Asked the lovely lady at my school's library for the wifi password. She pointed me to this integral.
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- čas přidán 7. 03. 2024
- Asked the lovely lady at my school's library for the wifi password. She pointed me to this integral. It's the integral of (x^3*cos(x/2)+1/2)*sqrt(4-x^2) from x=-2 to x=2. It looks very hard but we actually don't need advanced integration techniques to figure it out. This is a very famous "free wifi integral" problem on the internet. This post is from Reddit r/theydidthemath / iicysebdux
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When your calculus test has only one problem: czcams.com/video/wyORoB5Q2Hg/video.htmlsi=NQptnwoGli9NPji-
It's a differential equation because they have sqrt of dx.
I love how they expect you to be smart enough to do it but they can't be smart enough to put the dx outside of the square root
No one said the questioner was smart. Also the confounding "first digits" - first how many digits?
@@karthikeyank132010wifi passwords require a minimum of 8 characters. i would assume the first 8 digits of pi
That was the first thing I noticed!
Nobody likes a smart arse.
@@karthikeyank132010 they should've just said all of the digits lol
Luckily, they didn't ask for the last digits of the result 😅
"The last digit is one" Apo
They want the first digits but don't tell you how many digits you need.
most wifis require at least 8 symbols in password so i think 3.1415926 would be right
edit: the pass is 31415926
As someone on reddit pointed out, it's just a brute force problem, put in digits of pi until it works.
I love how in the end you were reading pi in chinese.
I think he has it memorised in Chinese
I noticed that too, my wife says she does counting like that in her head something about being able to visualize it better and she's been in the US since she was 7 years old. FYI, that as Mandarin... as counting to 10 in Mandarin is the only Mandarin I really know, well that and thank you shi-shi :)
@@Mike__B *xiexie
@@alinaqirizvi1441 Thanks, I was more spelling it phonetically since in the English language we really do that kind of sound with x's
Japanese and Chinese digit memorization is much easier than in English.
Old lady: *points toward sign*
Me: "sigh", *opens up photomath*
I was also thinking of a graphing calculator, but that's even faster lol.
The moment I saw the -2 to 2 I was like "yep, odd function to make the problem look harder than it is"
Do they cancel out?
Yeah one of the terms @@g_g... completely cancelled out because the -2 to 0 and the 0 to +2 portions are equal and opposite. X^3 cos(x/3) term is odd * even and is 0 over the range so that portion becomes 0.
@@Gulyus I'm gonna pretend like I understood most of it
@@g_g... Integration can be thought of as the total area under the curve between the numbers given, in this case -2 and 2. Any part where the line goes into the negatives is subtracted from the area. Since the function is exactly mirrored over the origin, the part to the left of zero is opposite of the part on the right. It ends up being like x - x, which is zero no matter what x is. So we don't even have to do the math to determine x, we just know the result of x - x is zero.
@@kingacrisius right, I understand that concept very easily, but I don't understand the mathematical terms and concepts mentioned within the explanation. It's like writing an entire paragraph on why 1 + 1 equals 2. I'm also not familiar with like two of the symbols in the equation, so that might explain why I'm a bit lost on some of the concepts.
So basically, you have to combine those two numbers. In this case turning into zero, so then that big symbol ends up dissappearing? Or did I just spout a bunch of nonsense? And why is it put like that?I find it hard to believe that two numbers that you simply have to combine will be put in such a frightening format. I am definitely missing something
when there is a puzzle/question like that, the answer is most likely pi or e. Try both first, if both fails, time to do some maths lol.
Then try sqrt(pi) and sqrt(e)
Or tau
@@user-hi8jv6cw8nHow to type in 8 digits from sqrt of pi or e? 🤔
in calculus we had online homework with unlimited tries and I would always try pi, 0, and 1 first
Yeah, but to how many decimal places?
The least they should have given should include how many first digits.
No wonder my '3' didn't work !
I'm sure that the shortest WPA2-PSK password is 8 characters long.
I really really need to start to learn some math again.
khan academy is free and great.
yeah man. really couldn't solve this one
aops textbooks ftw
It's really hard tho@@ipsojure2137
As other people have noted: Engineer's answer, it's going to be pi because that's the only "important" constant most people know. That was fun though, doing integration without doing any standard "mechanical" integration, all reliant on understanding properties of the functions being integrated.
My immediate reaction to these riddles would be to guess pi and e. So cool to see it actually can work out
"I am premed. Can you just give me the password? "
Chem TA here. I hate this with every fiber of my being.
4:48 - well at least I caught you right at the end there...
No good to bring back the maths memories, every little hint helps put all of the pieces back into place!
oh i did this one a few days ago, cool to see you doing it now
So relatable when you can’t help but count in Chinese if you grew up with it… I literally have the multiplication table memorised in Chinese.
It's a much more civilized language for naming numbers. You can learn just the numbers 1 thru 10, and count all the way to 99, without learning anywhere near as many irregularities as English.
Examples:
The inconsistent spellings of one, two and eight, that don't reflect their pronunciation
Eleven & twelve, instead of fitting the pattern of the teens
The one's place coming first for all the teens; a holdover from the reversed order of German two-digit number names
The fact that teens are even called teens in the first place, instead of "wunty wun" thru "wunty nine".
The fact that four has a u, and forty doesn't
The fact that the first syllable of fifty doesn't rhyme with five
All of these problems go away, in the Chinese number naming system
"How I need a drink, alcoholic of course, after the heavy chapters involving quantum mechanics" gives pi to 14 decimal places. What were you using?
Speaking of drinks and the premise of this video:
A guy walks into a bar, and sits down at the counter, and asks for the wifi password. The bartender replies, "please buy a drink first".
The man pays, and the bartender serves the guy the drink. The guy then asks for the wifi password again. The bartender replies, "pleasebuyadrinkfirst, all one word, all lowercase".
I think he just had it memorised in Chinese
I just have it memorized from Wikipedia. 3.14159265358979... what do we know, that's the exact one you have!
@@carultch That's savage
@@CST1992 I had a "Help your kids with maths" book when I was a kid; the front cover was like 200 digits of pi, so I memorized
3.1415926535897932384
I thought that first part looked a bit odd.
i see what you did there
Differential inside the square root, confiscate the router
I almost forgot you did this years ago.
Open Excel. Assign dx = 0.0001, and assign a name to make an absolute reference to it.
Set Column A for x from 0 to 1. Set up Column B for the x-values at the midpoint between each pair of x-values in column A.
Set up Column C to evaluate the integrand as a function of each Column B x-value. Add up all column C-values, and you have a numerical approximation to the solution, using the Midpoint Rule for Riemann Sums.
Can you explain how to do step one? Creating a named variable in Excel.
@@Qermaq Select the cell you want to name. Look for its ID in the upper left, next to the formula bar. This is a text field, where you can type in a custom name for making an absolute reference to that cell. You can also use the name manager. For instance, you can type 9.8 in a cell, and then g in that text field. From then on, you can refer to g in a formula, and it will fix the reference to that cell as a constant.
Some names are off-limits, so you can't use c or r for instance (which are hotkeys for selecting column and row respectively), or anything else that is reserved. You'd need to use c_ or r_, if it is natural for you to call your variable c or r. If you want a number subscript after the letter, you can use the underscore to indicate a subscript.
If dx _was_ inside the sqrt, would you need to do a u-substitution to extract any sense out of this formula?
I was lost at that point. When I saw dx outside, I got the even/odd thing.
i think if the dx is inside the root the integral would blow up to infinity
In this particular case the problem wouldn't be defined as the differential would only be applied to part of the term, so there would be no clear integration differential for the rest (yes I'm over-simplifying). I'm simplifying a bit as technically the square root isn't strictly speaking separable in terms like that, but you have a differential so you can do a binomial expansion and drop higher terms in dx. If you had sqrt(dx) outside, there are ways to do it, but it gets messy. That sort of thing shows up in relativity and advanced geometry as the differential interval involves a square root.
@@professorhaystacks6606: You can make sense of the Riemann integral of _any_ expression involving x and dx (barring issues like division by zero) by dividing [−2,2] into subintervals, picking a point in each subinterval, evaluating the expression on each tagged subinterval using the point as x and the subinterval's width as dx, adding these up, and taking the limit as the largest subinterval's length approaches zero, if this limit exists. (A more sophisticated limit can define the Lebesgue or Henstock-Kurzweil integral.) In this case, since the integrand doesn't approach zero as dx does, the limit will be infinite (really +∞ from about −0.8 to 2 and −∞ from −2 to about −0.8). But even the integral of √dx would be infinite (since the integrand approaches zero too slowly), while the integral of dx² will be zero (since the integrand approaches zero too quickly). On the other hand, there are useful expressions in a multivariable context, such as √(dx²+dy²+dz²−dt²), that give nontrivial results.
I feel like I watched this before in your original channel
Why is odd × even × even function = odd function?
Because you have 1 negative sign from the odd function only. Complete proof:
Suppose f is odd function, and g, h are even functions.
Let z(x) = f(x)g(x)h(x), then:
z(- x)
= f(- x)g(- x)h(- x)
= - f(x)g(x)h(x)
= - z(x)
Say o(x) is odd and e(x) is even.
By def, we have o(-x)=-o(x) and e(-x)=e(x)
Then we see o(-x)e(-x)*e(-x)=-o(x)e(x)e(x). the result is odd.
Thank you
Edit: I said something mistaken that was corrected below, just editing to not waste anyone's time.
@@iyziejane No, odd no. * even no. * even no. is even. For example, 3 × 2 × 4 = 24, which is even. Some say odd functions are given its name because x^n is odd if n is odd.
Now we have to ask how many significant figures
Time to integrate into wifi systems
dx is under the integral!
At that point, turn on mobile data and put this on a calculator
this guy makes this shit look to easy
Because it's not actual computation, it mostly requires quite a bit of mental gymnastics. The average person probably would not have seen the bounds and thought, "hmm yes, is the integrand even or odd?"
You're almost a week early for this one!
People with a ti84
I don’t have such weaknesses
damn i wish i thought of the first integrand being symmetrical. I ended up doing a taylor series approximation for it which took forever. :(
Yeah but it works. You want it done fast or do you want it done right? :P
something im confused at is when integrating the symmetric curve of the odd function why do you apply the concept of negative area? so it would be 2x the integral from 0 to 2 or is negative area only really applied when you are asked to find the magnitude of the area in a certain scenario and you arent taking into things like a negative direction?
I got this equation on my calc 1 final
You took this question from a video of BHANNAT MATHS, right??😅😅
Why dx outside the sqrt?
Give solution for dx inside the sqrt❤
It's not possible, dx represents smallest increments which form area under f(x). It has to be dx not sqrt(dx), you can't integrate it otherwise.
@@lazy_biscuits08root dx is greater than dx.
I'm just glad I have data
The video suddenly stops. I suspect that you might have accidentally trimmed away part of the video.
Probably because you were too early right after the upload.
No. I just did that on purpose.
@@bprpcalculusbasics I see. Thank you for your reply.
4:55 is a nice number
Your comment shows a day ago. How TF is this possible? @@cyrusyeung8096
Me solving without using pen in just 1.5 minutes
dx under the square root?
4:40 you remembered your childhood origins
Pretty easy!
Why does the square root include the "dx" in the poster?
Probably a typo. That or the person who typed it out looked up this problem online and didn't think dx in the sqrt was strange.
I get that it is even. But how would you know that there is symmetry without looking at the graph? Like what if the function did some funky stuff in the middle?
*odd
can you write an example of an odd function that isn't symmetrical about the origin? I actually don't get what you mean, how can it be odd and not be symmetrical?
funky stuff only happens if it diverges, i believe
Symmetry about the origin is the definition of an odd function.
Haha yes! I can do everything else in my head in English with ease, but numbers, have to do them in Chinese. The brain is weird in that way.
Fuji Speedway?
It's wrong because also the dx was inside the square root
It's hard to do calculus when your school never taught it. I didn't have any calculus until I went to college. High school just had algebra and geometry.
HA! I knew it would be Pi from the thumbnail.. (No, I am not smart enough to work it out, was a total guess, but with it being a library, I knew it would be)
Tried inputing this in my calculator, i think i fried it
plot twist. the password is the question but in string format.
"integral -2 to 2 (x^2 cos x/2....."
It's a bit tricksy that the sign doesn't say how many digits you need for the password.
Eight is the minimum so you'd most likely stop there.
i would have tried 'pi' before doing any of this honestly...
4 digit password? That’s only 10,000 possibilities, could brute force it very quickly
I would've brute-forced it: there are only 10 possible passwords regardless of the integral.
the dx was in the square root ???
I believe he mentioned that it wouldn’t be possible if it was during the first like 30 seconds of the video
@@upstander1233 ah yeah i didn't watch most of the vid lmao
The most difficult part is: how many digits is "the first digits"?
For the result, I agree, the answer is either π or e, or maybe √2. There's a cos in there, so it's most probably π.
the π doesn't come from the cos though
how do oyu get a pi if you integrate cos?
The cos doesn't do anything
Password fields usually require a minimum amount of digits from the user, so those are the first digits
@@user-yx2en7ei4dYes. Eight in WPA.
Wi-Fi password needs at least 8 symbols. It said just first few numbers, means it should be an irrational number. It have to be easy to remember for frequent users, it should be a famous number without further calculations. So pi, e and sq root 2 become very sus.
Odd functions f(-x) = f(x), so the integral is zero. Good.
Since the differential is inside the square root, the value of the integral is infinite.
(Really +∞ where the integrand is positive, from about −0.8 to 2, and −∞ where the integrand is negative, from −2 to about −0.8, giving no overall value.)
For the fist half of the integral, shouldn't you split it into -2->0 and 0->2 since negative area doesn't exist?
It's not "negative area" per sé, it's area that is substracted from the area above the curve
So, you need to write the entire answer sequence as the password 😂?
Usually it's 8 or 10 digits, it seems whoever wrote this sign forgot to specify
@@BryanLu0no they did specify it is the first digit so just 3.
@@diamond_player Actually, it says "first digits" not "first digit"
additionally, wifi passwords are required to have a minimum of 8 characters anyway...
Говорили же что тригонометрия пригодртся.
the problem the password is π , pi, pie, 22/7, 22:7, or 3.14.....
"The Wi-Fi password is the **FIRST DIGITS** of the answer"
How evil is that... ? ... What does she mean by "FIRST DIGITS"? I guess it will be some fixed number if digits, but how many? 1?, 12?, 100? more?
And, include the decimal point (which is not a digit)?
A WPA preshared key is eight characters minimum, so most likely you'll stop immediately when the OK button is no longer grayed out.
Why tf is the dx inside of the square root?
Lol you mentioned that immediately
They also didn't even say how many digits it was, just "the first digits"
So, only calculus students get to use the library🤫
This is a technique that should be taught more widely - integration by not integrating !
Just try 1 to 10 it's much faster. 🎉
Pi!!!
Laughs in scientific calculator 🤣
Sir where do you belong from?
From Taiwan and america
password: enter this expression using Latex
But, but, but.... what is the password now? I mean, what do you actually type in into the passwort box?
As many digits of π as the password needs. The sign specifies just the first digits. So, it's probably just "314".
@@remus_lupinI think Wi-Fi password cannot be this short, must be first 8 digits
I think it would just be faster to brute force the password using only numbers as input
Password has one digit
Can i just try 0 to 9 ....
I hate with a passion when the lecturer writes stuff like sin x/2 + 3 or something like it instead of sin(x/2) + 3 or sin(x/3 +3). Just write the damn parentheses ffs. I hate guessing what it's supposed to be.
That song helped... 3.14159265358979323846264338327950288419716939937510582097494459
but you can do integrals on a calculator 😂
desmos works offline i believe, ez clap
[I AM WRONG] The correct answer for the integral is 2 π, you applied 1/2 twice.
Remember that there is a factor of 1/2 outside the integral. Make that 1, and you get 2pi or tau. Then you can have the argument about which is better.
@@robertpearce8394 My bad, forgot about this one 😅
So is the wifi password "pi" or some undefined number of digits of pi?
It says first digits, but it doesn't say how many. Could be the first 8, could be the first 389492875929 digits
@@gasparsigmaehh... it can be anything between 8 and 63, longer passwords aren't allowed as per WPA spec, but hey just saying some random large number is funnier
So the library is discriminating against the stupid..... Not sure how i feel about this 😅
I am glad online integration websites do it for you Lel
....so it means that the password has an infinite length......really!?
It said first digits, but not how many.
IIRC, the original sign said it was the first 10 digits of the number.
Plot twist: dx _should_ be inside root not after.
Then it is not integrable. Not even by wolframalpha I suppose.
Hahaha! Even if you solve this, you still have no idea what the password actually is. Do you include the decimal point? How many digits do you use? It's still a guess work xP
Photomath
So what is the password? I need access to the Wi-Fi.
"The Wi-Fi password is the first digits of the answer"
First how many digits? It doesn't say. If it is "first digit" (one digit number) and not digits, then you don't even need calculus to find out. However, it doesn't tell you how many digits are the password. Still have to do the check and error method?
Most likely 8 since it is the minimum amount of symbols in the password
I can remember:
3.141592653589793238
Is it just me, or did you just gloss over how the first part of the integral is zero?
Wolfram Alpha....😊
What is are the integers of pi ? Proceeds to sum up pi in Chinees
This is why libraries are dying.
This question was already done and given to China students for wifi connection 2 years back
Reddit ~ ppl clearly dont get *Networking*
I had a math exam today so lemme guess before watching:
First open the brackets to break the integral into two parts.
The first part can be solved by replacing x with pi-x.
The second integral is solved with the formula sqrt(a² - x²)
_Plugs the problem into Wolfram Alpha_
Me, being a hacker, got all the information I need to brute-force a captured WPA handshake from "first digits of the answer"
cringe ngl
you're on reddit way too much