"It's just a Coincidence"

There are many surprising results in math, and some might say that they are just pure coincidences, but are they really?

[@digitalgenius111]

IMPORTANT At 1:02 I said that, in the first 1000 digits of pi, there is a 100% chance that we would see the same digit 3 in a row. That is false. Assuming the sequence is random, there is always a chance that we woudn't see the same digit 3 times in a row. The actual probability is not that easy to calculate. It's approximately 99.99%. Calculating the probability of getting 6 digits in a row also isn't straightforward. I said that that it's 0.1%. It's approximately equal to 0.93%. Thanks for all the comments pointing this out and sorry for the mistake, hope you enjoyed the rest of the video.

[@deezman4206]

also, at 0:31 you say that 123321 / 37 is 8679, when it is 3333. minor correction, and point still holds but just wanted to point it out

[@KyronAlison]

I HATE YOU FOR MAKING THAT MISTAKE DIGITAL GENIUS MORE LIKE DIGITAL BRAINDEAD ZOMBIE

[@Gafitas-Rdm]

​@@KyronAlison bro...

[@CadenzaPlayer]

@@KyronAlisonbro shut up

[@sayantanroy-o4s]

Suggest me a book that contains all these number facts

[@o_s-24]

The square being having Ramanujan's birth date is CRAZY!

[@tuures.5167]

Honestly, not that crazy. Ramanujan had an amazing intuition for numbers. He might have noticed his birthday had this property of summing to a prime when divided into two-digit numbers and decided to try if he could expand it into a bigger configuration.

[@WhoAmIdotIn]

​@tuures.5167 make a bigger square then. It ain't that crazy right?

[@ProfeSobico]

@@tuures.5167 actually, indeed, it's that crazy. Think about the probabilities that a math genius had born exaclty this square describes this birth day

[@Premium-ie5zd]

.

[@JohnWilliams-gy5yc]

God is a math nerd sounds more depressed than the devil is one.

[@ytkerfuffles6429]

Correction about pi: the chance of getting 6 of a SPECIFIC digit in a row in the first 1000 is 0.1%, but the chance of getting 6 of ANY digit in a row is 1% as it can be any of the digits 0 to 9. This is a super common mistake.

[@katakana1]

Hello

[@pixtane7427]

Still 1% is low

[@ytkerfuffles6429]

@@pixtane7427 yeah but this is such a common mistake that it even used to be on the wiki so its kinda infuriating

[@phiefer3]

correction: the chance of getting 6 of the same digit within the first 1000 digits of pi is 100%. The digits of pi are not random, it's a constant, that 999999 is always guaranteed to be there.

[@mrkitten999]

@@phiefer3People like you are the reason I have to solve all my math curiosities myself

[@jandor6595]

When Ramanujan was creating his square, math accepted his terms and conditions

[@TailicaiCorporation]

Romanujan is the main character with math living inside of his world

[@s.o.m.e.o.n.e.]

@@TailicaiCorporation why did the main character die by fricking tuberculosis :/‎

[@Amit_Pirate]

The author was mid ​@@s.o.m.e.o.n.e.

[@peterbach9276]

​@@s.o.m.e.o.n.e.💀💀💀

[@s.o.m.e.o.n.e.]

@@Amit_Pirate You just called God mid, bruh

[@emilebottoni3437]

why does this video gives a conspiracy theory vibe but about maths?

[@Fire_Axus]

your vibes are irrational

[@stardufs]

all of your reply on this vid are irrational ​@@Fire_Axus

[@bilkishchowdhury8318]

​@@Fire_Axusvibes>>>rationality

[@SBImNotWritingMyNameHere]

So is math artificial or natural?

[@corvididaecorax2991]

@@SBImNotWritingMyNameHere A bit of both. It started as being used to describe features of how things seem to work. If you have one apple, and another apple, then putting them together gives two apples. There are a lot of properties of math that are actually physical like that, which are then described using rules. But then those rules can also be used for other things, taking us into the realm of 'pure mathematics' which seems disconnected from the natural. But it is all still based in those rules that describe how natural things work. The thing is that occasionally the 'pure mathematics' is later discovered to actually apply to something real, after the math was developed. As an example imaginary numbers were found to be useful in mathematics hundreds of years before they showed up in electrical engineering and quantum mechanics. So it seems in some way that the natural world really does have math at its heart, and we are really just discovering it more than inventing it.

[@zorrath]

Please keep taking your medication.

[@shiminashafeeknasar4015]

Frr😂

[@Yash-Class9-JEE]

Take square-root of 1111....11(n times) in a high precision calculator. Increase n from 1 to infinity and look at the decimal expansion of the square-root.

[@BlueUltraUpgradedTSM]

@@Yash-Class9-JEEbro has 163626371837472947482757482757473737 to the power of uncountable infinity IQ

[@Miszek3756]

2:13 also after 18281828 there is 459045 which are the angles of half square triangle (45°, 45°, 90°)

[@FantyPegasus]

Also 1828 is the year of birth of Lev Tolstoy who is Russian writer

[@Robin-Dabank696]

Wow I've memorised e up to that part but I've never noticed that

[@WesStreet99]

Then there is the first 3 prime numbers 2, 3, 5 and then 360 (full revolution)

[@NopeNopeNope9124]

​@@FantyPegasus and of many more people probably

[@alexthedolphin0939]

i thought that six digit code was somethign else 💀💀💀

[@Yudentheepicboy]

WAKE UP MY MATH NERDS HES RISEN FROM THE DEAD AND BLESSED OUR INTELLECTUAL CURIOSITY YET AGAIN

[@the_Earth_3]

LET’S GOOOOOOOOOOOOOOOOOOO🎉🎉🎉🎉🎉🎉🎉🎉

[@xXImposterredbg]

Ok

[@Slerdus]

LETS GOOOOOOO🎉🎉🎉

[@bsHugoo]

🫡🫡

[@eaumitheartist1841]

WOOOOOOOOOOOOO

[@speedcheetah1630]

That magic square isn't magic, it's super-dimentional😮😮😮😮

[@midahe5548]

no it's just math. I proved it in three lines (because i was bored)

[@midahe5548]

nevermind I though you were talking about the 1st square where this scammer told us to take a numpad and remove the 0

[@ofridaniel2127]

The scammer ☠️☠️​@@midahe5548

[@Pizhdak]

This video's thumbnail and title are almost identical to the ones of the kuvina saydaki's vid. Is this just an another weird coincidence or it has some explanation?

[@sevenpenceLOLZ]

imagine just doing random stuff and then discovering these. (seriously, how did mathematicians figure this out? i’m curious.)

[@Vic-ty2be]

just playing around aimless. i figured on my own that the n-th derivative of x to the n is equal to n factorial

[@Faroshkas]

It probably is just because they were doing random stuff. Mathematicians do enjoy maths (surprising, I know!), and we do enjoy to just doodle with numbers and ideas. Some might have been discovered by computers programmed to find stuff like that, but there has been a mind behind it, that probably accidently came across something and wanted to check if it happened again any other time.

[@sevenpenceLOLZ]

@@Faroshkasas a math student (i like to study math a lot but i can’t really consider myself as a mathematician) i thought there was some more complex process behind it. i guess i overlooked it. 😅 thanks for the answer anyway!

[@sevenpenceLOLZ]

@@Vic-ty2beooh…imma try that.

[@Faroshkas]

@@sevenpenceLOLZ I guess there could be. But, in my experience, when it is something that has no real use, it's just people having fun lol. But maybe there was some deeper reasoning. Ramanujan's square, for example, definitely needed a lot of thought, but I doubt he was trying to solve a real world problem

[@Candy-0123]

3:55 this works for every number that is initially divisible by 9. im pretty sure everyone knows that you can figure out a number is divisble by 9 if its digits' sum is divisible by 9

[@henrysaid9470]

Yes, but it is actually always a number that is divisible by 9 (999=27, 981=18)

[@Kokice5]

​@@henrysaid9470Its really easy to find ones with 9 tho 1+4+4 = 9 144/2 = 72, 7+2 = 9 72/2 = 36, 3+6 = 9 36/2 = 18, 1+8 = 9 18/2 = 9

[@ІсаєнкоАртем]

I want to call 360 as "anti-prime". It's divisible by: 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 45, 60, 90, 120, 180. By adding them up you get 638, which is bigger, than 360(not including the 1 and 360 itself as divisors).

[@ІсаєнкоАртем]

Also did you knew, that 2^n is equal to all the previous 2^n + 2(not including 2^0)? For example, 2^10=2^9+2^8+2^7+2^6+2^5+2^4+2^3+2^2+2^1+2. You can check it

[@maddenbanh8033]

​​@@ІсаєнкоАртем0 has infinite factors adding up to infinity making it the better anti prime, infact 0 isn't a composite number because it has infinite factors so let's just call it that

[@kenuckz6505]

3:49 bro really had to pull of 69 in there

[@Nutball-Studios]

0:41 3.14159265358979323846264338327950288419716939937510582097494459230781640628620898628034825342117067 100 likes for a nother 100 digits

[@Nutball-Studios]

100 digits

[@davitdavid7165]

4:00 if a number is divisible by 9 the sum of its digits is also divisible by 9. When you divide by 2 over and over again you dont change the fact that the number ks dkvisible by 9. The fact that it is 9 instead of something like 18 is coinsidence, but there were few possibilities to begin with

[@kales901]

0:50 zero might appear unooften at the start, but maybe millions of magnitudes of digits into pi there is a ton of zeros, actualy, it has to happen at some point as pi is irrational and goes on forrever

[@Murzilla1]

8:14 got my soul escaped from my body

[@Joao-uj9km]

I'll actually lose sleep over Ramanujan's square

[@cannot-handle-handles]

Hope you don't! It can be done with almost every date. Here's one for today's date: 2 7 20 24 25 19 4 5 5 4 26 18 21 23 3 6

[@siamsami4115]

The 360 and 2^k ones aren't really coincidences. It has to do with modular arithmatic

[@orisphera]

4:15 The result is the original number mod 9 (assuming it's natural and a version of mod where 9 mod 9 is 9, but the usual numeral system is used). So, you can just 1*2 = 2 2*2 = 4 4*2 = 8 8*2 = 16 = 7 7*2 = 14 = 5 5*2 = 10 = 1 (all mod 9)

[@midahe5548]

congrat you found what was behind this "coincidence". Now you can do that for everything he said in his video (except for the approximation, these are just scams)

[@orisphera]

​@@midahe5548I remember making a separate comment about another one For the first one, I had some thoughts then, but I finally figured it out now. The second digit is the arithmetic mean of the other two. So, it's 111111(the second digit) ± (100001 - 1100)(the difference). Both are divisible by 37 (111111 = 91*1221 = 3003*37, 98901 = 81*1221 = 2673*37. In fact, all these numbers are divisible by 1221

[@orisphera]

I've re-watched and couldn't find anything I could have commented on. I guess I just mistook writing about the coincidence not in this video for that

[@FrostbearPlushies]

It’s amazing that EVERYTHING revolves around pi.

[@hawkbirdtree3660]

That’s a nice play on words😂

[@FrostbearPlushies]

@@hawkbirdtree3660 really? I didn’t notice.

[@chair7728]

@@FrostbearPlushies "revolves around pi"

[@FrostbearPlushies]

@@chair7728 Hm, I must not be an expert on math then. Because I’m not getting it.

[@chair7728]

@@FrostbearPlushies its nothing deep its just that pi is related to circles and revolutions

[@bacon_with_brussels_sprout]

Pi is quite literally the first real example of the library of babel. Every number that will ever be thought of, has already been made

[@youtubeepicuser4209]

No, that’s called an irrational number. Pi is one, sq rt 2, e, sq rt 3, sq rt 5, sq rt 11, etc.

[@Neigeden]

actually this is only true if pi is a normal number (roughly meaning all strings of digits are equally likely to be found in the decimal expansion). even though we know almost all numbers are normal, we still don't know if pi is or not.

[@teslacactus1135]

5:01 this makes sense since 10! is 8! * 90, from 8!, multiplying by 60 will convert to seconds, and multiplying by 1.5 will convert 4 weeks into 6. 60 * 1.5 = 90

[@aguyontheinternet8436]

1:28 I don't really like using probability for the decimals of known numbers. Like no, the probability of getting the same digit 6 times in a row in the first 1000 digits of pi is 100%, not 0.1%. No matter how many times you bring up the digits of pi in base 10, it will always have those 6 9's in there in the exact same spot. You can say this is assuming the digits are random, but that isn't really fair, is it? The digits of pi aren't random, they're pretty much set in stone with formulas and infinite series. this was all very cool tho

[@TriglycerideBeware]

I agree, the probabilities presented are only true for random sequences. It's a faulty assumption

[@staticchimera44]

@@TriglycerideBeware The idea is that it works off the assumption that the digits of pi really are random. If they aren't then it implies there has to be some reason as to why these digits are appearing in these kinds of interesting orders.

[@TriglycerideBeware]

@@staticchimera44 If you read my comment carefully, that assumption you said it relies on is _exactly_ what I was challenging...

[@staticchimera44]

@@TriglycerideBeware Yes but as I said, if it is not random then it implies there is probably a reason for the strange appearance of numbers that we haven't found yet

[@TriglycerideBeware]

@@staticchimera44 I'm afraid I don't understand the point you're making. Could you say it a different way? Pi obviously isn't random--it's the same every time. The probabilities he gave were assuming that the first 1000 digits were selected randomly from a uniform discrete distribution of [0,9], and I think his script was pretty explicit about making that assumption. All I was saying was it doesn't make sense to assume the digits were generated randomly, since they aren't. I feel like we're mostly on the same page, but it sounds like you're trying to make an additional point. I would like to understand it, if you're okay with explaining it a different way

[@GeoSphere-el8vk]

2:46 "almost " I swear why is math like this

[@houston4647]

Its 2:45

[@gswcooper7162]

The number 10^7.5 (or sqrt(10^15)) is almost exactly equal to the number of seconds in a leap-year; with the difference being just 6 minutes and 16 seconds (or an error of about 1 second per day).

[@midahe5548]

congrat. you made me laugh with your "almost exactly equal". NB: in mathematics, "almost exactly equal" is "not equal". So your sentence is correct that way: The number 10^7.5 (or sqrt(10^15)) is not equal to the number of seconds in a leap-year. Interesting right ?

[@Lege19]

0:57 this is just wrong. It’s like saying if you role a dice six times you are guaranteed to role at least one six

[@MissiFull]

statistically*

[@xian3themax311]

It’s around a 99.9% chance which is easily rounded to 100%

[@Lege19]

@@xian3themax311 imo 99.9% is effectively the same as 100% in statistics, but in most other parts of maths they are very different. I’m not sure what branch this is (number theory?), but it’s not statistics

[@pesaventofilippo]

@@Lege19 No, it's very different also in statistics. If an event has a probability of 99.99% it is very likely to happen but maybe it doesn't happen. WIth 100%, it is guaranteed that the event happens, which is very different

[@nou6206]

@@xian3themax311 The probability of rolling a six at least once if you roll a dice six times is around 66.5% Using probability, the calculation for this is 1-(5/6)^6, meaning the probability for everything except for not rolling a six for six rolls or something idk probability

[@HectorProRoblox]

Digital genius ur animation sound effect is satisfying it sounds like a chalk

[@Bruhzo]

He finally posted again

[@ry6554]

So is this just a base 10 thing or...?

[@chair7728]

yea a lot of them are just because we coincidentally use base 10, but there are also a lot of similar things in other bases

[@axbs4863]

the next digits of e are 45 90 and 45, the degrees in an isosceles right triangle, then 235, the first three primes, and 360, the amount of degrees in a circle

[@Grammulka]

5:10 look what I found for 4 digit numbers: 1420^3+5170^3+1000^3 = 142,051,701,000 2 digits have several solutions as well, like: 16^3+50^3+33^3 = 165033 22^3+18^3+59^3 = 221859 34^3+10^3+67^3 = 341067 44^3+46^3+64^3 = 444664 48^3+72^3+15^3 = 487215 98^3+28^3+27^3 = 982827 98^3+32^3+21^3 = 983221 After that I checked for two 3-digit numbers and 2nd powers, and found only this: 990^2+100^2 = 990100 But I guess these results are not that beautiful because of how we group digits in triples. I'll look for other powers then.

[@studyonly7888]

Bro … u ok?

[@Grammulka]

@@studyonly7888 yeah, I'm fine. At the moment I'm searching for 12-digit numbers. The closest I got was 531^4+174^4+170^4+819^4=531,174,170,818. One off =(

[@robertveith6383]

​@@studyonly7888-- Write an English sentence.

[@LeviathanTheGreat88]

1:00 this guy is really making a fool of himself saying that there is a 100% chance

[@midahe5548]

I mean, he is making a fool of himself with everything he said in that video

[@azysgaming8410]

@@midahe5548 lol yea he sounds like a conspiracy theorist when most results are probably coincidences.

[@Twenty4-n7n]

Each decimal of pi CANNOT be obtained by coïncidence

[@writerightmathnation9481]

1:35 You said that the probability that six digits in a row are equal in the first thousand digits of pi is .1%, but I beg to differ. As you have demonstrated in this first few minutes, the probability of that happening is 100%, because it actually happens. I think what you intend to say is that if we consider a number whose digits are generated randomly, then the probability of getting six equal values in a row is approximately 0.1%. While don’t think that the notion of random is coherent, I will concede that it may make sense in probability calculations that the event of having six equal digits in a row in the first 1000 digits of a number, under the equally likely assumption, maybe as you claimed .1%; this is certainly very different from the claim that a number whose expansion we know through the first 1000 digits has a .1% probability of a certain string of digits in that first 1000 digits.

[@writerightmathnation9481]

@@societyforart4629 That’s irrelevant to what was claimed.

[@PopUpScienceandArt]

This looks a lot like Kuvina’s mathematical coincidences video. I’m guessing you saw it.

[@ayushrudra8600]

4:37 the number that is outputted is just the remaidner when 2^n is divided by 9

[@derciferreira2523]

This magic square proves Ramanunja was the greatest mathmatician and genious of all times.

[@kales901]

That 100% from 1:05 is wrong. There is no way there is a 100 percent chance, as that is always. You could make a number that doesn't follow this simpily: 1234567890 repeated 100 times.

[@TriglycerideBeware]

With continuous probability distributions, the probability of any individual event happening is infinitely small, so we say 0%, but still events happen anyway. So sometimes our intuition about what it means when something has 0% or 100% probability needs to be loosened, to not merely mean impossible/certain. ...that being said, selecting random digits is a discrete process... so I have no idea where the 100% came from either. Unless he's trying to say that pi *isn't* a random sequence, and it's always the same? But then so many of his other points are completely invalidated. Either way, there are quality issues.

[@geekjokes8458]

​@TriglycerideBeware it's not just continuous distributions, infintine number of things can sometimes be like that - we expect pi and some other trancendental numbers to be "normal", which means we think we should be able to find any finite string of digits somewhere in them with 100% probability i think there's a mistake in the video because he says "within the first 1000 digits" which is just not true...

[@ClaudeSpeed32]

37 appeared quite a bit in this video, funnily enough the recommended video in the sidebar is veritasium’s why is 37 everywhere video

[@HugoNefario]

3:53 that not a coincidence, cause all numbers that can division by 9... Summ of figures of that numbers is always 9

[@frayo050]

This video almost get me an heart collapse

[@Serega_Breghko]

For those, who want some statistic, probability chances, fun facts and explanations: 0:52 A little error: Statistically, theres should be 10 triple numbers on average in 1000 random digits, and the mistake was, that you counted up only 1 possible outcome, when theres 10: (000),(111),(222),(333)...(999). And the fact, that there are less than 10, is just a statistic. Also, there's NEVER a 100% on anything random with digits. Even infinite amount of random digits could consist of every number except of 1 specific, and the chances are 1×10 / Infinity. Which is not a 0, but still, very-very unlikely to ever happen. 1:28 By the statistic, we have 10 different outcomes, so we multiply the probability chance by 10 assuming, that probability of the next number to be the same - is 1/10. We get probability of "1/10,000" So, on average we get: 1000 digits of pi / 10,000 and we get a 1/10 chance of getting 6 equal digits in a row of 1000 random numbers. Not a 0.1% as mentioned in the video ;) 3:06 If you assume thay everything is random (e^pi - pi ~ 20; 2143/22 ~ pi⁴; pi⁴ + pi⁵ = e⁶; pi = √2 + √3; sin(60°) ~ e/pi; etc.) than it may look that chances of those coincidences are very slim, but, remember: 1) Math is a science, and constant at every point of space and time; 2) The ammount of different combinations with pi, e, sin, are almost endless; 3) Aldo, never forget, that those specific numbers are known, to be infinitely precise constants of universe, and have more in general, than other numbers based on what they represent. 4:00 There wont be any numbers, but instead, a fun fact: Amount of degreece can be ANY number that we want, but people have choosen 360° as a standart of circle, cuz this number can be divided by a LOT of numbers: 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, (almost 16 "22.5"), 18, 20, 24, (almost 25 "14.4"), (almost 27 "13⅓"), 4:48 10! = 6 weeks; 4 weeks = 8! Heres an easier representation: 6 week (in seconds) = 6w × 7d × 24h × 60m × 60s 1h = 3600s 10! = 1 × (2×3) × (7) × (6×4) × (5×8×9×10) (5×8×9×10) = 40×9×10 = 360(circle😊) × 10 = 3600 3600 × (1×2×3×4) = 3600×24 = 79200 79200 × (6×7) 3628800 4 weeks (in minutes) = 4w × 7d × 24h × 60m 1d = 24h × 60m = 1440m 8! = 1 × 4 × 7 × (2×3×5×6×8) = 28 × (48 × 30) = 28 × 1440 = 40320 minutes

[@taskfailedsuccesfully738]

Apparently there's a whole tool for finding approximations like the one in the video (RIES)

[@midahe5548]

you are brave. My time in too precious for theses scammers

[@Serega_Breghko]

@@midahe5548 Bro, i just have no life. When i woke up i immediately checked telegram, and saw 1 guy, that typed me, and as a result i bursted out laughing about series we watch, and made a fkn 7 THOUSAND symbols long story, which had almost the same plot as a series, and worked out with HIS life in the Internet.. on a mobile (those 2 comments are written fully on mobile too)

[@tsaqifrizky5276]

The 360° coincidence extends way beyond 360 and under 11.25, it eventually increases by integer multiples of 9, 2880 (360*8) sums to 18, and 5.625 (360/64) sums to 18 as well. At 360/1024 or 0.3515625 it sums to 27, divide by 2 again and it sums to 36.

[@Morbius_Official]

Hitler when his plan fails: 1:24

[@danamaderas3382]

🇩🇪🥨🍺

[@bagr08]

bro this made me laugh way too hard

[@tomduke558]

I really like the Ramanujan square - i mean, not just because of the identical summing, and the hidden link to his BD, one easy approach for me is, for numbers 1-25 these are some of my fav piano concerto pieces of Mozart (to name a few, I listened frequently to No.9, 23, 24, and 25), and the years 86 - 89, is the periods 1786-1789 where he wrote most of his famous master pieces. for the sum 139, well I loved sym No.39 (in addition to No.41)

[@Robloxgod-np3tp]

3 and 7 are the main biblical numbers too…

[@levismith4174]

Yeah it is

[@mysticmoth1111]

Seeing this comment 7 days after it was posted

[@felixmaths]

These numbers are of the form abccba = 100001a + 10010b + 1100c. In 123321, a=1, b=2 and c=3.

[@felixmaths]

100001/37 gives remainder 27 10010/37 gives remainder 20 1100/37 gives remainder 27 27 + 20 + 27 = 74, and 74 = 37 x 2

[@MrBruteSmasher]

I would argue that’s not coincidental. Mathematics was probed and researched for thousands of years before the Bible was written. The significance of certain numbers is far older than the Bible.

[@kales901]

4:00 that is no coinceidence, as all those numbers are multiples of 9, so their sum is 9, 360=9*40, so we can divide a few times before we get to decimals

[@Sciencedoneright]

These results are not surprising at all. If you all knew basic mathematics, you would obviously substitute π = e = 3 = 2 😂

[@jaketinker9033]

Hating for no reason😭😭😭

[@iliagozalishvili2803]

respect to the guy who found these "coincidences"

[@JKBDTS]

4:00 Legit not surprising. If a number is divisible by 9, the sum of numbers is also divisible by 9 and it's not a coincidence.

[@JKBDTS]

4:20 Not surprising as well

[@douglaspantz]

The thing about numbers summing to 9 is less improbable considering that when you sum together the digits of a multiple of 9, you get a multiple of 9, and since we’re dividing by 2 all subsequent numbers will be divisible by nine.

[@blast_processing6577]

I often hear people say randomness is "fair", but it's really not. Randomness isn't synonymous with being evenly distributed.

[@xanderlastname3281]

Im confused am i missing something? The title is "its just a coincidence" in quotes, which seems to be saying "it isnt a coincidence" and then preceeded to list a bunch of things that seem coincidental without explaining why they arent Why is 6 9s not coincidental? Or is it just not coincidental because "pi is infinitely long therefore every combination of numbers will appear" In which case thats super dumb Or are the quotes around "its just a coincidence" useless and this video is actually listing coincidences In which case this is also super dumb The description seems to support my original view so.......... why is he not explaining why they arent coincidences

[@WildMatsu]

Spend eight and a half minutes telling me you don't understand probability without telling me you don't understand probability

[@LighterRacer1634]

speaking of the first 37 fact, all the quotients you get are divisible by 11 (as well as the dividends!) which makes all the dividends divisible by 407!

[@HectorProRoblox]

Every like i will train division

[@HectorProRoblox]

@@rodolfotayem519 u didnt even like

[@Im_Rainrot]

Are you training yet?

[@HectorProRoblox]

I'm gonna upload

[@sunilpeter9123]

The two power thing is probably because of the modulo 9 rule. Any number has the same modulo 9 (remainder when divided by 9) as the sum of its digits. Since 2^6 = 64 which is one more than a multiple of 9, the modulo 9 keeps on repeating. It will never be divisible by 9, so the sum will never be 0 or 9, leaving 8 distinct options for each remainder, and creating a cycle. Cool video!

[@Akhulud]

4:28 its juste powers of 2 mod 9, its not a coincidance

[@FranklinLee-t3k]

The number of seconds in a minute minus 1 is a prime number. The same is true for the number of minutes in an hour - 1, hours in a day - 1, seconds in a day - 1, and the number of minutes in a day - 1.

[@VladFound]

The most useful video I ever seen about math. Especially (1³+2³+3³+4³+...+n³) = (1+2+3+4+...+n)²

[@funnyfish1982]

3:54 It's not weird, because if the sum of digits in a number is divisible by 9, then the number itself is divisible by 9. Same works for 3.

[@AbsoluteCatLover-ux6zl]

It’s not a coincidence, it’s just fascinating. Math is a series of random numbers created by us humans that start out so simply but increase in complication the further you look into it. The randomness and repeated unexpectedness is truly amazing honestly and it’s crazy how many other coincidences there are out there that we still don’t know of. How did we ever even start out with numbers?

[@ChaseWalkerofficial]

For every like, I'll study one day

[@costinraspberrypi]

Like please

[@RoronoaDPuneeth]

What about dislike?

[@keyan1219]

shut up

[@FlyFlux]

Like beggars explained in 10 seconds:

[@funnyfish1982]

Hey, one more thing. Try experimenting with 1,1111... square. Look what happens.

[@e-safetyplus542]

when infinity gets involved, possibilities become certainties

[@whatdoinamethischannel9749]

within 1000 digits you have a 100% chance of getting six "9's" in a row because pi is an irrational number not a randomly generated number the odds of an irrational number containing six of the same digits in a row is infact 0.1% of irrational numbers

[@henriquefernandesbreves6003]

I would like to commend you, my good sir, for sacrificing the time and effort to make all these curious calculations. Great work!

[@buyucukral507]

I dont know why, but something about this video litterally gives me the creeps... it's like you are wandering around an abondened house, shrieking in fear while traversing, and suddenly start to hear noises... but those noises are from a video which is explaining the darkest secrets of dark web or something like that... sheesh I have watched too many horror stuff

[@iwersonsch5131]

So much p-hacking going on there...

[@n0tlenny]

Not only is each 6-digit number formed from rows, columns, and diagonals on a calculator keyboard divisible by 37, but they're also all divisible by 1. Amazing!

[@Ykulvaarlck]

4:17 is not a coincidence at all, it's a simple consequence of modular arithmetic and works with any modulo (not just mod 9 == sum of digits of a number in base 10) and any base number other than 2 similarly, at 3:53, we start with a number whose digital sum (= the number mod 9) is 9 (which is the same as 0 modulo 9), so dividing or multiplying that number by anything would keep the digital sum 9. if you get to fractional numbers, taking their digital sum is equivalent to multiplying them by a power of 10 then taking it mod 9, which would also keep the digital sum 9

[@bradyven]

You know you can find your Social Security number and the digit of pi

[@MarshiDev]

This is why you have to watch out when extrapolating patterns

[@AstroPatel]

We already have knowledge of the connections between things like Euler’s number and Pi, prime numbers and graphs, but seeing all of these ‘coincidences’ laid out almost feels like we’re teasing a ton of hidden, deeper connections and concepts that have yet to be discovered. Sure, many of these are just coincidences. But surely some of them are connected to larger concepts. I wonder what future mathematical research has in store for mathematics, but also, the practical applications of mathematics in domains like physics and CS.

[@DR-54]

the 3x3 square is not a coincidence because 111 is divisible by 37 and 111 is the common divisor of each number. for base 5 in a 2x2 square, its common divisor is 11. for base 17 in the 4x4 square, 1111. Note that these are all perfect squares and the base system is the product of the length by the width added by 1. 11 base 5, 111 base 10, 1111 base 17. This pattern always holds true and it must hold true (arrange every number formed by least to greatest and take the derivative to make this fact more obvious). 6, 111, 5220 in base 10

[@binh5806]

0:28 I think 37 REALLY is the most random yet popular number.

[@emptyptr9401]

Apart from the already acknowledged "100% mistake", the digits of pi having some parts in it that are theoretically unlikely is not actually unlikely in itself. You have to keep in mind that the question is not "How likely is it that there are 6 9s in a row", the question is "How likely is something to happen that could be considered unlikely in retrospect" or in simpler terms, the question isn't "How likley is X thing to happen", the question is "How likely is something unlikely to happen" and SOME unlikely thing happening is generally actually very likely. That is also the reason why so many theoretically unlikely coincidences happen in day to day life. After all, we only notice the few coincidences that DO happen, bot the billion that COULD but DON'T. Statistical analysis of the likelihood of an event can only be measured if you FIRST define what specifically you look for, and AFTERWARDS actually look for that specific thing, not the other way around. And I looked it up. The digits of pi have been statistically analysed and the actually do appear to be completely normally distributed.

[@puzzleticky8427]

POV: The Judge of Math accidentally put some things in order

[@anonymanonymus4706]

Srinivasa Ramanujan took "magic square" personally.

[@8fpsstopmotionstudios726]

Btw 3 raised to the power of n, such that n > 1 results in: 3 ^ 2 = 9 3 ^ 3 = 27 --> 2 + 7 = 9 3 ^ 3 ^ 3 = 81 --> 8 + 1 = 9 ... 3 ^ 3... no matter what, the sum of the digits, by repeating until we come to a single digit(18 would be 1 + 8), they will all be 9. for 4 raised to the power of n, the repeating sequence goes like 4, 7, 10, 4, 7, 10. for 5, it is undetermined. For 6, the same pattern appears just like 3. For 7, the sequence is 7,3,1,7,4,1 for 8, it is 8, 1, 8, 1. For 9, it is always 9. For 10, it is always 1. But for 11, where 11 is raised to the power of n(and add all the digits): n = 1 --> 2 n = 2 --> 4 n = 3 --> 8 n = 4 --> 16 n = 5 --> unfortunately, not 32. Cool, right!

[@ujkloin]

3:56 This one i know for sure is not a coincidence. You can take the sum of every multipile of 9, and it will always be 9. If it isnt, keep summing until you have one digit, and that digit will always be nine. The same thing works here, all the way from 1440 its 9, and 5.625 is 18, which can be summed to 9. This will always be the case. Also im pretty sure many more of these arent coincidences, so im not trying to sound smart here, its just some information. Also i figured this out while eating streetfood.

[@restcure]

e, trig functions, and π relate so closely (thanks, Mr. Euler) that I'm pretty sure there are equations to make those approximations as close as you want.

[@SusDoctor]

Me watching this at 3 am: You like numbers, huh? silly math man.

[@F1R3S74R73R]

3:58 isn't this true for all numbers divisible by 9?(or 3). In base 10 divisibility by 9 (or 3) is testable if the sum of digits are divisible by 9 (or 3), so if a number is divisible by 9, it has prime factors of 3*3, and if you divide by any number other than those that have a factor of 3^n, and the result is a whole number, the result will still have the prime factors of 3*3

[@mymo_in_Bb]

It's notable how many of these are just the results of us evolving ten fingers

[@funwithjlxrblx]

Sheldon cooper: the best number is 73

[@realleonardgibson]

1:29 one time I wrote pi up until this point for fun

[@kmjohnny]

That's a lot of stuff, but I don't really see what kind of pattern are we getting out of these. Although you did get my attention with the magic squares.

[@kcusuck5781]

Its more interesting to me that human psychology makes us care and be interesested in these random coincidences

[@kcusuck5781]

Even the example in thumbnail, 12th prime number is 37 and 21th prime number is 73. And mathematically its like "ok and?" but we see this and are like "wow cool"

[@minodore5176]

...yknow its kinda funny how one day a random monkey decided to count some funny rocks and berries, and then accidentally unlocked the secrets of the universe in doing so :)

[@BryndanMeyerholtTheRealDeal]

A lot of these coincidences are pretty interesting…

[@midahe5548]

beside the "almost equal" that are translated to "not equal" in real mathematics. I can prove half of his "coincidence" in five lines or less. The others ones are too boring to bother proving them. (BTW i'm not a good mathematician)

[@Echoes_act_3378]

@@midahe5548 prove them

[@rkidy]

The strong law of small numbers: any given small number appears in far more contexts that seem unreasonable.

[@yohann_kishibe]

Dude woke up and said let's make them smarter...

[@qweqqqw6972]

0:30 Yeah, it is not really a surprise In fact, every arithmetic progression has this ability. Not only 37, but 111 too. It's because of what numbers are formed when you multiply something by 111. 37 has this ability just because it's a devisor of 111

[@drachefly]

@4:05 that one's not a coincidence at all, and anyone who was taught factoring tricks in grade school should see why - any multiple of 9 will have the digits sum to a multiple of 9. That's progress, but we're not done. Given that the other factors are a few 2s and a 5, it's a multiple of 10. Which means that even though we started with 3 digits, we only up with 2 nonzero digits to add up through the whole sequence. And the only 2 digit multiple of 9 that doesn't add up to 9 itself rather than some other multiple is 99. That isn't one of the numbers in question. If you were to double instead of halving, it would still fit in 3 digits as 720 and add up to 9. And if you double it again, you get 1440, which again adds up to 9… but after that is 2880, whose digits add up to 18. So, the pattern broke almost as soon as that simple argument's assumptions were violated. @4:30 again, this is an interesting but not at all coincidental fact about modular arithmetic. @7:11 That's really nifty, but it doesn't seem like a coincidence. @ 8:10 is there a method for constructing such squares for a lot of given top rows? It seems like there might be.

[@futiled9304]

After a 3 month hiatus my man's finally back

[@BryanLu0]

4:39 This will happen for raising any number. it's just mod 9. It's impossible to not have a repeat since there are only 9 possible vapues

[@ichigonixsun]

0:00 Yeah, they're all divisible by 37 because they are all divisible by 111, by construction, and 111=3×37. Likewise, a 4×4 base 17 square would have have all numbers divisible by 1111 in base 17, which is 5220 decimal; then you could say that they're all magically divisible by 29, because 5220=2²×3²×5×29. 3:56 As others have mentioned, that happens because 360 is divisible by 9, and dividing it by 2 doesn't remove this factor. 4:13 "Digital root of x", a.k.a. mod(x,9). If you multiply any of the remainders by 2 modulo 9, you get the next remainder. Since there are finitely many different remainders, it is expected that you'll eventually reach a cycle. 6:55 Proof by induction. Done. 7:18 See wikipedia / wiki / Magic_square#Extra_constraints (KZbin doesn't like links) and make your own Ramanujan magic square with your own birthday. (the rest is left as an exercise to the reader)

[@FarahMoti]

pie in cooking: 😊 πe in math: 😨