Pi is a lie?

[eagerSnake]

So what is the length of the hypotenuse of a right-angled triangle with the other 2 sides length 1?

I did the math and it says sqrt of 2

I did the logic and it says it doesnt make sense

The closest answer I have is https://apod.nasa.gov/htmltest/gifcity/sqrt2.10mil

About 10 million digits so far. We'll get to the end eventually. Either that or math is lying to us.

[eagerSnake]

If √2 is rational then you can write it as m/n for integers m, n which have no common factors. Thus m = n √2 and by squaring both sides, m² = 2n². This shows us m must be even. So then there is another integer p such that m = 2p. Therefore 4p² = 2n² which simplifies to 2p² = n² which in turn shows us that n is also even. But if n and m are even, they have a common factor of 2! This is the logical contradiction.

So my theory may be wrong

[chamber]

Alternatively, irrational just means the number can't be defined with fractions of whole numbers. It says nothing about geometric space.

[implosion]

You also might be interested in the formal definition of a metric space.

[Davsto]

Distances are a continuous variable so they can be infinitely divided as you go smaller and smaller

Like imagine you have a distance of a metre. Then halve it. And again. And again. You can keep halving this distance infinitely and still have it be an actual measurements.

That's what an irrational number is. It just keeps going at the infinitely small level - smaller than atoms, smaller than protons, smaller than electrons, smaller than quarks. Infinitely small. If you think about it, most things are irrational lengths, as if you were to keep going on a smaller and smaller level chances are that it wouldn't land exactly on a micrometre or nanometre or femtometre or so on - it would always be slightly off down to an infinite level.

[Davsto]

I do understand the confusion here and it's because infinity - in any sense - is something that the human brain simply has a lot of trouble comprehending.

[Who]

Imagine you tried to measure something 1.5 meters long when your only measuring tool was 1 meter long. You couldn't do it, you'd only be able to tell that it was between 1 and 2 meters. However, you can divide your measuring tool in half and find that it is exactly 1.5 meters.

Irrational distances are similar except no matter how many times you subdivide your measuring tool you still won't be able to measure its exact distance.

[eagerSnake]

it's because you can't denote the number (i.e. pi) as x/y where x and y are integers

that's what makes it "irrational"

it's a real ratio, but it's not one we can denote using integers

but we fixed it

http://www.maths.surrey.ac.uk/hosted-si ... igits.html

Phi = 1·6180339... = phi–1
and
phi = 0·6180339... = Phi – 1 = 1/Phi = Phi–1

Phi denotes (sqrt(5)+1)/2 =1·6180339...
and
phi denotes (sqrt(5)-1)/2 =0·6180339... .

Phi = 1/phi = phi + 1
Phi^2 = Phi + 1 and therefore
phi^2 = 1 − phi.

And these can be generalized and give an important and remarkable pair of results for all integers n (positive, zero and negative):
Phi^(n-2) + Phi^(n-1) = Phi^n
phi^n = phi^(n+1) + phi^(n+2)

See what they did there?

[implosion]

Regardless of the base, there will still be real numbers that can't be expressed using finitely many digits. This argument is agnostic of what base you choose to represent your numbers; even if you use base phi, there will still be real numbers which can't be represented with a finite or repeating representation. The set of numbers represented in this way is countable regardless of what base you choose, and the reals are uncountable.

[eagerSnake]

Hm, that is not what they are claiming. I will have to study it more as this is the first time I've laid eyes on it.

Pedit: okay so I misinterpreted, read on

So if you take the diameter of a circle and divide it into equal parts (doesn't matter how small you go) and you use that as your unit of measurement, then you will never be able to fit them into the circumference, and vice-versa. You will always have a 'part' that doesn't fit at the end, regardless of how small of units you use.

[implosion]

From what I can tell the argument on that page shows that you can represent integers as sums of powers of phi. It seems analogous to Zeckendorf's theorem which talks about representing integers as sums of nonconsecutive fibonacci numbers.

It doesn't say anything about representing irrational numbers, or even non-integral rationals (I imagine there are likely rational numbers which aren't "rational" under base phi, although i cbf to think about it deeply right now).

[eagerSnake]

Guess I'll look into how well things like irrationals amd non-integral rationals convert

It seemed to me, at first glance, they were trying to say any number could be expressed rationally in base phi, which would be really profound, but you're probably right in that effect

[Annadog40]

The number pi isn't a lier.

[eagerSnake]

You know how we are with our math. It has to be precise. I just can't stand the fact that when dealing with pi the answer is never going to be precise unless you simply don't simplify your answer

Then I feel like if my answer is "2pi" that I haven't finished the problem because that's 2 x Pi = ???

Irks the hell out of me

Guess I just have to get over it and keep Pi in my answers

[Annadog40]

Being imprecise doesn't make pi a liar.

[Who]

You know how we are with our math. It has to be precise. I just can't stand the fact that when dealing with pi the answer is never going to be precise unless you simply don't simplify your answer

Then I feel like if my answer is "2pi" that I haven't finished the problem because that's 2 x Pi = ???

Irks the hell out of me

Guess I just have to get over it and keep Pi in my answers

But the answer will be precise. Pi, $\pi$, is precise. What makes it less precise than say, 1/3?

[eagerSnake]

1/3 feels a lot more finished than, say, 2pi

But I get it.

[McMenno]

Find out how

this

mafia scum dot net user disproved thousands of years of mathematics!

[Davsto]

wait until this poor sod discovers radians

[Randomnamechange]

I was ill the week that radian were taught and forgot to catch up on the maths lessons i missed. we then didn't use radians for several weeks and when we did I had no idea what was going on.

[eagerSnake]

poor sod

Lol because irrational distances don't make logical sense in the real world, only in the ideal mathematical world

[eagerSnake]

Find out how

this

mafia scum dot net user disproved thousands of years of mathematics!

Next I will prove that Forrest Gump was real and that the government didn't want him as a national hero which is why he isn't in the history books. And you think Elvis Presley came up with those moves on his own?

[chamber]

poor sod

Lol because irrational distances don't make logical sense in the real world, only in the ideal mathematical world

no, they still make sense even in the real world.

[Not_Mafia]

[eagerSnake]

poor sod

Lol because irrational distances don't make logical sense in the real world, only in the ideal mathematical world

no, they still make sense even in the real world.

Alright this is now the irrational distances thread

How do they make sense in the real world

Do you have proof of an irrational distance in the real world?