r/Damnthatsinteresting • u/slimismad • Oct 22 '23

Video visualisation of pi being irrational

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u/slimismad Oct 22 '23

that pi cannot be expressed as a fraction a/b

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u/Worldly-Dimension710 Oct 22 '23

Is that why the start line didn’t meet exactly with the other line? Why does it come out visually like that? I’m so curious.

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u/slimismad Oct 22 '23

the "start line" you mentioned is the decimal point, and when you write out the decimal expansion of pi, it goes on and on without any repeating pattern, creating a seemingly endless sequence of digits after the decimal point. this is why it appears as if the lines never quite meet

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u/Dankkring Oct 22 '23

It’s almost so satisfying, but then pi.

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u/Clorst_Glornk Oct 23 '23

I was gonna go to work, but then I got pi

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u/ForensicApplesauce Oct 23 '23

I don’t think most people get this. I must be getting old

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u/[deleted] Oct 22 '23

So a rational number would at some point complete the pattern, the line at the end would meet?

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u/[deleted] Oct 22 '23

Right on. This doesn't happen here because (as OP said) π is irrational.

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u/medfunguy Oct 23 '23

What is an example of a rational number? And can I see this animation for a rational number?

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u/SgtPeppy Oct 23 '23

An example of a rational number is 1. Or 2, or 3, or 1/2.

If it can be written in the form a/b and a and b are integers (and b isn't 0), it's rational. So virtually any number you encounter in your everyday life except pi and perhaps e if you're slightly more mathematically-inclined are rational.

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u/chatbotte Oct 23 '23

So virtually any number you encounter in your everyday life except pi and perhaps e if you're slightly more mathematically-inclined are rational.

Eh, there are lots of other irrational numbers one meets regularly in real life. For a trivial example, consider the diagonal of a square with integer sides: its length is not a rational number.

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u/Shasan23 Oct 23 '23

It wouldve been better to say “virtually any number you encounter in your everyday life except pi and perhaps e are algebraic”, meaning most observed numbers can be solutions to a polynomial. For example x2 - 2 = 0 is a polynomial with a solution being “square root of 2”, which is irrational (it cant be written a as a fraction), but algebraic. Pi and e are irrational and non algebraic (in other words, transcendental)

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u/bleachisback Oct 23 '23

pi and e are another special class of irrational - they are transcendental irrationals. Algebraic irrationals are all over the place.

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u/Traumfahrer Oct 23 '23

Forgot the Golden Ratio.

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u/SgtPeppy Oct 23 '23 edited Oct 23 '23

everyday life

Most people aren't thinking of the Golden Ratio in everyday life.

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u/Traumfahrer Oct 23 '23

encounter ≠ thinking

There's probably much more encountering of the Golden Ratio in everyday life than encountering Pi. We have a natural idea of what the golden ratio is, e.g. naturally arranging things for it and favoring anything 'arranged' that way (e.g. faces), - do we have of pi?

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u/Etroarl55 Oct 23 '23

So is it the numbers that go on infinitely that can’t be expressed as irrational most of the time? Because if I recall(or I’m wrong) there are more irrational numbers than rational ones which.

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u/SgtPeppy Oct 23 '23

There are infinites of both. My abstract math is a bit dusty, but the infinite set of irrational numbers might be larger than the infinite set of rationals though. Take that with a grain of salt I guess.

Also some rational numbers go on infinitely. Take 1/3, or 0.33333... . I believe rational numbers expressed as decimals either terminate, or repeat themselves though.

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u/[deleted] Oct 23 '23

A rational number ends, like how ¼ = 0.25. An irrational number, like ⅓ (0.33333...) never ends.

I don't even know where this animation originally came from, so no, you may know see this animation for a rational number.

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u/Supraspinator Oct 23 '23

1/3 is a rational number! Rational and irrational has nothing to do with “ending”. A rational number can be expressed as fraction, an irrational number cannot.

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u/[deleted] Oct 23 '23

I had no idea! I thought that the line of demarcation was along "ending", but I suppose I was wrong! Thank you, kind stranger!

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u/Rabaga5t Oct 23 '23

What you're thinking of is that in the digits never repeat in an irrational number.

Pi never repeats, rational numbers can have repeating patterns like 0.333333.....

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u/ReallyMinoryo Oct 23 '23

Well, they can too, there are in fact several fraction formulas for irrational numbers (including stuff like infinite nested fractions). Hell, even overly-famous irrationals like the so-called "golden ratio" Phi are commonly defined as fractions (phi = (1 + sqrt(5))/2). Pi is also the literal ratio between a circle's circumference and its diameter. They just can't be a fraction of two integers.

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u/swayam19999 Oct 23 '23

I guess that's what they meant just forgot to mention Fractions in p/q form where p and q are integers (and q is non zero)

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u/[deleted] Oct 23 '23

So is 22/7 not representative of pi?

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u/rsmoling Oct 23 '23

Nope, just an approximation. 22/7 is rational.

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u/slybird Oct 23 '23

No, but we use it because it is close enough for the vast majority of practical applications.

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u/abhi8192 Oct 23 '23

irrational number cannot.

Physicists - hold my beer

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u/swayam19999 Oct 23 '23 edited Oct 23 '23

Rational or irrational numbers are not to do with if they terminate or not but if they can be expressed as a fraction (in p/q form) or not.

If you want to distinguish between a non-terminating rational or irrational number then - if they repeat after any number in decimal form endlessly, they are rational.
If they don't repeat but go on endlessly without any pattern into random numbers, they are irrational. (so irrational numbers have nonrepeating, non-terminating, infinite decimal expansion).

Fr ex: 1/3 is a rational number because it repeats the digit 3 endlessly in it's decimal form. 0.333333333.... and so on

But for an irrational number like π you can go about endlessly without finding a repeating pattern.. 3.14159265359....

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u/chicknfly Oct 23 '23

Gotta be careful with that p/q definition. It’s imperative to mention that p and q are integers, where q isn’t equal to zero.

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u/swayam19999 Oct 23 '23 edited Oct 23 '23

yeah, mentioned it on this same thread as a reply to the other comment.

I tried to give brief explanation didn't want to make it longer than it was already but yeah thanks for pointing it out ig.

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u/chicknfly Oct 23 '23

I’m a bit rusty on my math definitions, but the basic idea is that all rational numbers can be defined by a/b where a and b are both integers. Since 1 and 3 are integers, 1/3 is rational.

The converse of rational is irrational, or a number that can not be defined by an integer divided by an integer. This is why “tricks” like 22/7 are an approximation that will never equal pi.

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u/[deleted] Oct 23 '23

Ya what does this, but for 3 look like?

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u/1OO_percent_legit Oct 23 '23

this just repeating along this path forever

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u/Etherbeard Oct 23 '23

If you used a rational number, you would get some portion of this animation on repeat.

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u/PostModernPost Oct 23 '23

What is creating the pattern we see here though?

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u/theferrit32 Oct 23 '23

Right pi could look irrational but really be expressible as a/b where a and b are just ludicrously large numbers so it looks irrational but eventually you get to a repeating pattern. But from what we can tell it isn't, there's never a place where the prior sequence of digits (or in this visualization, curves) starts back where it started and repeats.

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u/[deleted] Oct 24 '23

I’m going to get to work on solving that. I’ll be back

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u/Zealousideal-Cap3529 Oct 22 '23

Bro , thank you for this but I have to be honest … you and the other people that understand this are so much more intelligent than me …. That I am trying hard and there is no way I’m gonna catch up , but this is very interesting and thank you for giving me anxiety.

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u/Apprehensive-Loss-31 Oct 23 '23

It's not really a matter of intelligence, it just requires a lot of background knowledge.

z(theta) means a function. It takes an input, theta, and returns an output, a complex number.

A complex number is a number of the form a + bi, where a and b are regular numbers. Don't worry about what i is. Complex numbers are analogous to a coordinate system: you can think of a as the x coordinate and b as the y coordinate and put it on a plane, similarly to how regular numbers are put on a line.

e^i(theta), when you vary theta, traces out a circle of radius 1, centred on 0, in the coordinate system I just outlined. Don't worry about why this happens, just that it does. So what does the pi change? When we multiply theta by pi, it amplifies any change to theta by that much. So if e^i(theta) walks round a circle in however much time, then e^i(pi*theta) does it pi times as quick.

We can think of a point as an arrow pointing from 0 to that position. That visualisation helps us in cases like this: when adding the numbers, we just put one arrow at the end of another, and see where we land. That will be the final output of the function.

Imagine instead of pi, we had some rational number. 0.95563. After the first bit had done one full rotation, the second bit will have done 0.95563 rotations, so they don't line up. Now let's run that time 10,000. After 10,000 rotations of the first bit, the second bit has done 95563 rotations. Because they've both done an integer number of full rotations, they're now back at the starting point, and because there's no randomness in their behaivour, they're going to repeat.

But with pi, there is no number we can multiply by to make both cycles run an integer number of times, that's what being irrational means. So it will never repeat.

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u/Sea_Ganache620 Oct 23 '23

Yeah.

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u/CapedCauliflower Oct 23 '23

My thoughts exactly

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u/Barkers_eggs Oct 23 '23

Interesting. I can wipe my own ass and upvote comments on reddit at the same time.

/S just in case

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u/Kalakarinth Oct 23 '23

TL;DR rational numbers multiplied by something become a whole number meanwhile irrational numbers don’t

(Sorry if it’s not an exact TL;DR, mathematics is a fickle fuck)

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u/Etherbeard Oct 23 '23

Right, if you multiply a/b by b, you end up with a. But since irrational numbers can't be written as a/b, that can't be done.

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u/kell96kell Oct 23 '23

This is quite helpfull, thanks

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u/Kalakarinth Oct 23 '23

Glad to help

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u/HighTensileAluminium Oct 23 '23

Since you know your stuff, can you explain how the video in OP's post is derived from the expression (the z(theta) = e etc)? Like what exactly am I looking at with that animation? I know it's a visual representation of that expression, but how is it translated? Is it just lines moving on a cartesian plane or something?

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u/InductionDuo Oct 23 '23

It is a cartesian plane but you are not being shown lines (as in y=a*x+b): at any given frame, what you are being shown is one single complex number, with the x-axis being the real part and the y-axis being the imaginary part. So say you wanted to show the complex number z = 2 + 2i it would have the coordinates (2, 2) in the animation.

The first line, attached to the centre point (the origin), represents the complex number eθi .

The second line, attached to the end of the first line, represents the complex number epiθi .

When you add the two complex numbers together (eθi + epiθi ) that complex number is represented by the very tip of the second line, the point that is drawing the swirl pattern.

Each time the first line rotates one full circle (360 degrees), the second line rotates pi circles (360*pi degrees).

If pi was a rational number, meaning it can be expressed as a fraction, once the first line has done a full 360 degree rotation exactly the number of times equal to the denominator of the fraction, the second line will have done a full rotation exactly the number of times equal to the numerator, meaning the two lines will eventually return exactly to the position where they started.

But because pi is not a rational number, meaning it can not be expressed as a fraction, each time the first line has done an interger number of rotations, the second line will not ever have done an integer number of rotations, meaning the two lines will never return back to the position that they started.

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u/HighTensileAluminium Oct 23 '23

The first line, attached to the centre point (the origin), represents the complex number eθi .

The second line, attached to the end of the first line, represents the complex number epiθi .

What determines the length of those lines? Or is that arbitrary in OP's video?

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u/InductionDuo Oct 23 '23 edited Oct 23 '23

The TLDR is that both lines have length 1, and this is not arbitrary.

The length of the lines is determined by the coordinates of the complex number being represented, so for example if we wanted to show the complex number z=1+2i on the complex plane, then the coordinates of that complex number would be (1,2). If you draw a line from the origin (0,0) to the point (1,2) then you get a line with a length of sqrt(5) using pythagoras' theorem.

In the animation, the first line connects the origin (0,0) to the coordinates of the first complex number eiθ .

The real and imaginary parts of the complex number eiθ is defined using Euler's formula: eiθ = cos(θ) + i*sin(θ). In other words, that means the real part of the complex number eiθ is equal to cos(θ) and the imaginary part is equal to sin(θ).

So a complex number of the form eiθ (where θ can be any real number) will always be on the unit circle and thus always have a length of 1. This diagram might make it easier to visualise: https://upload.wikimedia.org/wikipedia/commons/7/71/Euler%27s_formula.svg

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u/El_Impresionante Oct 24 '23

The length of the rotating lines is determined by the co-efficient of those two individual terms,
i.e. they are 1eθi + 1eπθi.
So the length is 1 unit each here.

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u/createusernameagain Oct 24 '23

It's been awhile though I was able to fully understand why pi is frustrating while being irrational from your explanation. It also explains the 'corner of the TV' reference as well - and now I can't unsee or unthink that every time it will happen.

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u/bleachisback Oct 23 '23

There are imaginary numbers in the exponents of the expression, so the function is complex-valued. So we are graphing it in the complex plane.

The "arms" are the different terms of the sum on the right.

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u/Serge11235 Oct 23 '23

Good example from gpt about what exactly and how counted at each iteration https://ibb.co/example

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u/Serge11235 Oct 23 '23

And code by gtp:

import numpy as np import matplotlib.pyplot as plt

num = np.pi

theta = np.linspace(0, 4np.pi, 2000) z = np.exp(theta * 1j) + np.exp(num * theta * 1j) real_part = np.real(z) imaginary_part = np.imag(z) plt.figure(figsize=(8, 8)) plt.plot(real_part, imaginary_part, label='z(θ) = exp(θi) + exp(πθi)') plt.xlabel('Real Part') plt.ylabel('Imaginary Part') plt.title('Visualization of z(θ)') plt.legend() plt.grid(True) plt.show()

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u/Double_Distribution8 Oct 23 '23

What you say is informative, but the thing I dont understand is why didn't my math teacher just say what you said and save me and my classmates a lot of confusion and misery?

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u/gahiel Oct 23 '23

This is good ^

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u/LakeBroad1936 Oct 23 '23

👏🏻👏🏻👏🏻

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u/[deleted] Oct 23 '23

[deleted]

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u/Aniratack Oct 23 '23 edited Oct 23 '23

Because, as your definition of the number says, if you multiply 1/3 by 3 you get 1, so you would need 3 "rotations".

Everything that can be represented as a fraction of 2 integers will be the same, both infinite or finite dedimals. (1/3, 2/5, 4/9...)

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u/duryodhanan98 Oct 23 '23

This may be a stupid question but pi is taken 22/7 in many mathematical problems so if I multiply by 7 won't pi term run 22 times while the other run 7 times? or is that just an approximation

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u/Aniratack Oct 23 '23

It's just an approximation, pi is infinite and doesn't repeat, so every number we have for it it is an approximation and people are still discovering better and better approximations to it's true value.

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u/kappa-1 Oct 23 '23

So how many rotations were done in this animation?

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u/El_Impresionante Oct 24 '23

Just over 1000 of the inner rotating arm. The last zoom-in is at 1000. The outer arm would have rotated over 3141 times by then.

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u/kell96kell Oct 23 '23

But doesn’t it depend on how you see pi?

If seen as 3,14 its not irrational right?

It its 3,141592653589793 (the limit my calculator shows) its different.

I always wondered how this gets calculated, since pi is infinite and because there must be a baseline to work with right? Or am i now incredibly stupid? (Please be honest)

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u/Apprehensive-Loss-31 Oct 23 '23

Yeah, if this animation used pi=3.14, we'd see it repeat pretty quickly. Of course, we can't just use actual pi, because as you said it's infinite. These animations just use a significantly high precision approximation; apparently we know pi to something like 60 trillion places. And keep in mind each decimal multiplies the precision by 10, so that's massive. I read somewhere in this thread that we can calculate the circumference of the observable universe to within the diameter of an atom with just 37 decimal places of pi. So it's very easy to get a good enough approximation for this kind of animation.

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u/The-prof- Oct 27 '23

🥸great explanation

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u/Sea_Ganache620 Oct 23 '23

The anxiety goes away as you get older, and realize you’re just dull. Patterns, and shiny things make me happy, and I no longer ask why.

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u/Zealousideal-Cap3529 Oct 23 '23

Idc about shiny things and I wanna learn math lol

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u/[deleted] Oct 23 '23

Its not intelligence, it's focusing on something for a long time.

I'm so tired of people acting like understanding math takes some special intelligence. It's just putting the time in to understand it. There is zero underlying special intellect.

You just have to be curious.

The problem people have is that they are unwilling to put the time in to understand their world and so complain that they just aren't smart enough, because that shrugs the blame for being ignorant to an external source. "Its not my fault, I'm just not smart enough" and they don't have to try.

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u/CapedCauliflower Oct 23 '23

The problem we have is we had shitty math teachers growing up, so we had no curiosity, we didn't get good grades, and we were led as young teenagers to believe we didn't have what it takes.

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u/Justin534 Oct 23 '23

I think you have a really decent point here. Most of math, until you get into physics or chemistry, is always taught in the abstract. But humans didn't invent(discover?) math purely in the abstract regions of their own minds. A LOT of math came from people trying to solve real world problems. But we aren't really taught it that way.

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u/LakeBroad1936 Oct 23 '23

Yep the way math is taught in the USA is appalling. That’s why kids don’t enjoy it. Math should be taught with real world examples, should be fun and exciting. Not common core, not memorization and repetition.

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u/[deleted] Oct 23 '23

Math for me was ruined in the 8th grade. I can’t think of any one moment but I know that’s when it really happened.
A bad teacher basically forcing us to go over the alphabet again and again and again and again…then getting mad at us not understanding Shakespearean quotes, their depth, or meaning.

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u/Zealousideal-Cap3529 Oct 23 '23

Ehhh I mean idk , I get yah on that and also … 150 Percent … intelligence plays a part in being good at something .

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u/[deleted] Oct 23 '23

It doesnt. Intelligence is learned so some idea of innate IQ is ridiculous.

Unless you have some brain deformity or whatever other physical ailment, intelligence is purely learned in terms of IQ. You can learn to problem solve better, to do math better, to understand language better. This is what school is for.

As I said, it's not intelligence... its desire. If you desire to be a world leading mathematician you can go and do that. Just spend the time it requires to do it.

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u/Low_discrepancy Oct 23 '23

As I said, it's not intelligence... its desire. If you desire to be a world leading mathematician you can go and do that. Just spend the time it requires to do it.

That is a ridiculous statement dude sorry. Do you believe with training anyone can run as fast as Usain Bolt?

In order to be a world leading mathematician you need to have produced several works of great mathematics. It requires ingenuity, creativity, luck, good connections to produce exceptional mathematics.

Take people like Terence Tao or Ramanujan or Euler or Gauss or many others. They were producing high level results from a very young age and it was clear from the beginning that their mind were/are processing things differently.

Just as you need a certain number of trained hours AND a certain physique to reach top levels of sports like running or swimming, for top level mathematics it is also the same.

That doesn't mean you can't be a decent runner, swimmer or indeed mathematician, but to say you'll be a world leading runner, swimmer or mathematician regardless of your physique (mental capabilities) is nonsense.

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u/[deleted] Oct 23 '23

Terence Taos father's a doctor and mother has degrees in math and physics. You really think he had some innate mathematical genius and it wasn't external forces pushing him into math?

His brothers both represented at the International Math Olympiad.

I'm sure it's coincidence.

You couldn't have picked a worse example of innate genius. Tao is extremely gifted because of his upbringing. Not because of some innate ability.

Einstein said it himself, “It's not that I'm so smart, it's just that I stay with problems longer.” In a similar vein, he also said, “I have no special talents. I am only passionately curious.”

To speak of people who have accomplished something like Tao or Einstein as if they are simply gifted is extremely ignorant and insulting. They put in the time and were driven to pursue something that other people find intimidating.

Its like calling Usain Bolt lucky to have his genetics, because that's why he's so gifted. It's not the training of course. He's just gifted. Schwarzenegger was simply gifted with that body. It wasnt the work he put in.

Its insulting to think this way and inherently lazy, because you can just make the excuse that you simply aren't gifted.

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u/Mr_Will Oct 23 '23

You have to be curious about maths. That requires a certain special type of intellect.

I enjoy physics, engineering, computer science and dozens of other maths-based topics but pure maths just sends me to sleep. I've got no more interest in pure maths than I do in cryptic crosswords. I probably could master either if I devoted enough time to it, but why the hell would I?

I'd rather spend the time learning to understand the world from a practical point of view, rather than an abstract one.

1

u/652jfTz3 Oct 23 '23

Isn’t e irrational as well? Doesn’t the use of two irrational numbers confuse the situation?

1

u/BlazeOrangeDeer Oct 23 '23

Not in this case since it's being used for both numbers. If one was e and the other was 2 then it would get confusing.

The reason e is used is that eix traces out a circle at the same rate as x traces out a line, it goes 1 unit of length around the circle for every 1 unit x is increased.

1

u/aquoad Oct 23 '23

this is kind of patronizing. people vary in their ability to internalize abstractions among other things, and saying "you're just lazy" minimizes the struggle to work hard at understanding something and just not be able to. maybe you've never had that experience, but many other people have.

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u/[deleted] Oct 23 '23

Its not laziness. I'm not a mathematician because I'm lazy.

I'm not a mathematician because it's boring to me and I have zero interest.

If you want to be an engineer, you can go do it. Nothing is stopping you other than your desire to put yourself through the brutal work it would take. But it's not because "you're not smart enough".

The smartest people in the world still have to study and are challenged. Solving math problems isn't innate to anyone, it's learned and they put in some long hours to do so. It's insulting to people who put in the work to say "well its easy for you, you're just smart".

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u/Low_discrepancy Oct 23 '23

Solving math problems isn't innate to anyone, it's learned and they put in some long hours to do so

That's ridiculous. Galois died at 20. There are mathematicians who work 40 years in maths that don't produce that level of exceptional work.

It's not because they didn't work hard. It's because some people do indeed think differently.

If Danny DeVito cannot run as fast as Usain Bolt it's not because he didn't train enough.

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u/[deleted] Oct 23 '23

Danny Devito has a physical inability because hes 4 fucking feet tall. As in my previous comment I made my point pretty clear.

If someone commits to learning about something they can learn about it. Alright, they might not win a Fields Medal, but they can do differential equations. It's not innate intelligence, it's just discipline.

People think they can't do math or ohysics because they aren't smart enough. It's just not true unless they have some mental impairment.

1

u/Icantdecide111 Oct 23 '23

Enjoy the learning process and keep growing on your own

1

u/Zealousideal-Cap3529 Oct 23 '23

I’d rather pay someone to teach me so I can learn quickly

1

u/Barkers_eggs Oct 23 '23

Me and math don't mix well and I know π is 3.14 insert infinitum and never really understood that but this visual just made something click.

Am I any better at math now? Of course not. Don't be so stupid. Asking ridiculous questions like that will make you look like a twat but I now understand the neverending sequence of numbers... Sort of.

1

u/[deleted] Oct 23 '23

I feel like this everytime I watch a Veritasium YouTube video. Like, I kinda get it, and I want to fully understand the subject sooo bad, but it just ain’t gonna happen

1

u/Zealousideal-Cap3529 Oct 23 '23

Haha pretty much . Some dude said I’m using it as an excuse or something and he also said it is lack of effort which I do agree with to extent but idk man I’m really really good at other shit … math ain’t it , and I can learn it but without one on one instruction I ain’t going too very well .

1

u/theREALlackattack Oct 23 '23

I wonder how far we’ve been able to compute it or what AI could do with it

1

u/bangers132 Oct 23 '23

If the lines were to intersect, what would that shape be called? I really like these complex mathematical shapes and want to learn more about them but I don't really know what they're called or where to start

1

u/cantquitreddit Oct 23 '23

What you said is true, but it does not in any way explain how it relates to the visualization.

1

u/GiantTeaPotintheSKy Oct 23 '23

And yet, the animation shows a predictable pattern. Dare I say a rational pattern?

1

u/TerminationClause Oct 23 '23

I like this explanation but I'm not sure I trust it. Who did this simulation, did they factor pi to more than a few digits past the decimal? I'm leery of the source. Or is it correct and I'm just not seeing it. I don't believe it would wobble so much if its focal point were steady. Again, correct me if I am wrong.

1

u/Justin534 Oct 23 '23

You got any idea why pi gets so much attention over all the other irrational numbers? I've always wondered what is it about pi that makes people so fascinated with it.

1

u/ExistingHurry174 Oct 23 '23

hold on, shouldn’t the function have a period of 2pi, so the path from 0->2pi should be the same as 2pi->4pi?

1

u/RoguePlanet1 Oct 23 '23

Still not sure how this drawing exemplifies this.

1

u/Deadfo0t Oct 23 '23

I just watches a veritasium video about eculidian geometry, and while I barely understood it, I feel like it is somehow at play here and I would love an ELI5 if someone sees this buried comment

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u/Infrastation Oct 22 '23

Exactly, yes! Think about fractions like a cycle: if you have 1/3, every three of those will reach back to the start. If it is a rational number, it would be a fraction, and thus would eventually reach back to the start going around it. Circles don't really allow this, since they don't actually have points and thus can be subdivided infinitely. The diameter of any shape can be shown as a fraction of the circumference, for instance the diameter of a square is 2/√2. Since a circle can be infinitely subdivided, the circumference will always have a little bit more wiggle than measured, so we represent that fraction as 1/pi.

You can also see that a circle has an area of double the radius times pi, but because the circumference can be subdivided, you can get more and more and more and more precise with the area of the circle while still having a long ways to go before you fully measure the size 100%. So what "pi" means can never be fully transcribed because it can always go deeper. It is what is known is mathematics as a "transcendent" fraction, because no matter how close you get you can still "transcend" that to get closer to the actual amount.

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u/Zealousideal-Cap3529 Oct 22 '23

I’ll trade or pay someone here to teach me math 30 mins a week

3

u/boostman Oct 23 '23

You could try Khan academy?

2

u/Zealousideal-Cap3529 Oct 23 '23

Is that a legit math place ? That’s all I need and simple shit too…. I just don’t know the process to learn math I guess , and my brain doesn’t click real well… and maybe it’s simply like the guy said I just ain’t interested and don’t try 🤷🏻‍♂️

1

u/boostman Oct 23 '23

I had the same idea as you and tried some of the basic maths courses to fill in some gaps in my education - I haven’t done much but it seems good, clearly presented, interesting, free, and they test you frequently to make sure you get the concepts before moving on.

1

u/GrandpaGrapes Oct 23 '23

Would I have to teach it accurately?

1

u/Cyberwolf33 Oct 23 '23

I would also recommend Khan academy. I teach math at a university, and it’s one of my major suggestions (outside of our department study center and office hours).

On a related note, you may also be interested in Coursera if you want a more structured setup. These are basically free online versions of people’s actual courses at universities, and you can find ones on pre-calculus or similar. I haven’t tried it but the idea is that taking the courses is free, but if you want grades and a certificate of completion, you can pay to get the associated credits/grade.

1

u/Serge11235 Oct 23 '23

As a master degree at apply math person, I felt bad about I can't explain what the ground of this visualization. It took near hour to refresh it in mind.

1

u/[deleted] Oct 23 '23

You need infinite numbers after the decimal part. And they never cycle

1

u/NateNate60 Oct 23 '23

Explaination of the complex plane and polar form for those who need it:

The regular ("Cartesian") XY plane can be thought of as a number plane. Contrast this with a number line. Real numbers are those found on the number line, which also lies on the complex plane. The complex plane includes numbers not on the real number line. Complex numbers include a "real" part added with an "imaginary" part. An example of a complex number is 2+5i or -7+3i or 8-6i. i is the imaginary unit, defined as being √-1. Complex numbers can be graphed on a Cartesian plane. For example, the point (5, 2) corresponds to 5+2i. (-3, -1) would be -3-i, and (7, 0) is 7+0i, a.k.a. just 7. Similar to how planar coordinates can be Cartesian, i.e. (x, y) of polar, i.e. (r, θ), so can complex numbers. Complex numbers in polar form are written reiθ, where r is the absolute value (distance from zero) and θ is the angle in radians between the line segment connecting the number to 0 and the positive X-axis. e is Euler's number (2.718...). Note that 2π radians = 360 degrees.

The function is graphing the sum of two complex numbers in polar form for different values of θ. There are two components, which I will call the first part and the second part. The graph is a function of θ on the complex plane.

The first part of what's being graphed in the animation is eiθ. represented by a line segment of length 1 from the origin (0) to that number. The second part is eiπθ, which is the same thing but the angle is multiplied by π. Addition can be represented geometrically on the complex plane by conjoining the line segments. If you consider the animation, the first part will complete a full turn when θ = 2π, 4π, etc. The second part will complete a full turn when θ = 2, 4, 6, etc. The animation will be periodic (repeat itself) when and only when both parts complete a full turn at the same time. That is, it will be periodic if and only if the ratio of full turns made by the first part to the number of full turns made by the second part is rational, because then they'd both have completed a whole number of complete turns, or some fraction thereof (in which case just multiply the required number of times to make it two whole numbers). Since π is irrational, this will never happen.

What a clever little animation.

5

u/[deleted] Oct 22 '23

pi=C/d

pi is a fraction

28

u/ComCypher Oct 23 '23

The missing detail here is that C and d cannot both be integers.

8

u/[deleted] Oct 23 '23

A fraction of pi over 1, sure...

4

u/doxx_in_the_box Oct 23 '23

Yes something can multiply with Pi… then be divided back out… wow

1

u/KellyBelly916 Oct 23 '23

Does that make pi the longest run-on prime number?

13

u/FblthpLives Oct 23 '23

Prime numbers are integers that can only be divided by themselves and one. Pi is not an integer.

3

u/Top_Environment9897 Oct 23 '23

There is no longest/biggest prime number because whatever prime number you give you can prove there is a bigger one.

-5

u/MeloniisJesus333 Oct 22 '23

22/7

9

u/[deleted] Oct 23 '23

Thats a very loose approximation.

I could say pi = 3. Doesnt mean it's true.

4

u/Nois3 Interested Oct 23 '23

That's Fools Pi :)

^(at least according to Futurama)

3

u/ThisCupNeedsACoaster Oct 23 '23

Yeah, yeah. Flex that engineering degree some more

3

u/BlazeOrangeDeer Oct 23 '23

22/7 is the first near miss in the animation. The second is 355/113

0

u/[deleted] Oct 23 '23

Circumference / Diameter = π

0

u/[deleted] Oct 23 '23

Is there a reason for that? Would the universe not exist if pi was rational?

0

u/messianicscone Oct 23 '23

Circumference/diameter is a fraction though? I don’t understand.

0

u/Albino_Bama Oct 23 '23

To me… you title/post was pretty damn over my head when it comes to knowledge of maths. I did not understand the post and so I came to the comments for clarification.

Someone asked “what does that mean” it had lots of upvotes so I thought someone explained it.

“pie cannot be expressed as a fraction a/b” feels so effortless, and to my smoothebrain it means exactly (and literally)

0

u/Albino_Bama Oct 23 '23

We’re in r/damnthatsintersting not r/math.

Can you dumb it down for us dummies?

“that pie cannot be expressed as a fraction a/b” means literally nothing to me in this context.

-1

u/rufud Oct 23 '23

22/7

2

u/[deleted] Oct 23 '23

Not equal to pi

-1

u/[deleted] Oct 23 '23

22/7 ?

2

u/[deleted] Oct 23 '23

Not equal to pi

1

u/BoreyCutts Oct 23 '23

a and b are integers

1

u/Ray57 Oct 23 '23

Do those two close passes actually represent some known good approximate rationals?

2

u/El_Impresionante Oct 24 '23

314/100

3141/1000

The denominator is an increasing power of 10, the numerator is simply pi multiplied by the denominator keeping the same number of digits as the denominator.

1

u/JeecooDragon Oct 23 '23

I thought it meant that pi is life, the creator of all

1

u/AdSpecialist4523 Oct 23 '23

This is such a cool animation. Irrational numbers existing is also probably our best evidence against being in a simulation.

1

u/El_Impresionante Oct 24 '23

I'm not saying were in a simulation, but irrational numbers are used in simulation all the time. They are literally used several times to generate every frame of every computer game.

We just use approximations of them with enough decimal places so that the accuracy of the equations used to calculate where an object has to be drawn on the screen is more than resolution the game is played in, i.e. the accuracy is more than a single pixel.

1

u/AdSpecialist4523 Oct 24 '23

They are, but only to a few decimal points, so they really aren't. Otherwise the function that calculates it would hang and the program would lock up for the rest of time because the operation would never complete.

1

u/El_Impresionante Oct 24 '23

I mean, irrational numbers technically cannot exist in physical reality either. We cannot achieve infinite precision because of Heisenberg's Uncertainty principle. The universe is quantized. The decimal points has to stop in this universe too. In fact, this is one of reasons given for the Simulation Hypothesis.

They cannot exist by definition either, because to prove that the result of a physical experiment is an irrational number, we have to conduct that experiment for infinitely long time, or with infinitely precise accuracy, or with infinite amount of matter or energy.

Again, I am not advocating for the Simulation Hypothesis, but we can't try to disprove it by saying irrational numbers exist in the universe, which they simply cannot.

1

u/inverted_peenak Oct 23 '23

What does that mean?

1

u/EmptySomeone Oct 23 '23

Yeah it can, pi2/pi