4 𝙢𝙞𝙣𝙪𝙩𝙚𝙨 𝙤𝙛 𝙄𝙉𝙏𝙀𝙍𝙀𝙎𝙏𝙄𝙉𝙂 𝙈𝘼𝙏𝙃

[@bnb-gn4uo]

Bro it really is a shame how the algorithm treats u, ur channel is like the perfect medium length math style video that's informative but beginner friendly, genuinely feels like watching a baby 3 blue1brown. Even if youtube views are discouraging sometimes I hope u keep it up out of passion bc this channel is very interesting and a great addition to youtube

[@nealghai7043]

Second this ^, keep up the great content bro I love this shit

[@FebruaryHas30Days]

He gets thousands of views while I barely get half a thousand a day

[@alihesham8167]

@@FebruaryHas30Daysyou get more than 100 bro?

[@NowNormal]

​@@alihesham8167Half a thousand = 500

[@DavidMuñizWessels]

@@alihesham8167u guys get wievs?!?!

[@Nartymer]

1:20 that actually holds true for a reason. when you want to go from n^2 to (n+1)^2, you're basically adding 2n+1. Why? n^2 + n = n(n+1) n(n+1) + (n+1) = (n+1)(n+1) = (n+1)^2 you added 2n+1 to transform n^2 into (n+1)^2. Basically every time you add the next odd number to the ongoing sum, you're also adding +1 to n in n^2. I think you can apply a similar logic to the next 2 facts in your video. Interesting math indeed my friend

[@Wzpdanger]

Oh wow thanks for letting me know I was actually wondering how this happened as it was mentioned in one of my school textbooks

[@oinkoink3669]

everything in math is true for a reason. You can find a proof behind all of these mentioned concepts

[@Nartymer]

Quite interesting you mentioned it, I remember math being labeled "incomplete" a century ago. We have some hypothesis that are literally unsolvable as far as we know. For example, every whole number bigger than 3 can be written as the sum of 2 prime numbers and we cannot prove it, but it holds true for any number as far as we know.@@oinkoink3669

[@Nartymer]

I was wondering the same thing a while back haha. Patterns like these are really nice when you even have a proof of their existence. My personal favorite is this one: if you have 2 whole numbers, a, b such that a + b = n, the maximum product of a*b will be when a = b = n /2 (or a=b-1=n/2, if n is odd). I noticed this because 5*5 = 25 while 4*6 = 24 and did some math proof where n*n > (n+1)(n-1) because (n+1)(n-1) = n^2 - 1 < n^2, and the same logic will be applied to (n+1)(n-1) vs (n+2)(n-2) and so on @@Wzpdanger

[@Nalogpi]

If you want to go from n^2 -> (n+1)^2 . It is obvious that you should add (2n+1) Let x be the number that should be added to n^2 to get (n+1)^2 -> x = (n+1)^2-n^2 -> x = n^2 + 2n + 1 - n^2 (Expansion) -> x = 2n + 1 (n^2 and -n^2 cancel each other out) Thus, always (2n+1) should be added to n^2 to get (n+1)^2

[@goldenwarrior1186]

Fun fact: the median of the first n odd numbers is always n

[@goldenwarrior1186]

Also, I’m kinda curious how you’d go about proving these math facts

[@Smallpriest]

Absolutely mind-blowing 🤯

[@Fire_Axus]

I think it also works for the mean.

[@jayktomaszewski8738]

it works for even numbers too

[@krazyman791]

@@jayktomaszewski87381 would lead to 2, so not quite.

[@musicofficial6924]

Reason is area of square is a×a and addition of numbers form the product of lenght and bredth of rectangle formed after addition❤

[@DoomRutabaga]

Yep. It's just a Fibonacci rectangle without the diagram :D

[@sertymop3472]

also induction: (x+1)^2=x^2+2x+1 0^2=0 (0+1)^2=0^2+2*0+1=1=1^2

[@GoogleAccount-pi9ct]

This is amazing!!! Keep it up!

[@user006_SKVN8G6LH]

I love watching your videos 😊

[@matveytsarichansky8953]

3:01 you can just say you always get a number thats divisible by 9 so there are no edge cases for example when you got 27 instead of showing that it adds up to 9 eventually you can just say its divisible by 9(which is basically the same) and now you dont have the edge case of same digits numbers because 0 is divisible by 9.

[@DavidMuñizWessels]

Is 0 tecnically divisible by 9?

[@artzified]

​@@DavidMuñizWesselsI mean yeah? 0/9=0 0*9=0

[@ricepaperpencil1195]

@@DavidMuñizWesselsYes. By the definition of divisibility, 9 divides 0 if there exists an integer k such that 0 = 9k. As k = 0 satisfies this equation and 0 is an integer, 0 is divisible by 9.

[@matveytsarichansky8953]

@@DavidMuñizWessels yes, im pretty sure 0 is divisible by every number except 0

[@svz5990]

3:06 another exception is that if a multi-digit number cotains a number bigger than the first digit in that number, then you could put the order of the numbers in such a way that you would get a negative number, for example 452 - 524 = -72, which is not nine

[@lukejones4851]

Here’s a few things I discovered myself. Take a number and reverse it, then subtract them and the result is always a multiple of 9. For example, 83-38 is 45. This is true for all numbers. If we are talking about single digit numbers assume that there is a 0 in front. For example 9-90 is -81. If you take a number and subtract the sum of its digits, it will also be a multiple of 9. Let’s take 83 again, 8+3 is 11, 83-11 is 72, which is a multiple of 9. If you put a 0 anywhere in a number, and subtract the original from it, it will always be a multiple of 9 too. Let’s use 83 again, and put a 0 in the middle. 803-83 is 720, which is a multiple of 9. 9 is an interesting number, and no, I did not find any of this online I thought of it myself.

[@bene2451]

these are just less general forms of the effect explained in the video, except for the adding a zero in front of the single digit number, that is kinda just doing it backwards. nice try though

[@sadyoshhours2769]

22

[@lukejones4851]

22 works for the first one, if you treat it like 022 then subtract 220, it will not work for the second rule, numbers with all the same digits are exceptions to it, but will work for the last one

[@bene2451]

@@lukejones4851 0 is a multiple of every number

[@SerGio-xs9ss]

Right. Let's say the number 10.x + y And its reverse 10.y + x If you substrat the one from the other : 10.(x-y) + (y-x) = 9.(x-y) It is a multiple of 9 You can do the same operation with any number of 3, 4, 5, .... digits, it will always be a multiple of 9 for the same reason.

[@user-xy5yg6se1k]

the last one isn't really that impressive because, i'm not 100% certain, but i'm pretty sure that 4 would be the only number (in english) with the property of having the same letters as its value, so its the only one that would "trap" you on a loop, plus the bigger the number the bigger the difference between its value and its number of letters so it will always reduce up to single digit letters and 4 out of ten (almost half) of the single digit numbers have four letters so it's most likely not going to take too long to get to 4 great video tho! the first fact really blew my mind

[@quentind1924]

If five had 3 letters, you also could’ve been trapped in the circle 3-5-3-5

[@sabikikasuko6636]

O, tw, tre, four, faive, seikse, saebven, aeyighth, nnaaeenne (?)

[@ffreeze9924]

3:01 this works for other number bases! In base 6 doing this process results in 5: 31 - 13 = 14 => 1 + 4 = 5 453 - 345 = 104 => 1 + 0 + 4 = 5 I’m not sure how you’d prove this or why it works, but I’d guess that for any integer base n the process yields the value n - 1

[@FebruaryHas30Days]

Here's a list of languages that spell four letters for the number four. Bisaya: upat English: four Filipino: apat German: vier Norwegian: fire Can you think of more?

[@MichaelDarrow-tr1mn]

I can think of two more: toki pona: mute toki pona: tu tu

[@erdmannelchen8829]

I just realised that in German most number words from one to nine only have 4 letters. With the exception of two, 6 and 7, so its much easier to fall to four in German. Sieben would bring you to Sechs would bring you to Fünf would bring you to Vier. Eins Zwei Drei Vier Fünf Sechs Sieben Acht Neun

[@ricsix2.0]

Hungarian: négy

[@CosmicHase]

If you count transliterations, char (চার) in bangla

[@FebruaryHas30Days]

@CosmicHase Also works when using IPA

[@goatgamer001]

The last part is different for other languages. Some may have two words for number with exactly that number of letters, or even cycles ( a has b letters and b has a letters for example)

[@Psi_Fan123]

1:11 yeah, i accidently discovered the difference of prime numbers in grade 6, its pretty well known, this is just a byproduct of it

[@ginbing123]

3:07 is really cool

[@Hosib666]

I'm surprised that everything doesn't equal 42

[@thatrobloxguy]

My dumb head putting in a giant number for the last one:😂 My reaction when two thousand is outputted:😭

[@vadlocksvadlearn7746]

These facts are easy to prove, but it's really beautiful

[@sparshsharma5270]

The last one is also called Black Hole trick.

[@rewixx69420]

mista hates the thumail

[@kashmirandal6282]

4:10 I actually made my brother insane with this a few months ago. He tried everything, even decimals, He tried numbers that would take hundreds of letters. But, still, it didn't take long to get to 4. If you have a really, really big number, you should expect it to only have a few hundred letters. In that case, it could easily condense into 4. Even numbers that take millions of letters to spell are under this spell (pun intended) because any number from 1 million - 999 m are easy to spell.

[@PotentialDevGcimOgism.]

3:20 and we do this again

[@FranklinLee-t3k]

First Happy Numbers: 1, 7, 10, 13, 19, 23, 28, 31, 32, 44. As you can see a lot of the happy numbers are prime numbers.

[@THE_HONOURED_ONE_LOL]

Is there a kind of formula or pattern to this sequence of numbers?

[@THE_HONOURED_ONE_LOL]

Never-mind, i didn’t watch the video far enough😅.

[@LinaWang-be5hj]

*INTERESTING*

[@_Doctor_14]

I discovered a similar interesting fact in math. Take a random number x. Add the same number. From the result, subtract the number x. Multiply the new result with x and divide the result with x. At the end you get the xth odd number. The operation is like this: [(x+x)x-x]/x Example: [(3+3)3-3]/3= (6*3-3)/3=(18-3)/3=15/3=5 which is the 3rd odd number.

[@randommetalleux7741]

first of all, i think you emmelled your pinceaux a bit, cause your english description doesn't correspond to your mathematical expression (you've described [(x+x-x)*x]/x which is just x ). anyways, your calculs are correct, but if we look closer, [(n+n)n-n]/n = [2n²-n]/n = 2n-1 that is just a very convoluted way to say that the Nth odd number is, indeed, 2N-1 Sorry for my bad english and have a good one !

[@_Doctor_14]

@@randommetalleux7741 Sorry for the mistake. I also found out that there's a more simple explanation than what I wrote, I just discovered the complicated operation while playing with my calculator.😅

[@sparshsharma5270]

@@_Doctor_14 I was like, what the hell are you saying before looking at the mathematical expression you are talking about. You would be having tough time to write in words the equivalent of the mathematical expression.

[@Woah9394]

An intresing fun fact that i found Let f(x) be a n degree polynomial such way f(0)=0, f(1)=1 f(2)=1,....,f(n)=(n-1)th fibonaci number then f(n+1) will always be equal to 0

[@orisphera]

3:00 I think this is wrong: if we take 2762 and subtract itself with the first and last digits swapped, we won't get 9 after doing that, either

[@sparshsharma5270]

That's why there's a different version of this puzzle: that the sum of digits will always be multiple of 9. Since the difference between the two set for the number that you gave is 0, so sum of digits is 0 too and 0 is multiple of 9 so the puzzle holds true.

[@musicofficial6924]

3,6,9 are the most mysterious numbers I already know about these subtration because 0 represent singularity and 9 universe

[@VeeTubers]

what is the font of the title

[@rohail9886]

4:28 What if I use “pillow”(6 letters)

[@gary.h.turner]

"Pillow" has six letters "Six" has three letters "Three" has five letters "Five" has four letters "Four" has four letters

[@rohail9886]

@@gary.h.turner didn’t think of it like that

[@ClassicSphere]

Bro, How did you bolded and italicited video text

[@orisphera]

4:00 I once did a similar thing and got двадцатиоднобуквенный. I did that after seeing двадцатичетырёхбуквенный somewhere

[@chow4444]

Mista's nightmare

[@DavidMuñizWessels]

Sooo much great stuff in one video

[@fmlpa]

Hey! Where's Terrence Howard????..lmao...❤❤❤

[@Camman18family]

I found out the a Fibonacci number times the golden ratio then rounded is the next one

[@eightdogstreet]

3:38 isnt that such a random number

[@arcturusgd]

The second one is because m²-n²=o, odd number

[@kazisafeerzayan8597]

Ahhh yes. Everything is 4. Even this video’s length.😂😂

[@simonm-m8106]

Shoulda made it 4:44

[@white_145]

one squrd plus tu squrd plus three squrd

[@littlemurrcat08]

Миста:☠️☠️☠️☠️

[@eapenninan4950]

👍👌😄❤️

[@K0mf0rtble]

4

[@Aiharon]

I wish you proved all of them, facts are useless if not proven mathematically

[@qwertek8413]

Yea i'm sure you asked your teacher to prove that 2+2=4 in 1st grade, otherwise it's just a useless fact

[@Aiharon]

@@qwertek8413 Yea I'm sure you are the type of person to think that 2+2=4 it's interesting maths and a fun fact to be shared, otherwise your comment would be meaningless

[@HalfBreadOrder]

​@@Aiharon????

[@mustooch]

these are very easily proven, and finding the proofs is vwry satisfying. Do it yourself if you're not satisfied with the video.

[@mahirooyama9424]

As my old professor would say “this is not a proof course”

[@KENTAURUS-ff9yh]

this is NOT 5 minutes

[@randomcuber230]

skwerd

[@MilTTr411]

Everything≈4

[@tanyamclean5056]

*-Sus-*

[@lkdragon7941]

This is very interesting for a 4th grader