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Archive for the ‘Mathematics’ Category


Hello world, how is it going?

Collatz Conjecture, ever heard of it? It’s probably most known as “3n+1” or “Half Or Triple Plus One” .

The procedure is pretty simple and starts with a simple number picking. So yes, pick any number, let’s call this number n.

algorithm: (<– : stands for assignment)

  • if your number n is odd then do the following instruction: new_n <– n * 3 + 1; n<– new_n;
  • if your number n is even, then divise it by two: new_n <– n/2; n<– new_n;
  • Repeat the algorithm until you get your number n‘1’

Now you see, you’re always going to converge and get “1” at the end or to be more exact “4-2-1” sequence. And that would be with any number you take!

 

Well, that’s nice, but I have other words to say about these.
As the goal of the algorithm is to make 1.5*n converges, then 3N+1 wouldn’t be the only maze in here!

5*N+1, 7N+1, 11N+1 would all fit if an algorithm is well implemented!

Now here is my proposed algorithm to make 5*N+1 converges

  • if your number n is even: n <– n /2; 
  • if your number n is a multiply of 3: n<–n/3
  • else : n<–5*n+1
  • Repeat the algorithm until you get your number ‘1’

or perhaps

  • if your number n is even: n <– n /2; 
  • if your number n is a multiply of 3: n<–n/3
  • if your number n is a multiply of 5: n<–n/5
  • else : n<–7*n+1
  • Repeat the algorithm until you get your number ‘1’

Conclusion, Collatz Conjecture isn’t about 3*N+1, but it’s more about 5*N+1, 7*N+1 …. , P*N+1 where P stands for a prime number

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In old days, We used to use an invention called Calculator for calculating stuffs. It’s not used anymore unless you don’t work and do your studies in front of the computer 😉

So… My point is, I was very satisfied with Google. It not only do your calculations but it converts it to you!

look:

λ  = C * h / Wph

C = 3.108 m.s-1

h = 6.62. 10-34 J.s

Wph = 10.2 eV

I just wrote in google:

(3e8 * 6.62e(-34) / 10.2)

and I got:

(3e8 * 6.62 * e * (-34)) / 10.2 = -1.79950257 × 1010

sugoi desu yo!

Nah, that’s not all 😉

I wanted the results in nanoJoules . so I wrote

(3e8 * 6.62e(-34) / 10.2) eV to nanojoules

and I got

((3e8 * 6.62 * e * (-34)) / 10.2) * eV = -2.88312066 nanojoules

Conclusion: If you want real calculation, Google is your friend 🙂

edit: come  to think of it, I’ve committed a mistake in calculations… I am almost cursed when comes to them or to web hosting 😛

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[Archive/Maths] X5²


the video is in french, however it stands for :

every number in form “X5” : X5² = [X+1]*[X] * 100 + 25

25² = ?
2 * (2+1) = 2 * 3 = 6

5 * 5 = 25

=> 25² = 625

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