These Equations will Blow Your Mind
HTML-код
- Опубликовано: 29 сен 2024
- Here are some absolutely incredible math facts! This is my top 10 list of the most incredible math equations I could find.
🙏Support me by becoming a channel member!
/ @brithemathguy
Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information.
#math #brithemathguy #maths
![Intro to Tool Dev in Unity - An Improvised Live Course [part 1/4]](http://i.ytimg.com/vi/pZ45O2hg_30/mqdefault.jpg)
![Intro to Tool Dev in Unity - An Improvised Live Course [part 1/4]](/img/tr.png)
🎓Become a Math Master With My Intro To Proofs Course! (FREE ON RUclips)
ruclips.net/video/3czgfHULZCs/видео.html
Why did you delete your newest video?
My favorite number is 118, why? Cause 118 is 63
That golden integral is too good it needs a dedicated video!
I’ll do my best!
Definitely does!
@@BriTheMathGuy WE NEED ONE PLEASE
I vote for this as well!
Yes please!
Take the digits of 81.
8 + 1 = 9
9^2 = 81
10a + b = (a + b)^2 can be satisfied with a being 8, and b being 1.
the top 8th integral was given in IIT advanced exam . and also most of the people were confused between these 2 options : 22/7 - pi and 0
Interesting!
@@BriTheMathGuy man , pls once try IIT advanced maths paper . It's supposed to be the most hardest exam in the world top 4 . If possible then make a video . Like you just give your opinion on the question paper. Pls pls try
@@deorteuryt7795 they're not the hardest in the world, the questions themselves aren't impossible if you actually study the material. what makes it hard is how competitive it is.
@@deorteuryt7795 those "hardest in the world" are just bull spread by a special type of journalists that GH Hardy (Ramanujan's guy) criticized in his book A Mathematician's Apology.
@@gasun1274 man , I am just giving the background of iit exam coz this guy is not an indian so he don't know how iit exams are. These words which you said are right but if u compare with the exams then u can't say this . The people , the higher officials have announced that iit exam is top4th world's most hardest exam
the 22/7 - pi integral is a way of proving that pi < 22/7 since the integrand is always positive
WE NEED THE GOLDEN PROOF FOR THAT GOLDEN INTEGRAL!
Stop yelling your post in all caps.
@@robertveith6383 is it annoying tho?just sayin
Similar to the 3456 problem, there's a way to make a cubic triple with every integer through (n)^3+(6n)^3+(8n)^3=(9n)^3
Neat!
Kind of, but isn't this just multiples of 1^3 + 6^3+8^3 = 9^3 ?
Another beautiful equation I recently came across has to do with powers of φ.
It's a well known fact that φ² = φ+1.
Now, φ³ = φ(φ²)=φ(φ+1)=φ²+φ=(φ+1)+φ = 2φ+1
Similarly, we get the following results;
φ⁴ = φ(φ³) = φ(2φ+1) = 2φ²+φ = 2(φ+1)+φ = 3φ+2
φ⁵ = φ(φ⁴) = φ(3φ+2) = 3φ²+2φ = 3(φ+1)+2φ = 5φ+3
...
φⁿ = F(n)φ + F(n-1) where F(n) denotes the n-th fibonacci number, with F(0)=0 and F(1)=1.
A proof for this pattern is as follows:
First, we'll prove that it holds for n=1. φⁿ = φ¹ = 1φ+0 = φ
Now, assume it holds for any natural number k, strictly larger than 1. Then we see that φᵏ⁺¹ = φ(φᵏ) = φ(F(k)φ+F(k-1)) = F(k)φ²+F(k-1)φ = F(k)(φ+1) + F(k-1)φ = (F(k-1)+F(k))φ + F(k) = F(k+1)φ+F(k).
So if the statement holds for k, then it holds for k+1, for any natural number k.
By the principle of mathematical induction, the statement is now proven for any natural number n.
What Greek letter is this? I want to look it up but don't know how
@@scarmackd1498 it's phi.
@@scarmackd1498 Im greek xd φ is f in English
Checkout a french exam and it covers exactly that: ccs 2019 math 1
My mind was blown multiples of times during the whole video! Amazing video, Brian!
Thanks a ton!
@@SimonHansson-rq2zg🤡
Ramanujan was a master at finding mathematical diamonds buried 10 miles deep in an active volcano. Finding these identities, like your nr 1 on the list, is completely beyond my comprehension.
I want to see you derive Ramanujan's 1/pi identity!
1/pi identity proof contain a lot of advanced functions like theta function , modular forms and much more So I don't he will make it that's already hard enough
Might be a little tough for me 😅
@@BriTheMathGuy break it into little pieces as a series showing gems along the way. We don’t need to understand it all - just the milestones. You could even include the maths of calculating root 2 and reciprocals of billion digit numbers.
I saw this formula in Scientific American back in Feb 1988 and it has mesmerized me ever since.
@@idjles You are talking about breaking into small pieces, and making explainable to the masses, the proof & calculations, from the mind of one of the most gifted humans of the last 1000 years, in an attempt to explain his mind, to the RUclips world. Why don't you give it a try - and I say this as a person with a degree in Mathematics knowing this will probably take you years to do well - if it is doable at all without full and complete dedication.
Nah... no... the formula was a generalized algorithm stemming from a summation which requires deep elliptic curve algebra and analytics.
You'll need a series to even get to the foundations.
Mistake at 4:42, k should be 0, not 1.
I tried computing this based on the given formula and it didn't work. But once I set k to be 0, it worked.
🥲
Yeah you are right buddy. Great observation
Bruh...how did you calculate it😨😨😨
@@raunakkumar9377 The first value when k = 0 is actually already a good approximation of 1/pi. The ones after it just make incremental changes
3³+7³+0³= 370
And
3³+7³+1³= 371
This was in my Math Book. There were two more but I don't remember it
153 and 407
I'd love to see some backgrounds on your #1, how does one even come up with it? How do I approach something like that
Look into Ramanujan-Sato series. It looks pretty random, but there's a pattern and a whole theory to it. That article on Wikipedia is very complicated though. You can also in general look into analytic number theory.
@@perrydimes6915 You are making it sound way too easy. If you give consideration to where he was born, his access to information when young, and when he was born, the result is just mind-boggling. He was a once in a 500yr human mind.
@@wallstreetoneil Oh, I agree do not get me wrong. I was not trying to diminish the achievements of Ramanujan. I was only trying to point to resources that will help learn more about the identity and the theory surrounding it.
It is pretty miraculous that such an identity was found at all. But if you want to dig into it, the resource are there on the internet to understand a lot more about the topic. It's not magic, it's math, which somehow makes it even more magical in my opinion.
@@perrydimes6915 I think Burkard Polster, Mathologer of RUclips fame, might have the resources to do this - but even he understands the time and resources need to do this justice in a RUclips fashion. You should contact him and suggest it. It would be amazing to see - and would only bring more attention to Srinivasa Ramanujan who the world, outside of Mathies, should know more about.
RAMANUJAN IS PRINCE OF MATHEMATICS
🙂🙃
So to get many of the number patterns pairing up in question and answer, you pick your pattern first, then look for the numbers to fill the equation that will pattern the way you want. They are often easier to reverse engineer than brute force.
I kinda expected #1 to be Euler's formula but that Ramanujan's equation is literally INCREDIBLE.
(I mean, why do 396, 9801, 1103 and 26390 end up in 1 over pi???)
the proof is trivial and left to the viewer
@@mismis3153 Fermat's method is the strongest method since the quadratic equation.
@@cameronbigley7483 Can you explain ?
@@mismis3153 Fermat's Last Theorem famously doesn't have a proof in the original texts, saying something along the lines of "I don't have enough room to show the proof here."
@@cameronbigley7483 Ah yes how could I have forgotten that
There are some mathematicians out there who have too much time on their hands.
SUM OF ALL NATURAL NUMBERS IS -1/12 THAT SHOULD ON THE NO 1 SPOT
03:55 - you mean "INdefinite" ?
What about Euler’s identity???
e^(iπ) + 1 = 0
This, in my opinion, is THE MOST BEAUTIFUL equation in all of mathematics
I think he was going for ones in which a majority of his audience hasn’t seen before
There’s also the one where i^i is about a fifth.
On the one side, all imaginary numbers. No reals in sight. On the other side? _All real_ .
he coulda at least given an honorable mention to e^i(pi) +1 = 0
You wrote it wrong. It is e^(i*pi) + 1 = 0.
@@robertveith6383 ooohh i see what u mean, i meant that the pi is in the exponent too, but i didnt want to write it like ipi or pii... i dont know why i didnt just use a * sign
Get the fibonacci algo... you know that at let's say that with F(41)/F(40) you have a pretty aproximation of the golden ratio...
Now do the same, but instead using 0 and 1 as seeds for the algo, use something weird, like 24567 and 4321 then make F(41)/F(40) and see how far are you from the golden ratio...
The takeaway from this, is that the golden ratio is independent from the seeds, it only depends on the algo.
Hugs from Catamarca, Argentina.
I absolutely love the fact that infinite sum of n/2^n is 2 and infinite sum of n^2/3^n is 3/2. calculations were never easier
1:00 It would have been very cool to see a graph of this function, just so we can get a visual for how close to 0 it really is.
it isnt a function so there is nothing to graph, unless you want a dot on a number line
its about 0.0013
Then just put that equation in desmos graphing calculator
Cutest equation for me is
d/dx Sin^2x = Sin 2x
1:20 BriTheMathGuy.exe has stopped responding
Me watching the video: wow these are so amazing!
Me on seeing the 22/7 - pi integral: vietnam flashbacks
Get independent!
#2: plots itself
0:49 you can use this integral to prove that π is bigger than 22/7 since the integral is positive, since the function is positive over this domain form 0 to 1.
6+9*6+9=69
"3+4+5 is 6" is my favourite phrase
The last one is obvious just by looking at it. It clearly has got to be be 1/pi. 🤣
What the hell is a golden ratio x -x {Fn} what
Love from Bangladesh 💖
The second one was ridiculous, I mean the way that equation graphs itself is awesome...
1/2+1/4+1/8+...=1
1/3+1/9+1/27+...=1/2
*what*
I wanna see that golden integral a lot!!!!
I’ll do my best!
Is there any proof of the last equation??
*the proof is left as an exercise to the reader*
seriously though, yes, but it's pretty involved
1:20 same thoughts bro
#2 is by far the best imo
The best one is e^(i pi)+1=0
Put a multiplication symbol in there: e^(i*pi) + 1 = 0.
I'm grade 10, can't understand what's an integral
An integral is used to find the area under a function
#2 mathematical quine
Better approximstion for pi is 355/ 113
1:01 pi: im your father
Please, make a video about this integral at 4:06
I’ll do my best!
WARNING: Number theory is interesting to learn about but never fun to be tested in a college course that your life depends on. Trust me, I figured that the hard way.
4:48 Should have said "why"
Wow! How did you get like that?
Every time he says "This was too good to not include in the video",
I do *one* pushup
Jesus Christ
The most basic one:
1+2=3
123
The most confusing one:
ruclips.net/video/094y1Z2wpJg/видео.html
For number 10 you can also multiply the in the desmos calculator ( I know its wrong but I got 216)
In the fast intro equation why to put cube on additional part as in once digit if we put like (3+4+5)³ than it never equals to 6³
also the sine value of pi is 0
btw pi = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989
Magic trick: What is the sum of the digits in your social security number? The product of the digits?
How do you find the equation in the graph of the equation that graphs itself? (My daughter would like to know)
3³ x 2³ = 6³
My favorite equation is Euler's identity which is e^iπ+1=0
the squares are deliberately teaming up for something
great
Surprised e^(pi(i)) + 1 = 0 wasn't here
1+9+1x9=19 (it only works with 9x table) 125+9+125x9=1259
10 squared + 11 squared + 12 squared = 13 squared + 14 squared + 12 squared is 14 squared
unfortunately, 3^4+4^4+5^4+6^4 does not equal 7^4 :/
I couldn't make fool my friends by using this equations
i got #9 right and #7 also 34 and 35 if you split 3435 making this 34|35
10^10^10=1 with 10,000,000,000 zeros or 2,000,000,003 zeros less than 1 tred-nanillion
Values:
5² = 25
13² + 14² = 365
25² + 26² + 27² = 2030
phi ≈ 1.618
π²/6 ≈ 1.645
1/π ≈ .318
You should have included Euler's identity.
Can you please explain why
11^2 =121, [ditto]
12^2 = 144, 21^2 = 441
13^2 = 169, 31^2 = 961
14^2 = 196, 41^2 = 1681 (still about to make sense, 16 + 180)
but the pattern breaks at 15^2 vs 51^2
I just realised it also works with 10^2 and 01^2
10^2=100, 01^2=001
Make the video of the golden integral!
I’ll do my best!
2⁵•9² or 2⁵×9² =
2⁵ = 32
9² = 81
32•81 or 32×81 = 2592?
Yes or no? / Y/N?
1:19 I like your hands and head movement lol
3435 problem is wrong (5^4=3,125)
The equation 10^(1,000 is out of accepted calculation range on my device but slap a percent sign on it to make it 10^(1,000% it let's me calculate it and it gives me 10,000,000,000,000
1,000% is 10, sorry bud, but you gotta do the math. 10^n is 1 with n digits after it.
3 to the third + 4 to the fourth + 3 to the third + 5 to the fifth = 3435
3:31
…
although e^iπ=-1 is short, I think it deserves to be here
6+9+6•9=69
I can’t understand #5 could someone please help me to😢
1:20 ayy that is why my phone number ends with 3435
4:25 Actually, it can plot anything on a grid of ANY SIZE! Just use some other number instead af 17. That number is the height.
i checked, 3^4 + 4^4 + 5^4 + 6^4 does not equal 7^4
I accidentally made the video play twice at the same time lamo
Integral #8 would also deserve a special video.
0:50
Him: Why?
Me: Mind, analysis.
Im gonna show this kto my class, they are going to thing im a god
First time in my life I've seen a formula take a selfie
you didn't show the turkey curve ;-;
Me- wut is an integral (I'm in8th)
I honestly thought there would be more comments.
0:43 I noped out of this vid after i saw that Thing
Indefinite integral Int(1/(1+x^φ)^φ,x) can be quite easily integrated by parts
Int(1/(1+x^φ)^φ,x)=Int((1+x^φ)/(1+x^φ)^φ,x)-Int(x^φ/(1+x^φ)^φ,x)
Int(1/(1+x^φ)^φ,x)=Int(1/(1+x^φ)^(φ-1),x)-Int(x^φ/(1+x^φ)^φ,x)
Now we can integrate Int(1/(1+x^φ)^(φ-1),x) by parts with
u = 1/(1+x^φ)^(φ-1) and dv = dx
After integration by parts we can add integrals we will get
If we want to calculate this integral using antiderivative we have to
calculate the limit
here is another: phi = 0.5 * (5^0.5) *0.5
Thanks lol my mind broken it’s 2am
6 • 9 + 6 + 9 = 69
These are not equations. These are equalities.
At 1:38, if the given sequence N = π²/6, is that to say that π = √6N? And that thereofre π can be defined by a sequence?
Cause I thought π couldn't be defined (irrational, transcendant). I'm confused (and not particularily good at maths by the way).
Thanx ahead for any enlightening answer.
Ramanujan number, my favourite.
My favorite is 9+10=21