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.
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.
@@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
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.
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.
@@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.
9 | 99 9 + 9 = 18 ≠ 9 The real property is that all multiples of 9 have digits which add up to another multiple of 9, but not necessarily 9 itself. a LOT of these are "literally not a coincidence", yes, 360 included (in fact, the whole point of still using 1/360th of a turn as a degree is bc 360 is a highly composite number, so it divides neatly by a bunch of factors. No surprises there). Still, sum of digits of ANY multiple of 9 isn't always 9 so this property isn't especially more or less coincidental than other entries in the video imo
BEAUTIFUL I love statistics and how in math there isn't really a "coincidence" the unexpected is expected, every number will theoretically have infinite "special" values and coincidences which will fascinate us, it is expected.
For some of them it's true, but all of the patterns of numbers repeating in irrational numbers are coincidences, because they exist only in a base 10 counting system, which is human made. Maths works regardless of how many digits we use to form our numbers, we could write pi only with 0s and 1s if we wanted to, and for any number of digits we use for a counting system, there will be different patterns, so yes. Those are actually all coincidences.
@@theterron7857 While it's not entirely wrong to call them coincidences due to how obvious the patterns are in base 10, looking at the representations in other bases for long enough is bound to lead to the discovery of interesting patterns, simply due to the sheer number of possible patterns one could find. Since the fact that patterns can be found is essentially guaranteed, what the patterns are is irrelevant and calling them coincidences feels a bit disingenuous.
I like how most of these are actually coincidences, it's just so many chances for something "exceptional" to happen it's almost inevitable something will.
It is. That was my first thought too. I think he means that, for every 100 digits or whatever, each number will appear ten times. It’s a dumb, non-real assumption, but a lot of these things are ridiculous.
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.
@@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 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
i feel like you dont understand probabilty, you wouldnt have a 100% probability of getting three digits in a row even if you were considering the first quadrillion digits.
What he means is that it is not rare that there is three digits, because the probabilities of it happening were already met, is like being suprised of winning a 1% prize at your 100 attempt, it still is just 1%, but it had to appear at some point, because you already met the 100% probability, so if it didn't pop off, then it would start being bad luck
@@matitello4167 nah. I don't think there is such a thing as meeting percent change at some point, from which point things become more likely or surprising. A 1% event need not happen within the first 100 trials. It need not come every hundred trials. It does not even have to come within the first 1000 trials, or every 1000 trials. The idea that it must, is the gamblers fallacy: the idea that certain outcomes become 'statistically due' to happen if they haven't come in a while, as if the amount of trials, and their outcomes, have some kind of influence on the next one in order to force statistics to balance out. Trials are only independent if such influence does not exist. So while you expect a 1% event every 100 times, there might not be one for 100000 trials and then, suddenly, there could be 1010 in close succession, and the stats would still work.
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
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).
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
@@user-hs7hw6hq7w0 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
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?
I made a video on this in January. My video actually explains what is and isn't a coincidence (a lot of these are not). Also, intentional or not, you totally ripped off my thumbnail.
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
37*3 = 111. that's why all "repeating digit" numbers are in some way related to 37. for exemple 111, 222, 333, 444, 555,..., 121212, 131313, 141414, ... 134513451345, ... are divisible by 37. I made the proof of why anumber in a form abccba is divisible by 37, with c = b + i and b = a + i with i being the offset (for exemple 123321 have an offset of 1, whereas 135531 have an offset of 2). these numbers divided by 37 are equal to a*3003 + i*330 with a being the lowest digit
These numbers are of the form abccba = 100001a + 10010b + 1100c. In 123321, a=1, b=2 and c=3. 100001/37 gives remainder 27 10010/37 gives remainder 20 1100/37 gives remainder 27 abccba/37 gives remainder 27a + 20b + 27c = 27(a+c) + 20b When b is the median of a and c, this is = 27(a+c) + 20(a+c)/2 = 27(a+c) + 10(a+c) = 37(a+c) divisible by 37 But b on the keyboard is always in the middle of a and c, and is also always their median, so it always holds.
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 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 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
@@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
@@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
@@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
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
For those wondering, how can you find or prove the Percent Error, you can use Taylor/MacClarean Series. So you can find up to what point you need digits to match up or not. My explanation needs more conciseness but that’s enough for now.
8:25 if anyone wonders why basically if you extend e^x into the complex plane you get a rotation around (0|0) where x represents the angle The circumference of a unit circle is 2pi so a rotation by pi is equal to -1. Add one and you get zero
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).
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 ?
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.
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)
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)
@@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
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.
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)
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.
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.
@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...
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
@@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)
4:00 Given base N, any number that has a digital sum of N-1 is divisible by N-1. This also applies to integer roots of N-1. So no matter how many times you divide 360 by a number, so long as the divisor doesn't have 3 as a root, the resulting number will have a digital root of 9.
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 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 =(
I'm a person who generally loves to collect random fun facts and then share them with my friends, I'm also a math nerd. To say I'm this video's targed audience would be an understatement
The *dalton* (1⁄12 of the mass of a *¹²C* atom) is still "around" (that is determined experimentally and is known only with finite accuracy), but the Avogadro number from now on is fixed and is equal to an integer with 9 higher significant digits, the rest of them (lower 15 digits) being 0.
@@pumpkin_pants3828Agree, that way it makes perfect sense. Though drawing the audience's attention to the fact that now it is an *exact* number would have served a much better purpose.
He said it was "around 6.02·10²³" because he omitted the last 6 decimal places. What makes this property of Avogadro's number such a big coincidence is how arbitrary its definition originally was. Avogadro's number was originally defined as the number of hydrogen atoms in one gram of hydrogen. A gram was originally defined as the mass of one cubic centimeter of water. And a centimeter was originally defined (during the French Revolution) as 10⁻⁹ times the distance from the North Pole to the Equator along the meridian passing through Paris.
4:37-4:48 1,2,4,8,7,5 are exactly the digits that appear in the decimals when any number is divided by 7 Only that the numbers have a definite arrangement. Example 1/7= .142857
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.
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
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!
The digits of all integer multiples of 9 themselves sum to 9. 45 is a multiple of 9, so it and all of its multiples all do this. It's interesting that those two decimal multiples also do that. At a guess, I think that decimal multiples of 9 that were the product of 9 and a non-repeating decimal might also have this property.
I was watching the video as this thought randomly crossed my mind. It's crazy to think that trying to find all digits of π is literally like trying to explore the entirety of space.
3:55 Not a coincidence tbh. When a number is divisible by 9, its sum of digits will also be able to be divided by 9. Since 360 is divisible by 9, dividing it by 2 doesn't takes out its 9 factor
At 5:36 when you talked about the cubes I wondered if the same thing worked for the squares. If found 12 ^ 2 + 33 ^ 2 = 1233 and 88 ^ 2 + 33 ^ 2 = 8833. I also searched the 4th power and I found 1485 ^ 4 + 5308 ^ 4 + 5017 ^ 4 + 1603 ^ 4 = 1485 5308 5017 1603. That took quite a while and I have not searched all yet. Anyways I was wondering where or how you found the initial 4 examples?
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.
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
I HATE YOU FOR MAKING THAT MISTAKE DIGITAL GENIUS MORE LIKE DIGITAL BRAINDEAD ZOMBIE
@@KyronAlison bro...
@@KyronAlisonbro shut up
Suggest me a book that contains all these number facts
For every like I'll study for 1 hour
16 hours now
more than a day if study now
Good luck
2.5 days now
Have fun lil bro
When Ramanujan was creating his square, math accepted his terms and conditions
Romanujan is the main character with math living inside of his world
@@TailicaiCorporation why did the main character die by fricking tuberculosis :/
The author was mid @@s.o.m.e.o.n.e.
@@s.o.m.e.o.n.e.💀💀💀
@@Amit_Pirate You just called God mid, bruh
The square being having Ramanujan's birth date is CRAZY!
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.
@tuures.5167 make a bigger square then. It ain't that crazy right?
@@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
.
God is a math nerd sounds more depressed than the devil is one.
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.
Hello
Still 1% is low
@@pixtane7427 yeah but this is such a common mistake that it even used to be on the wiki so its kinda infuriating
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.
@@phiefer3People like you are the reason I have to solve all my math curiosities myself
I think I'll now call my calculator the 37-pad
😂😂😂
And if you ask random people to tell you random digit 1-100 they'll answers are 37.the most and second more 73.
@@janhorvath1417 besides 69 and 42 of course lol
@@janhorvath1417veritasium has a good video on this
@@thedude142of course, the stoners
why does this video gives a conspiracy theory vibe but about maths?
your vibes are irrational
all of your reply on this vid are irrational @@Fire_Axus
@@Fire_Axusvibes>>>rationality
So is math artificial or natural?
@@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.
WAKE UP MY MATH NERDS HES RISEN FROM THE DEAD AND BLESSED OUR INTELLECTUAL CURIOSITY YET AGAIN
LET’S GOOOOOOOOOOOOOOOOOOO🎉🎉🎉🎉🎉🎉🎉🎉
Ok
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4:05 that's how multiples of 9 work. That is literally not a coincidence.
9 | 99
9 + 9 = 18 ≠ 9
The real property is that all multiples of 9 have digits which add up to another multiple of 9, but not necessarily 9 itself.
a LOT of these are "literally not a coincidence", yes, 360 included (in fact, the whole point of still using 1/360th of a turn as a degree is bc 360 is a highly composite number, so it divides neatly by a bunch of factors. No surprises there). Still, sum of digits of ANY multiple of 9 isn't always 9 so this property isn't especially more or less coincidental than other entries in the video imo
Yeah, the number was too small for the sum of digits to get up to a higher multiple of 9.
@@cactus6157 But 9^(-1) is not a multiple of 9, just a power.
It would be 18, or 27, or 36 or any 9k for positive k integers. Its impressive that stays for that much 2^k dividers (360/2⁰ to 360/2⁵)
@@mustafaseyitt I thought he was talking about something else that is my fault thank you for your input.
2:13 also after 18281828 there is 459045 which are the angles of half square triangle (45°, 45°, 90°)
Also 1828 is the year of birth of Lev Tolstoy who is Russian writer
Wow I've memorised e up to that part but I've never noticed that
Then there is the first 3 prime numbers 2, 3, 5 and then 360 (full revolution)
@@FantyPegasus and of many more people probably
i thought that six digit code was somethign else 💀💀💀
BEAUTIFUL
I love statistics and how in math there isn't really a "coincidence" the unexpected is expected, every number will theoretically have infinite "special" values and coincidences which will fascinate us, it is expected.
For some of them it's true, but all of the patterns of numbers repeating in irrational numbers are coincidences, because they exist only in a base 10 counting system, which is human made. Maths works regardless of how many digits we use to form our numbers, we could write pi only with 0s and 1s if we wanted to, and for any number of digits we use for a counting system, there will be different patterns, so yes. Those are actually all coincidences.
all statistics he showed are wrong or misleading
@@theterron7857 While it's not entirely wrong to call them coincidences due to how obvious the patterns are in base 10, looking at the representations in other bases for long enough is bound to lead to the discovery of interesting patterns, simply due to the sheer number of possible patterns one could find. Since the fact that patterns can be found is essentially guaranteed, what the patterns are is irrelevant and calling them coincidences feels a bit disingenuous.
your feelings are irrational
your feelings are irrational
I like how most of these are actually coincidences, it's just so many chances for something "exceptional" to happen it's almost inevitable something will.
90% of them feel like coincidences, especially whenever anything is approximated ngl.
Assuming all digits appear randomly, the chance of having 141592 behind the comma of pi is 1 over a million! What a coincidence!
0:58 um, that's not at how probability works, what is this guy on?
Idk man but im sure its good stuff
He just made a small mistake. See in the pinned comment , he accepted it.
It is. That was my first thought too. I think he means that, for every 100 digits or whatever, each number will appear ten times. It’s a dumb, non-real assumption, but a lot of these things are ridiculous.
That magic square isn't magic, it's super-dimentional😮😮😮😮
no it's just math. I proved it in three lines (because i was bored)
nevermind I though you were talking about the 1st square where this scammer told us to take a numpad and remove the 0
imagine just doing random stuff and then discovering these.
(seriously, how did mathematicians figure this out? i’m curious.)
just playing around aimless. i figured on my own that the n-th derivative of x to the n is equal to n factorial
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.
@@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!
@@Vic-ty2beooh…imma try that.
@@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
i feel like you dont understand probabilty, you wouldnt have a 100% probability of getting three digits in a row even if you were considering the first quadrillion digits.
yea the whole video is a scam
@@midahe5548 no
What he means is that it is not rare that there is three digits, because the probabilities of it happening were already met, is like being suprised of winning a 1% prize at your 100 attempt, it still is just 1%, but it had to appear at some point, because you already met the 100% probability, so if it didn't pop off, then it would start being bad luck
your feelings are irrational
@@matitello4167 nah. I don't think there is such a thing as meeting percent change at some point, from which point things become more likely or surprising.
A 1% event need not happen within the first 100 trials. It need not come every hundred trials. It does not even have to come within the first 1000 trials, or every 1000 trials.
The idea that it must, is the gamblers fallacy: the idea that certain outcomes become 'statistically due' to happen if they haven't come in a while, as if the amount of trials, and their outcomes, have some kind of influence on the next one in order to force statistics to balance out.
Trials are only independent if such influence does not exist. So while you expect a 1% event every 100 times, there might not be one for 100000 trials and then, suddenly, there could be 1010 in close succession, and the stats would still work.
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
Yes, but it is actually always a number that is divisible by 9 (999=27, 981=18)
@@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
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).
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
@@user-hs7hw6hq7w0 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
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?
I made a video on this in January. My video actually explains what is and isn't a coincidence (a lot of these are not). Also, intentional or not, you totally ripped off my thumbnail.
yikes
Damn
It might be a coincidence (pun intended)
Yeah it seems to be a ripoff, down to the thumbnail
Definitely ripped off
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
No, that’s called an irrational number. Pi is one, sq rt 2, e, sq rt 3, sq rt 5, sq rt 11, etc.
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
This video almost get me an heart collapse
I'll actually lose sleep over Ramanujan's square
It’s amazing that EVERYTHING revolves around pi.
That’s a nice play on words😂
@@hawkbirdtree3660 really? I didn’t notice.
@@FrostbearPlushies "revolves around pi"
So is this just a base 10 thing or...?
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
Srinivasa Ramanujan took "magic square" personally.
Digital genius ur animation sound effect is satisfying it sounds like a chalk
0:29 37 was also recently talked about in Veritasium’s latest video. Tf is going on with that number??
Edit: There it is again at 1:45
This is a case of selection bias. By these standards, the numbers 2 and 3 are hundreds of times more special than 37
37*3 = 111. that's why all "repeating digit" numbers are in some way related to 37. for exemple 111, 222, 333, 444, 555,..., 121212, 131313, 141414, ... 134513451345, ... are divisible by 37.
I made the proof of why anumber in a form abccba is divisible by 37, with c = b + i and b = a + i with i being the offset (for exemple 123321 have an offset of 1, whereas 135531 have an offset of 2). these numbers divided by 37 are equal to a*3003 + i*330 with a being the lowest digit
And this has 37 likes????
@@floutastic3511 Yeah the comment has 37 likes like what
These numbers are of the form abccba = 100001a + 10010b + 1100c. In 123321, a=1, b=2 and c=3.
100001/37 gives remainder 27
10010/37 gives remainder 20
1100/37 gives remainder 27
abccba/37 gives remainder
27a + 20b + 27c = 27(a+c) + 20b
When b is the median of a and c, this is
= 27(a+c) + 20(a+c)/2
= 27(a+c) + 10(a+c)
= 37(a+c) divisible by 37
But b on the keyboard is always in the middle of a and c, and is also always their median, so it always holds.
He finally posted again
The strong law of small numbers: any given small number appears in far more contexts that seem unreasonable.
It's good to see you on CZcams again
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
I agree, the probabilities presented are only true for random sequences. It's a faulty assumption
@@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.
@@staticchimera44 If you read my comment carefully, that assumption you said it relies on is _exactly_ what I was challenging...
@@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
@@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
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
statistically*
It’s around a 99.9% chance which is easily rounded to 100%
@@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
@@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
This is thoroughly enjoyable, but I'm sick and tired, so I don't think I'll be able to stay awake to finish it. I'll have to save it.
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
Bro I really don’t need this video re wiring my brain I have my math final tommorow 💀💀
These results are not surprising at all. If you all knew basic mathematics, you would obviously substitute π = e = 3 = 2 😂
Hating for no reason😭😭😭
For those wondering, how can you find or prove the Percent Error, you can use Taylor/MacClarean Series. So you can find up to what point you need digits to match up or not. My explanation needs more conciseness but that’s enough for now.
8:25 if anyone wonders why basically if you extend e^x into the complex plane you get a rotation around (0|0) where x represents the angle
The circumference of a unit circle is 2pi so a rotation by pi is equal to -1. Add one and you get zero
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).
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 ?
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.
Dude woke up and said let's make them smarter...
POV: The Judge of Math accidentally put some things in order
When digital genius posts I’m like poooog
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)
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)
@@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
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
На самом деле в квадрате Рамануджана нет ничего удивительного, если вы присмотритесь, то поймёте, что это обычный математический фокус
After a 3 month hiatus my man's finally back
4:37 Bravo, you discovered modular arithmetics
3 and 7 are the main biblical numbers too…
Yeah it is
Seeing this comment 7 days after it was posted
These numbers are of the form abccba = 100001a + 10010b + 1100c. In 123321, a=1, b=2 and c=3.
100001/37 gives remainder 27
10010/37 gives remainder 20
1100/37 gives remainder 27
27 + 20 + 27 = 74, and 74 = 37 x 2
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.
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.
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)
This looks a lot like Kuvina’s mathematical coincidences video. I’m guessing you saw it.
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.
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.
@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...
4:37 the number that is outputted is just the remaidner when 2^n is divided by 9
It's notable how many of these are just the results of us evolving ten fingers
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.
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
Apparently there's a whole tool for finding approximations like the one in the video (RIES)
you are brave. My time in too precious for theses scammers
@@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)
It feels like Cartman explaining why Kyle is behind 9/11.
4:00 Given base N, any number that has a digital sum of N-1 is divisible by N-1. This also applies to integer roots of N-1. So no matter how many times you divide 360 by a number, so long as the divisor doesn't have 3 as a root, the resulting number will have a digital root of 9.
For every like, I'll study one day
Like please
The sum of digits stuff isn't really coincidental, though; that's just modulo 9*
*caveat: taking it to be 9 if it would be 0
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.
Bro … u ok?
@@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 =(
The most useful video I ever seen about math. Especially (1³+2³+3³+4³+...+n³) = (1+2+3+4+...+n)²
Spend eight and a half minutes telling me you don't understand probability without telling me you don't understand probability
I'm a person who generally loves to collect random fun facts and then share them with my friends, I'm also a math nerd. To say I'm this video's targed audience would be an understatement
your feelings are irrational
some of these left me stunned
Frontbenchers :👁️👄👁️
Backbenchers :👄👁️👄
3:40 It's no longer "around", The Avogadro number is *exactly* equal to 6.02214076·10²³ (since the 2019 redefinition of the mole).
it is still "around"
The *dalton* (1⁄12 of the mass of a *¹²C* atom) is still "around" (that is determined experimentally and is known only with finite accuracy), but the Avogadro number from now on is fixed and is equal to an integer with 9 higher significant digits, the rest of them (lower 15 digits) being 0.
if you listen to the voice he said "around 6.02 times 10 to the 23" so i think the "around" was referencing 6.02, and not the number on-screen
@@pumpkin_pants3828Agree, that way it makes perfect sense. Though drawing the audience's attention to the fact that now it is an *exact* number would have served a much better purpose.
He said it was "around 6.02·10²³" because he omitted the last 6 decimal places. What makes this property of Avogadro's number such a big coincidence is how arbitrary its definition originally was. Avogadro's number was originally defined as the number of hydrogen atoms in one gram of hydrogen. A gram was originally defined as the mass of one cubic centimeter of water. And a centimeter was originally defined (during the French Revolution) as 10⁻⁹ times the distance from the North Pole to the Equator along the meridian passing through Paris.
This video is the definition of how easy it is to lie while using statistics
oh man i was waiting so long for another video
there is no creator
We will see
@@midahe5548 may allah guide u brother
4:37-4:48
1,2,4,8,7,5 are exactly the digits that appear in the decimals when any number is divided by 7
Only that the numbers have a definite arrangement.
Example
1/7= .142857
Cool but what’s the point?
Math is developed by government and Illuminati!
It's all connected 😱😱😱
Fun
There is no point, it's just fun
That's the point
There's none
Do you ask yourself that a lot?
0:28 I think 37 REALLY is the most random yet popular number.
Wow, thanks, i was just waiting for someone to say that i am not the only one that notices coincidences like that
that's a coincidence you found that video
magic squares also have the "property of constant differences"
The ones where you sum up the digits of a number are NOT coincidences though. It's just the remainder modulo 9.
4:08
This actually works for any rational multiple of 9 (must contain a factor of 9 when represented in p/q form)
For several of these relationships, I really wonder how someone actually figured them out, i.e. how they were motivated to find them.
Wow, this is a strange and very specific coincidence.
this was a rollercoaster ride and a half
Me watching this at 3 am: You like numbers, huh? silly math man.
Hey, one more thing. Try experimenting with 1,1111... square. Look what happens.
This is why you have to watch out when extrapolating patterns
3:21 We can get pi by 22/7 too,the difference is 1/3142
The maguc square has more magic than my life-
You know you can find your Social Security number and the digit of pi
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.
now i wonder what can be done in other numerical bases
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
pie in cooking: 😊
πe in math: 😨
3:49 bro really had to pull of 69 in there
its like flipping a coin 100 times and saying "I am so lucky! The probability of that sequence happening is 1/2^100
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!
1:00 this guy is really making a fool of himself saying that there is a 100% chance
I mean, he is making a fool of himself with everything he said in that video
@@midahe5548 lol yea he sounds like a conspiracy theorist when most results are probably coincidences.
But... it IS just a coincidence
The digits of all integer multiples of 9 themselves sum to 9. 45 is a multiple of 9, so it and all of its multiples all do this.
It's interesting that those two decimal multiples also do that. At a guess, I think that decimal multiples of 9 that were the product of 9 and a non-repeating decimal might also have this property.
I was watching the video as this thought randomly crossed my mind. It's crazy to think that trying to find all digits of π is literally like trying to explore the entirety of space.
how to melt a non-mathematical person's brain
3:55 Not a coincidence tbh. When a number is divisible by 9, its sum of digits will also be able to be divided by 9. Since 360 is divisible by 9, dividing it by 2 doesn't takes out its 9 factor
At 5:36 when you talked about the cubes I wondered if the same thing worked for the squares. If found 12 ^ 2 + 33 ^ 2 = 1233 and 88 ^ 2 + 33 ^ 2 = 8833. I also searched the 4th power and I found 1485 ^ 4 + 5308 ^ 4 + 5017 ^ 4 + 1603 ^ 4 = 1485 5308 5017 1603. That took quite a while and I have not searched all yet. Anyways I was wondering where or how you found the initial 4 examples?