot of perhaps weird theories about numbers.
I am not offering this as a proponent of anything he says; its just a bit....different.
https://youtu.be/Xw9lTB0hTNU