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.

For every like I'll study for 1 hour

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

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

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.

I think I'll now call my calculator the 37-pad

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

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

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

4:05 that's how multiples of 9 work. That is literally not a coincidence.

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.

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.

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.

0:58 um, that's not at how probability works, what is this guy on?

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

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

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

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.

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

I'll actually lose sleep over Ramanujan's square

It’s amazing that EVERYTHING revolves around pi.

This video almost get me an heart collapse

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

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

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

Srinivasa Ramanujan took "magic square" personally.

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

He finally posted again

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).

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

It's a shame videos online do a significantly better job at making me like math than my school

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.

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

It's good to see you on KZfaq again

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 💀💀

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

It feels like Cartman explaining why Kyle is behind 9/11.

The ones where you sum up the digits of a number are NOT coincidences though. It's just the remainder modulo 9.

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)

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.

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

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

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

After a 3 month hiatus my man's finally back

Frontbenchers :👁️👄👁️ Backbenchers :👄👁️👄

3 and 7 are the main biblical numbers too…

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

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.

На самом деле в квадрате Рамануджана нет ничего удивительного, если вы присмотритесь, то поймёте, что это обычный математический фокус

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.

4:37 Bravo, you discovered modular arithmetics

pie in cooking: 😊 πe in math: 😨

With numbers appearing in pi, is it really a chance probibility if its already set in place? We didnt create pi, we found it. Is it actually random if all the numbers were already there to behin with?

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.

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

But... it IS just a coincidence

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

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

math lore is crazy fr

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?

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

3:40 It's no longer "around", The Avogadro number is *exactly* equal to 6.02214076·10²³ (since the 2019 redefinition of the mole).

some of these left me stunned

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

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

This video is the definition of how easy it is to lie while using statistics

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

For several of these relationships, I really wonder how someone actually figured them out, i.e. how they were motivated to find them.

Cool but what’s the point?

For every like, I'll study one day

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)

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

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.

Sounds like he just messed around with a calculator

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

math lore is crazy

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!

magic squares also have the "property of constant differences"

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

this was a rollercoaster ride and a half

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

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.

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

The first one becomes a lot less mysterious when you realize that 111=3×37 and that they are all divisible by 111.

bro the beginning having 37 is crazzyyy

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

Hitler when his plan fails: 1:24

Everytime i pop with a number theory coincidence on my own especially primes,feels like i finally cracked the RH😂

There needs to be an april fools version of this video where everything is kust not true

its like flipping a coin 100 times and saying "I am so lucky! The probability of that sequence happening is 1/2^100

now i wonder what can be done in other numerical bases

This is why you have to watch out when extrapolating patterns

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.

This convinces me that everything is a simulation

That first one is just because they're all divisible by 111. Not very surprising imo

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.

The first one is not a coincidence. They are all divisible by 111 (which equals 37*3), which is much more obviously connected to what you're doing.