this problem is really easy to implement with a recursive function and actually lead me to writing my first bit of c++ code in some years to get a solution. definitely more of a bruteforce approach than what you did, but i'm glad to know i'm not too rusty :)
I keep thinking about repeating the function again and again to see where it converges because I’ve had too much experience with the collatz conjecture
Notice how your video is picking up in the algorithm after you increased the production quality. Its not a coincidence trust me. Keep up the the good work boss. 🙏
That was a nice problem ! I kinda regret to have been lazy and not try to find right away the solution, but instead just code a recursive program in python that does exactly what f(n) do (and it's matching, 455 possible numbers n such as f(n) = f(2011) ) Well, it is still a proof of the theory, in the practice. Never a bad thing to do both ways :)
Substituting n=1 into f(2n) = 2f(n) gives f(2) = 2f(1) = 2 In general if you're finding f(m) write m as 2k or 2k+1 and then find f(k) and k is strictly less than m so repeating the process gets you down to f(1) Hope that helps!
Nailed the form of f, but brute forced the combinatorics as a partitioning problem and missed two of the partitions of 11, leading to an answer 40 too low...
A lot of people might start working on a solution simply based on the video title, without getting any clues by watching more of the video, right away. In this case, was just trying to find a polynomial expression for the function "f(n)" that produced the right mapping of values, as stated. It would be nice to have an upfront warning if there is actually more to the problem statement.
Your comment is purely juvenile. Nothing more pointless than people who don't think before they type. Have you heard of cryptography? Or do you store your money in the flush tank?
polya isn't pregnant but he sure delivers
proof that he isnt pregnant?
@@RubyPiecI have a truly marvelous demonstration of this proposition which this margin is too narrow to contain.
Gregnant
@UCEbh7mg1hOvVcHN6cef0zdQlink it, it's not the era of fermat
@@ianweckhorst3200gradient
this problem is really easy to implement with a recursive function and actually lead me to writing my first bit of c++ code in some years to get a solution. definitely more of a bruteforce approach than what you did, but i'm glad to know i'm not too rusty :)
My favorite part about this is its simplicity after the fact. Just look at the thumbnail again, and the f(n) flows into the answer.
Glad you enjoyed it!
@@Polyamathematics Glad you shared it!
I keep thinking about repeating the function again and again to see where it converges because I’ve had too much experience with the collatz conjecture
I challenge what you define as facts. Narrow minded fools find meaning in math
this video was good bro keep it up and the style is nice
Notice how your video is picking up in the algorithm after you increased the production quality. Its not a coincidence trust me. Keep up the the good work boss. 🙏
Thanks a lot. (Next video is going to be a whole level above this one in production quality)
@@Polyamathematics amazing to hear bro. What software are you using to animate your videos?
Davinci resolve (free version). Although I'm also playing around with some 3D stuff in blender
That was a nice problem !
I kinda regret to have been lazy and not try to find right away the solution, but instead just code a recursive program in python that does exactly what f(n) do (and it's matching, 455 possible numbers n such as f(n) = f(2011) )
Well, it is still a proof of the theory, in the practice. Never a bad thing to do both ways :)
Awesome!
Video is great but microphone is abrupt. If it was smooth then video would be really good
Yeah, hopefully the microphone issue should be fixed in the future.
After watching the video I thought you would have a lot more views and subscribers. This is really good!
Appreciate it, that means a lot
thought about it for like 5 minutes so probably wrong is it 461
damn i forgot to exclude numbers up to 2048
Couldn’t even edge to this… exploded immediately! Clean up on aisle my pants!!! 😂😂😂
Thank you Polymathiszyzz for this information
@@seon3350Thank you Polyamathiszyzz for this information
this is highly inappropriate he is a minor
@@nosang69Agree. Reported immediately, I hope you did the same.
@@nosang69 Agreed. Reported immediately, hope you did the same. Great video as usual @polyamath
Without a doubt a fantastic video, I appreciate you sharing it!
Nothing fantastic except for you being a fool. I find it hilarious
Wow!
How do you even calculate that f(4) equals 2?
It just tells you that f(4) = f(2*4) = f(8) and so on.
Set n=2. Then f(2) = f(2*2).
Set n=1. Then f(1) = 2f(2*1)
So f(4) = f(2) = 2f(1) = 2. In general the goal is to iterate all the way down to f(1).
@@Polyamathematics but f(1) is not = 2f(2*1), its = 1
im just wasting your time because im not going to understand the "grammar".
@@rejected4760 f(4) = f(2·2) = f(2) ⇒ f(2) = f(2·1) = 2f(1) = 2·1 = 2
I'm a programmer so I'm unable to solve even f(2)
If I substitute n for 2, it cascades in the positive direction.
Substituting n=1 into f(2n) = 2f(n) gives f(2) = 2f(1) = 2
In general if you're finding f(m) write m as 2k or 2k+1 and then find f(k) and k is strictly less than m so repeating the process gets you down to f(1)
Hope that helps!
Gotchu fam, check my comment.
Nvm, it's garbage. Programmer's life lol.
I need to start considering change of basis in the future
Very neat, but I wouldn't call it number theory
Words of someone who has taken highschool number theory
I'm curious now what kind of mathematical function you'd have to make for it to have the described behavior
Nailed the form of f, but brute forced the combinatorics as a partitioning problem and missed two of the partitions of 11, leading to an answer 40 too low...
nicee
wysi
Yes, you can find a polynomial equation of the 4th degree.
In fact you can find whatever you want as soon as you have 5 parameters.
Sorry it's not clear from the thumbnail but the function f is defined in the video. The video wasn't about Lagrangian interpolation
amazing
A lot of people might start working on a solution simply based on the video title, without getting any clues by watching more of the video, right away. In this case, was just trying to find a polynomial expression for the function "f(n)" that produced the right mapping of values, as stated. It would be nice to have an upfront warning if there is actually more to the problem statement.
I'll take that on board in the future. Thanks.
Bro is the goat 🔥🔥
The pattern is purely imaginary. Nothing more pointless than people who find meaning in mathematics.
I bet you like your house to stand upright, your car to drive, your phone to charge, stfu
Your comment is purely juvenile. Nothing more pointless than people who don't think before they type.
Have you heard of cryptography? Or do you store your money in the flush tank?
2011=11111'011011(2)=10101(2) 1,1,3,7✓