Pi is a lie?

[eagerSnake]

Since pi is irrational, either circumference or diameter must be irrational. Distance can't be irrational; it is measurable.

Thoughts?

[eagerSnake]

But in reality we know that it's not irrational. There are no irrational numbers in real life. So, what is the true ratio? How can we find it?

This is the "golden ratio" people don't speak about, isn't it?

Not even a computer can figure out the distance? Is there something wrong with our number system? Is there any changes we can make to our number system to make it easier to calculate?

It blows my mind because if we have a circle with a known absolute circumference, then we draw a line through the center and erase the circle we have a line segment which should be able to be measured.

Is it just a matter of our abilities to measure things not being accurate enough? Most likely. In order to find the true ratio I guess we would have to change the unit of measurement to particles or something, which I'm assuming we don't have the tech to do yet (maybe?)

[eagerSnake]

First off there is nothing that says there can't be irrational distances in the real world. I'm curious where you derive that notion from.

Because an irrational number is infinite. It's not measurable. Never ending.

Distances are finite. Measurable. Beginning, and ending.

[eagerSnake]

Excuse my candor but I'm not sure you understand what "irrational" means in this context.

It has no pattern, no repetition, and no end.

<- requirements to be considered irrational pedit: unable to be shown as x/y where x/y are integers

Your example of 0 is no good because it's not irrational because it has a pattern that repeats itself, which is great! Also can be shown as 0/1.

[eagerSnake]

At this point, when you accept irrational numbers in measurements, math becomes art, rather than science.
This is what they don't teach you.

[eagerSnake]

And you believe what, that an irrational distance is a real thing?

[eagerSnake]

Distance is measured in units that we count

If you get down to the particle level unit of meaurement, there will be no more irrational distance, because you can count the particles.

[eagerSnake]

Therefore our calculations of pi is wrong, but close

Because pi, as we figure it, is an irrational number

And that would mean either the circumference or diameter of the circle is irrational, which is not rational (pun intended)

[eagerSnake]

The next question is, why is it wrong? Well I'm guessing that has to do with our measurements or our number system.

[eagerSnake]

Going to chew on that one now.

That doesn't make sense either. There must be an end to these numbers.

Otherwise it doesn't make logical sense.

[eagerSnake]

long live tau.

Never saw this but I'm looking into it now.

Bob Palais and all that. Looks interesting.

[eagerSnake]

Pi is still wrong

[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

[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?

[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.

[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

[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

[eagerSnake]

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

But I get it.

[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?

[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?

[eagerSnake]

Second, you can't measure anything exactly. Measuring instruments have limited precision. So any measurement you're going to make is really just a rational approximation to whatever the real length is. It says nothing about whether the distance itself is rational or irrational.

[eagerSnake]

Catch 22.

Further, the world at a very fine level is fuzzy, so where do you decide the measurement should start/stop at?

[eagerSnake]

10/10

[eagerSnake]

How do perfectly rational distances make sense in the real world? You can not have exact measurements in the real world. There is always going to be some +/- margin of error. You will only find a perfect unit distance as a mathematical ideal.

I never claimed they did make sense

Burden of proof

[eagerSnake]

Exact nonzero distances don't make sense in the real world, rational or irrational.

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.

IDK who is in the right but I'd put money on Who

[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.

[eagerSnake]

The bias is pretty clear I think

[eagerSnake]

My statements aren't contradictory.

[eagerSnake]

You said irrational distances make perfect sense outside of idealistic mathematical planes

You said that

Now YOU'RE trying to shift the blame for me not specifying "exact" which I was driving at as you can see in #52

[eagerSnake]

I feel like we've reached a common ground at least.

The next question is whether the following statement is true:

No matter how small of a unit you divide the diameter into, if you try to use that unit to measure the circumference, at the end you will have a space too small for that unit, and vice-versa.

Furthermore, the ratio of that space left over to the unit must be irrational.

[eagerSnake]

Based on what we know, anyway, it must be true.

Why could I not theorize that there is a unit of measurement so infinitesimal that if everything was measured using the unit there would be no irrationality?

[eagerSnake]

I did read some things about einsteins theory of relativity being thrown out as a fallacy (and possibly that he knew it was one). I need to fact check it more myself, and it's a bit off-topic, but did you hear about this and can you confirm or deny it?

Assuming this is true, it seems we almost continuously disprove things that we were universally confident about.

I could then infer the proofs re ratio between a circles circumference and diameter being irrational are simply based on measurements that may have been off by even just 1 of these infinitesimal units, skewing the computations causing the irrationality.

[eagerSnake]

Intriguing. I guess, at this point, I would have to "debunk the Pythagorean Theorum" to show that sure, sqrt2 is irrational, but that there is no proof that this distance could exist.

[eagerSnake]

Yeah, I'm looking into them now and then seeing if there is any leaps in logic, such as assuming the theorum to be true first.

[eagerSnake]

Do you believe the universe is infinite?

[eagerSnake]

So if I travel in a straight line in one direction, I would eventually return to original location; much like flying around the earth or any other planet?

[eagerSnake]

Then what happens when I reach the end of the finite universe?

[eagerSnake]

Or is it?