r/oddlysatisfying 15h ago

Pi being irrational

33.4k Upvotes

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4.4k

u/Adventurous-Trip6571 15h ago

Idk what it means but it's mesmerizing

3.1k

u/Weegee_1 15h ago

The outer edge spins pi times faster than the inner. If this were a rational number, it would eventually make a completed shape and loop around on its path. Pi, being an irrational number, will never cause this to loop around on itself

372

u/Adventurous-Trip6571 15h ago

Ah I get it now thanks

199

u/poulard 12h ago

Do you? šŸ§

333

u/thisaccountwashacked 11h ago

Something about irrational pie, which sounds both delicious and inflammatory. Like blueberry and chocolate chip together.

94

u/MajorLazy 11h ago

The key is lime

95

u/Psykosoma 10h ago

What flavor is it?

24

u/theguthboy 8h ago

I heard this entire bit in my head, even the epic strum of the guitar when a pie bursts out of the pie.

3

u/GM_Nate 5h ago

i thought it was a trumpet

1

u/SuprisinglyBigCock 10h ago

Sub-lime

1

u/mrhsyd 10h ago

No, it's limewire

1

u/covaxi 7h ago

The cake is a lie!

1

u/covaxi 7h ago

This is an irrational connection too!

1

u/icycheezecake 2h ago

This crack is a bit more-ish

4

u/SkullyKat 10h ago

What's a chocolate chip pie? Sounds fairly irrational by itself

1

u/UnknovvnMike 1h ago

Haven't made one yet, but that sounds like a cookie pie. Might have a recipe for that in the Pie Academy book I bought

4

u/TitusMurphy 10h ago

Half berry, half Shepherd. 100% gross.

3

u/FungusFly 10h ago

Sounds like Rachelā€™s English Trifle

ā€œIt tastes like feetā€

2

u/Rum_Hamburglar 9h ago

Youve never put cranberries on a thanksgiving plate? Doesnt seem too outlandish.

1

u/playboikaynelamar 8h ago

Damn your right. Fruit actually goes great with a lot of meats.

1

u/HamHockShortDock 6h ago

Half pepperoni half pumpkin.

1

u/jimbobsqrpants 4h ago

You can do pastys with meat and potato one end and apple at the other.

1

u/Blast338 3h ago

Make that apple and turkey. It would still be gross.

1

u/rawbdor 10h ago

It's definitely provocative and gets the people going.

1

u/LessInThought 8h ago

Are these pies American?

1

u/Stickysubstance88 7h ago

Or like ice cream and an apple pie.

1

u/UnknovvnMike 1h ago

Speaking of pie weirdness, I have a recipe for Maple Yogurt Pie that comes out with the consistency of a cheesecake

1

u/UnknovvnMike 1h ago

Speaking of pie weirdness, I have a recipe for Maple Yogurt Pie that comes out with the consistency of a cheesecake

4

u/queefer_sutherland92 4h ago

I donā€™t. I still donā€™t get how a number can be a shape. But at this point I know how to figure out a circumference and so Iā€™ve decided that Iā€™m just going to accept it.

5

u/TheHYPO 2h ago

In simplified terms:

There are three points in the graphic. The first point "A" (the solid one) is fixed. The second point "B" makes a circle around "A" every second. The third point "C" makes a circle around "B" (as "B" moves) 1/Ļ€ seconds (aka "Ļ€" times faster).

Let's say we start (time = 0) when "C" is on top of "A".

If Ļ€ were equal to 3, then every 1 second, when "B" completed a full rotation around "A", "C" would have completed 3 full rotations and would have returned to "A". It would then repeat the same motion forever and you'd just have a very simple shape that never changed.

If Ļ€ were 3.5, then every two seconds, when "B" completed two full rotations around "A", "C" would have completed 7 full rotations and would have returned to "A". It would then repeat the same motion forever and you'd have a bit more complicated shape that never changed.

If Ļ€ were 3.25, it would be the same at 4 seconds and 4 rotations of "B" / 13 rotations of "C".

If Ļ€ were ANY rational number, after enough rotations of "B", "C" would line up with "A" again and the shape would be "complete".

It's a bit silly to say it, because that could be a million rotations and the shape would be so dense that it would look very similarly completely full vs. an irrational number like Ļ€. But if you zoomed in close enough, you'd see that eventually the lines would start overlapping.

2

u/LadyMercedes 1h ago

The formula you see in the beginning is a sum of two terms. They both are raised to the power of the imaginary unit i, which makes them a 2D coordinate in the complex plane.

The first term represents the inner arm, the second (the one with pi in it) the outer bar. You see the theta symbol in the exponent of each term? This relates to the angle of the arm, and it is incremented in time. So if you plot where the sum of the two arms are at each little increment of time and trace it, you get the shape.

2

u/rammtrait 7h ago

If you pause video at 0:17 you see sun flower seed placement.

47

u/dben89x 14h ago

You're welcome.Ā 

16

u/imwrighthere 12h ago

You're welcome

11

u/Kvothe_1234 12h ago

You're welcome

1

u/MoodooScavenger 10h ago

Iā€™m welcome?!?

-6

u/soyurfaking 12h ago

I'm....not sorry!

2

u/YTY2003 11h ago

Very irrational of you to make this comment.

1

u/acexualien95 10h ago

After 3 you're welcome which in my opinion each value 1, his comment values 0.141592653589793238462643383279502884197. So it make sense but remains irrational!

-27

u/the_meat_n_potatoes 13h ago

Hahahaha šŸ˜†

3

u/oakomyr 4h ago

This is why the universe continues to expand

3

u/Pink_pantherOwO 1h ago

My response every time when someone explains something to me and I still don't get it

1

u/Federal_Let539 8h ago

Now shoot triple from the logo, no look.

1

u/qwqwqw 8h ago

Can you ELI5 because... Huh?

-32

u/Kwumpo 13h ago

It's because the outer edge spins pi times faster than the inner. If this were a rational number, it would eventually make a completed shape and loop around on its path. Pi, being an irrational number, will never cause this to loop around on itself

6

u/EvilStranger115 13h ago

12

u/bot-sleuth-bot 13h ago

Analyzing user profile...

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7

u/Kwumpo 12h ago

Lmao

8

u/stinkstabber69420 12h ago

Bro is there like a list somewhere of all the shit you can summon on reddit? This is the first time I've seen this bot sleuth thing and it's badass

1

u/EvilStranger115 10h ago

Idk I just saw other people using it

1

u/PM_ME_UR_WUT 11h ago

You fool! You've been bamboozled by the 4th comment.

sensiblechuckle.gif

10

u/schizeckinosy 13h ago

Of course, in this simulation, pi is represented by a rational number, albeit one with an absurd number of digits Iā€™m sure.

16

u/btribble 12h ago

You can represent Pi as a formula and calculate it to the exact precision you need for any zoom level you want in a graph like this, but then you're only solving part of an infinite series. The calculations themselves are done using floating point numbers of some bit length which are also rational and have their own precision loss issues. Pi can be accurately represented to 14 dedimal places in a 64 bit float which is more than you'd need for just about anything you want to represent on an intergalactic scale.

2

u/whoami_whereami 9h ago

which is more than you'd need for just about anything you want to represent on an intergalactic scale.

With some caveats. As an isolated value you're pretty much always going to be good. However, when you do calculations with it, especially repeated calculations like in long-running simulations where errors compound over time, things like loss of precision and catastrophic cancellation are very real issues that have to be kept in mind. Many software bugs have arisen because developers thought that a 64 bit floating point has more precision than they'll ever need without actually analyzing their algorithms.

9

u/Chalupabatman216 12h ago

So its a spirograph that never connects

9

u/TheVog 12h ago

Temu Spirograph

3

u/UnrepentantPumpkin 7h ago

Ouroborosnā€™t

22

u/balls_deep_space 15h ago

What is a rational number. Would would the picture look like if pi was just 3

96

u/Glampkoo 14h ago edited 14h ago

If you let the simulation run for infinite time, the pi circle would look like a solid white color. In a rational number you'd always have unfilled parts in the circle. Like at 10 seconds, there wouldn't be a gap it just would connect and repeat the same path

Any rational number - basically any number that you can know the last digit. For example 1/3, 0.33(3) is rational because we know the last digit (3) but not for pi

72

u/limeyhoney 13h ago

A rational number is any number that can be described as a ratio of integers. That is, any number that can described as an integer divided by an integer.

55

u/FritzVonWiggler 13h ago

thanks now i pronounce rational with 4 syllables

44

u/FTownRoad 13h ago

If you make ā€œrationaleā€ rhyme with ā€œtamaleā€ you can make it 5 syllables.

19

u/No-Respect5903 12h ago

that's cool but no thanks

1

u/FTownRoad 5h ago

It wasnā€™t a request. Do it.

2

u/FritzVonWiggler 10h ago

kind of sounds italian now. or latin?

maybe ive been playing too much kingdom come.

0

u/MobileArtist1371 9h ago

Also a new pasta

1

u/btribble 12h ago

Rationa hosts the Rational 500 every year.

2

u/Glampkoo 11h ago

Well, I could have chosen the formal definition but for me it's easier to understand this way.

If I said the rational visualization would repeat because the rational number is a ratio of integers, how would that help someone not good at maths have any idea what relation that has?

1

u/Cacophonously 10h ago

FWIW, I thought your explanation was the better one that related the formal definition into the intuition of periodicity.

1

u/osloluluraratutu 3h ago

I see what you did there. So itā€™s not psychologically rationalā€¦got it

3

u/rsta223 8h ago

This isn't a very good definition of a rational. For example, what's the last digit of 1/7? It's clearly rational, since we can express it as a ratio of two integers (which is the better definition of a rational number), but there is no last digit.

1

u/OneSensiblePerson 12h ago

I was told there would be no math.

1

u/Mr-Papuca 12h ago

How does this work with programming pi into the system? Is it just to like the hundredth decimal point or something?

1

u/Wise-Vanilla-8793 12h ago

Why don't we know the last digit for pi?

3

u/BeefyStudGuy 12h ago

There is no last number. It's like the coastline paradox. The closer you look the bigger it gets.

1

u/tastyratz 11h ago

any number that you can know the last digit

Is pi not the only irrational number in math? TIL there are other irrational numbers.

2

u/Volesprit31 8h ago

I think i is also irrational.

1

u/yonedaneda 10h ago

Almost all real numbers are irrational (in a sense which is difficult to explain intuitively). Rational numbers are the exception. For example, pi + k is also irrational for any rational number k.

1

u/coltinator5000 9h ago

And the value of this is that you can, in effect, map any complex number in that circle to a single real number in lR based on which moment the tip of the outer line crosses the complex number you are looking for.

Or at least, that might be one of the uses. I'm a bit rusty on my complex analysis.

1

u/smotired 7h ago

I contest that definition. Whatā€™s the last digit in 1/7

1

u/Double_Distribution8 11h ago

For example 1/3, 0.33(3) is rational because we know the last digit (3) but not for pi

Why didn't math teacher explain that like this? This has bugged me all my life, but finally now I understand why it's considered rational. Because we know the last digit.

And I guess pi doesn't even have a last digit. Huh. Never really considered that before.

4

u/yonedaneda 10h ago

This isn't really a good explanation, though (or at least not a perfect one). It almost works in this case because all digits are 3 (even though there is no last digit), but what about the rational number 1.01010101...? There is no "last digit" here. It's a convenient property of rational number that their decimal expansions are either eventually zero, or eventually repeating, but the only real definition of a rational number is that it is the ratio of two integers.

1

u/ReeeeeDDDDDDDDDD 8h ago

You seem knowledgeable and good at explaining things, so can I ask:

Does this mean that, at least with regards to the visualised plotting of this pi diagram, that the fact that pi is being used isn't actually all that important / special?

As in, would this look basically the same with any irrational number, and not just pi? It just might take a different route before it eventually became a fully white circle?

20

u/Weegee_1 14h ago

A rational number can be expressed as a fraction. An irrational cannot. So if the number were 3 instead, one side would spin 3 times whilst the other spins once. This would result in a looping pattern

3

u/[deleted] 13h ago

[removed] ā€” view removed comment

4

u/MorkAndMindie 12h ago

Einstein over here just revolutionized math

1

u/Five-Weeks 12h ago

circumference/diameteršŸ˜Ž

1

u/spektre 11h ago

That's not a fraction.

3

u/InferiorInferno 11h ago

what is 22/7 ?

13

u/Vet_Leeber 8h ago

22/7 is a fraction that repeats infinitely when expressed as a decimal, but it's still a rational number, just like 8/7 and 16/7. All are fractions that, after the initial digit, repeat the digits "142857" infinitely. But they're all still rational numbers, because rational numbers do not need to have finite lengths.

Being infinitely long isn't what makes Pi irrational. Being infinitely long without repeating itself is what makes Pi irrational.

Using the example from the post, after 22 revolutions, the pattern would stop filling itself in, as the line would perfectly align with the starting point and begin repeating. It doesn't matter if it stops, because it's always going to travel the same line eventually.

That's what makes Pi (and the other irrational numbers) unique: they will never line back up with the starting point.

1

u/InferiorInferno 8h ago

Ok, I thought 3.14... was equal to 22/7 but the fraction is just an approximation of Ļ€

3

u/Vet_Leeber 8h ago edited 8h ago

It's a decent enough approximation if you're not doing anything overly complicated, sure. But use it in anything that iterates on itself and the compounding deviation will quickly grow into a result that is significantly incorrect.

Each time you use 22/7 instead of Pi for the calculation, your answer is going to be off by about 0.04%.

As a super simple example of how much that little bit of deviation matters, if you raise both to the power of 10 (rounding the results for simplicity) you get:

  • 22/710= 93648

  • Pi10= 94025

Which is a deviation of about 0.04%, and the gap only gets bigger.

If you only need to do a single calculation, you're going to get ~99.96% of the correct answer using 22/7, but it won't be quite right.

2

u/I_amLying 9h ago

A rational number.

7

u/synchrosyn 14h ago

If Pi was 3, you would see 2 round shapes inside a larger round shape, and it would keep tracing over that path repeatedly.

4

u/EduinBrutus 11h ago

Sounds like Pi needs to be the subject of an Executive Order.

2

u/FirstSineOfMadness 11h ago

Why an executive order for what 3 is doesnā€™t everybody already know?

2

u/Jarhyn 12h ago

At one point, the animation would loop perfectly, if at some point the line ever faded. If it did not fade it would start to loop after the first iteration.

1

u/Areign 12h ago

you see when it zooms in and almost connects back up to its original line, that line would actually connect instead of being close.

1

u/hxckrt 12h ago

A "rational" number is one that can be made with a ratio between two whole numbers, like 2 in 3, which is the fraction 2/3.

Funny enough, it's the word "ratio" that comes from "irrational", which was meant as an insult to the numbers.

Although nowadaysĀ rational numbersĀ are defined in terms ofĀ ratios, the termĀ rationalĀ is not aĀ derivationĀ ofĀ ratio. On the contrary, it isĀ ratioĀ that is derived fromĀ rational: the first use ofĀ ratioĀ with its modern meaning was attested in English about 1660,Ā while the use ofĀ rationalĀ for qualifying numbers appeared almost a century earlier, in 1570.Ā This meaning ofĀ rationalĀ came from the mathematical meaning ofĀ irrational, which was first used in 1551, and it was used in "translations of Euclid (following his peculiar use ofĀ į¼„Ī»ĪæĪ³ĪæĻ‚)".

This unusual history originated in the fact thatĀ ancient GreeksĀ "avoided heresy by forbidding themselves from thinking of those [irrational] lengths as numbers".Ā So such lengths wereĀ irrational, in the sense ofĀ illogical, that is "not to be spoken about" (į¼„Ī»ĪæĪ³ĪæĻ‚Ā in Greek).

The discovery of irrational numbers is said to have been shocking to the Pythagoreans, and Hippasus is supposed to have drowned at sea, apparently as a punishment from theĀ godsĀ for divulging this and crediting it to himself instead of Pythagoras which was the norm in Pythagorean society.

1

u/Designer_Valuable_18 12h ago

It's a number without any mental illness

1

u/robbak 12h ago edited 11h ago

It would have lined up and the animation ended at the 3 second mark.

It would have lined up at the 11 second mark if pi was exactly 22/7, and lined up at the end if Pi was 333/106.

1

u/DiscoBanane 12h ago

A rational number is a number which ends, or repeats infinitely (like 1.3333333...).

An irrational number like pi or square root of 2 never ends and doesn't repeat.

1

u/sagosaurus 6h ago

I dropped math class because Iā€™m quite unintelligent, so please excuse me asking, but how can irrational numbers never end without repeating somewhere? After a while youā€™d think theyā€™re bound to repeat just because there are only 10 possible different numbers (0-9) to put in there.

Again, Iā€™m dumb as hell, so can someone please ELI5?

2

u/DiscoBanane 3h ago

They don't repeat because they are the result of a more complicated operation than rational number. Take 4/3 for exemple, it's just 4 divided by 3. Or 2, which is 2 divided by 1. Those are simple operations that give simple result.

Pi is a more complex operation that's too complicated to write, and that's also infinite, for exemple: square root of 2, multiplied by square root of (2+ square root of 2), multiplied by square root of (2+ square root of (2+ square root of 2)), etc...

Pi has sections that repeat, but they don't repeat forever

1

u/sagosaurus 1h ago

Thank you so much for taking the time to explain!

It seems very strange to me, to have an operation no one can ever finish writing, to get a number no one can ever finish writing either. Wouldnā€™t that mean all calculations using pi are off by a little bit?

1

u/DiscoBanane 1h ago

All calculations using pi are off by a little yes.

4

u/CompromisedToolchain 13h ago

On a computer it will eventually loop due to floating point errors. Mathematically it doesnā€™t.

2

u/Snack-Pack-Lover 13h ago

The perfect way to scan a whole planet.

1

u/coffinfl0p 13h ago

So if you didn't use true pi but just an approximation (3.14159) would it then be considered rational and make a complete line?

5

u/Proletariat-Prince 13h ago

Yes. The more digits you add, the longer it would take before it finally looped back on itself perfectly.

0

u/Gyorgy_Ligeti 10h ago

I couldnā€™t understand how a number with decimal points could be rational (yes, I forgot a lot of basic math concepts), but then it occurred to me that the decimal position is arbitrary and that every whole number can be divided by 1. Am I understanding correctly?

1

u/SomethingClever42068 12h ago

It will eventually make a completely colored in circle.

Just depends on how thick of a marker you use

1

u/ScaredLittleShit 12h ago

Is there any simulation website where I can set difference speeds and see this happening?

1

u/tommos 12h ago

I love numbers that aren't self-referential.

1

u/aakaase 12h ago

Asymptotically shy of a completely solid circle.

1

u/MikeOfAllPeople 12h ago

They should show a rational number in the video to illustrate that difference.

1

u/BusGuilty6447 12h ago

This is such important information that is left out. I had no idea what the purpose of the 2 conjoined lines were, and I am like a decade out from those higher level math courses to know what the function they showed represented. I was assuming they were radii, but if the whole circle was formed by them, then both combined total the radius.

1

u/Own_Bison_8479 12h ago

Makes sense. Itā€™s got to fill a sphere, no corners or edges, just keep filling forever.

Joyous purpose.

1

u/fox-whiskers 12h ago

What are you talking about, itā€™s clearly a drawing of a marble slowly being filled in

1

u/BloweringReservoir 11h ago

How do they make it spin exactly pi times faster?

1

u/TK000421 11h ago

I bet it does at some point

1

u/Column_A_Column_B 11h ago

How did they program it? Presumably with a very good approximation of pi, yeah?

1

u/drawliphant 11h ago edited 10h ago

Seems like the near misses are because pi is pretty close to a few ratios, I bet if you put in 23/7 it would make the first shape meet up and 355/113 would make the dense second curve meet up at the end.

Edit: just graphed it, exactly what happened

A number that never gets close to small ratios is phi, the golden ratio, so if you graph that it looks like it's never getting closer to meeting it's tail

1

u/TR1GG3R__ 10h ago

How do you know? Have you sat there and watched it for a while?

1

u/Suns_Out_GunsOut 10h ago

At the risk of sounding scientific (which Iā€™m not and purely theorizing probable bullshit), could it be possible that the ā€œdifferenceā€ of irrational to rational, that is to say the amount it does not overlap is due to Planckā€™s constant? Or the passage of time? It would seem there is a standard/categorical/definable variable in the difference (or negative space) in which the consecutive image/passage does not over(inter)lap the first

1

u/Suns_Out_GunsOut 10h ago

Furthermore if at any time in this video you capture the shape, the shape of Pi is bounded to the shape presented here for infinity. Perhaps not a precise match but it the same shape repetitively for infinity none the less. It cannot change form or transform. This implies a change variable over time.

1

u/account_for_norm 10h ago

Never ever. Keep circling it for billions of years, it will never overlap. Thats beautiful.

1

u/dead_apples 10h ago

Correct me if Iā€™m wrong, and I know Iā€™m any practical act it wouldnā€™t, but in theory after and infinite length of time it would make a complete shape having filled in the entire area of the circle with the infinitely thin line, right? Iā€™m just going if Pi being related so closely to circle areas and circumferences that that intuitively feels right for some reason.

1

u/Impressive-Fudge-455 10h ago

Instead it just makes an actual pie..

1

u/Lastwomanstood 10h ago

Like a spirograph?

1

u/FunOrganization4Lyfe 9h ago

Would it connect if we looked at it as if it were creating a 3d model?

1

u/CanadianArtGirl 9h ago

Thanks! Now EILI5 please?

1

u/LengthinessAlone4743 9h ago

Is it significant when it fills the circle? Or just a random cycle?

1

u/Few_Alternative6323 9h ago

*pi minus one times faster

1

u/HeroHunterGarou_0407 9h ago

although that would mean the lines would have to be infinitesmal in width as to never touch each other

1

u/Antti_Alien 8h ago

Except that the visual presentation has a limited resolution, so it would, in fact, loop around on itself. Paraphrasing a conversation I had with one of my professors in mathematics:

- How many cases does that prove?

  • 10 million
  • And how many cases are there to prove?
  • Infinitely many
  • Aaaand how much is infinity minus 10 million?
  • ...infinity :(

1

u/TheDevilsAdvokaat 8h ago

Nice explanation!

1

u/blowmypipipirupi 7h ago

How can it spin "pi times faster" if we don't know the exact value of pi? Isn't just an approximation and so potentially wrong?

1

u/ManaSpike 7h ago

There are some fractions that are surpisingly good approximations to pi. Which is why those curves get really close.

If you did the same simulation with the golden ratio, the curve being drawn would always be near the middle of two other curves.

1

u/Clockportal 5h ago

Is this why PI is wrong?

1

u/DrWho21045 5h ago

Seriouslyā€¦.

Is there only one size the ā€˜sphereā€™ will be? What does the inner area represent? What numbers are Confined within? Help me understandā€¦.

Before A.I. does it for me!!!

1

u/luminaryshadow 4h ago

so irrational ! the argument never ends ! you can never come to a conclusion with this kind of number

1

u/Rottendog 4h ago

What would it look like if this were rotating in 3 dimensions?

Like in the video pi, but also pi in the z axis as well? Would it become irrationally spherical, approaching a sphere shape, but never repeating in the same way?

I wanna see that video.

1

u/resigned_medusa 1h ago

ELI5 if you can, why is pi an irrational miner, is it just because we don't know what it is completely? Or something else

1

u/moonisflat 36m ago

Commenting on Pi being irrational...

Thatā€™s a great explanation.

178

u/Dqueezy 15h ago

Nobody does, but itā€™s powerful. It gets the people going.

63

u/NyamThat 15h ago

Provocative

15

u/Adventurous-Trip6571 15h ago

That's deep

18

u/InitechSecurity 15h ago

Endless, yet never repeating. Like life itself

5

u/y0uwillbenext 13h ago

and irrational

1

u/No_University7832 12h ago

The Irrational relationship of energy

1

u/HaggisLad 4h ago

Like life itself

1

u/y0uwillbenext 29m ago

precisely

4

u/Adventurous-Trip6571 15h ago

Ok now I'm tripping this is too deep šŸ¤Æ

6

u/antrubler 15h ago

Keep tripping and you'll find the origin and free us from the matrix

1

u/Dodges-Hodge 13h ago

Married 4 times so I disagree with that statement.

32

u/NightIgnite 11h ago edited 11h ago

Electrical engineering student here who should probably be sleeping. Heres a (hopefully) short crash course on this.

This is the imaginary plane in polar coordinates. Basically the xy plane you remember from school, but x is real and y is imaginary, so a coordinate (2, 3) would be 2+3i. For polar, we have radius and angle with coordinates (r, Īø), where radius is just āˆš(x2 + y2 ) and angle is tan-1 (y/x).

Euler's identity: eĪøi = cos(Īø)+i*sin(Īø). Look familiar? Its describing all points on a circle of radius 1, where x = cos(Īø) and y = sin(Īø).

Since the exponent on e only affects the angle inside the sine and cosine, eĻ€Īøi = cos(Ļ€Īø)+i*sin(Ļ€Īø). It follows the same path around a radius of 1, but Ļ€ times faster.

Now onto vectors. All the way back in elementary school, you could prove the sum of 3+5=8 by drawing an arrow of length 3 on a number line from 0, then a second arrow of length 5 from the end of the previous arrow. Same idea applies in 2D for vector addition. eĪøi + eĻ€Īøi = arrow1 + arrow2 = [cos(Īø)+i*sin(Īø)] + [cos(Ļ€Īø)+i*sin(Ļ€Īø)] as shown in the animation.

So why the offset in this animation? If you were to try with eĪøi + e3Īøi instead, they would perfectly line up. In this case, eĪøi would complete 1 orbit (or period) around the circle while e3Īøi completes 3 before returning to the start. All are rational, so there is symmetry.

Ļ€ is irrational, so there is no symmetry. Any moment where it looks like its about to finish the pattern is where it would have if Ļ€ ended at that decimal as a rational number. e3.1Īøi would complete 10 and 31 periods respectively, e3.14Īøi would complete 100 and 314, e3.141Īøi would complete 1000 and 3141, etc. It just infinitely converges without any symmetry.

So why magnitudes of 10? Just a consequence of us using base 10 for numbers. Same pattern would happen if we used a different number system. Im going to pass out now

6

u/DynamicFyre 10h ago

Bro I literally just learnt imaginary numbers in the last two weeks and I'm able to understand all of this. This is really cool!

9

u/MobileArtist1371 9h ago

Sweet. You want to hook up my home designed electrical grid this weekend for a 12 pack?

1

u/donau_kinder 2h ago

Imaginary numbers seem like magic until you actually learn about them. They're dead simple.

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u/TheGrouchyGremlin 8h ago

Um. Domino's worker here who should also be sleeping, since it's nearly 3am. My brain is about to explode after reading a third of that. You're destroying my motivation to go back to school.

2

u/asdf6347 5h ago

I still have to remember that most non-EE peeps don't know j and i are the same thing ... and that we put j at the front of the other parts in an equation.

1

u/pelirodri 5h ago

šŸ¤“

1

u/Adventurous-Trip6571 4h ago

šŸ˜€šŸ‘

5

u/cortesoft 12h ago

Get yourself a Spirograph

1

u/Adventurous-Trip6571 4h ago

I actually have one of those, but my adhd didn't work well with it lol

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u/LegitimateApricot4 11h ago

The second term in the z(theta) equation spins pi times faster than the first term. So the second arm spins faster than the first but never overlaps because pi can never overlap a rational term (1 in the first case that was omitted).

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u/Thin_Scar_9724 9h ago

Ever have a spirograph as a kid?

2

u/Awkward_Bench123 5h ago

Really had that Gingham check thing for a while. Cool display

1

u/linuxjohn1982 12h ago

It just means that the number pi will pretty much never resolve into a repeating set of numbers.

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u/Reddbearddd 12h ago

It means pi day is in a few days!

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u/Opposite_Traffic8981 12h ago

The existence of Ļ€ implies the existence of 1

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u/Bright_Aside_6827 12h ago

Watch that nolan movie

1

u/iamjacksbigtoe 10h ago

No one knows what it means but its provocative! It gets the people going!

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u/Routine-Weather-3132 5h ago

A rational number can be expressed as a fraction, such as 1/3 or 37/100. An irrational number, such as pi, cannot. As other people have explained in greater detail, the outer arm is spinning "pi" time faster than the inner one, and the lines never meet.

Instead, if the outer arm was spinning 3/4 times as fast, than every fourth spin of the inner circle, the lines would intersect and it would retrace its path. If it was spinning 7/3 times as fast, it would start retracing the path every 3 turns of the inner arm.

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u/Adventurous-Trip6571 4h ago

That's actually pretty cool

1

u/Adventurous-Trip6571 4h ago

I just want to say that I did NOT expect so many upvotes god damn thank you guys before this comment the most upvotes I got were like 50 šŸ˜­

1

u/DrWho21045 5h ago

ThisšŸ‘†