Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 Re: Help Me ! » Golden Key - Riemann Zeta Function » 2013-01-08 01:35:25

I guess it just comes down to that the right side of the equation has to equal one before you can do this? I guess that's it...

#2 Re: Help Me ! » Golden Key - Riemann Zeta Function » 2013-01-08 01:29:42

Nevermind lol, I have solved my ignorance on my own.

example:

(5)(5)(5)x=1
x=(1/5)*(1/5)*(1/5)

Man I'm retarded, sorry to waste anyone's time.

#3 Help Me ! » Golden Key - Riemann Zeta Function » 2013-01-08 00:42:04

therussequilibrium
Replies: 3

Okay, I'm confused on something that's probably rather basic but it's really annoying me so a little help would be appreciated.

I'm reading a book and it's going over how the Golden Key was arrived at by basically using the Sieve of Eratosthenes on the Riemann Zeta Function.

And it gets to this point

ζ(s)=1+1/2s+1/3s+1/4s+....
Then you multiply both sides by the fist expression and subtract the new expression by the first expression and you end up hypothetically with something like:

...(1-1/7s)(1-1/5s)(1-1/3s)(1-1/2s)ζ(s)=1

Well here’s the part that just isn’t computing to me, it’s saying that the next step that was taken was dividing the left side by the right side, fair enough if it ended up being ζ(s)=1/(the entire term that was on the left).

Instead, it says that after dividing the left side by the right side we end up with:
ζ(s)=[(1)/1-1/2s))*((1)/(1-1/3s)]...

This makes absolutely no sense to me, and I tried working it out myself by doing this:
(1/2)(1/2)(1/2) = a; where a obviously is equal to 1/8

and if you divide how it shows to divide, you end up with:
1= (.125/.5)x(.125/.5)x(.125/.5)

And this obviously isn’t right, so could someone please explain how this was arrived at correctly?

#4 Re: Help Me ! » question... » 2012-12-22 12:04:30

The way I look at it is like this, much like when you are working in algebra, if you do something to one side of an equation you have to do it to the other side of an equation for it to still be equal.

Well, like that, if we are working only on one side of an equation, if we do something to that side of the equation we have to do the opposite or inverse of that action for that side of the equation to still hold true. Simple example: if our equation was 5+5=10

If we decided to subtract 3 from the first side we'd get 5+5-3=10, well that's not true , but as long as we did the opposite of that our equation would still be true. 5+5-3+3=10, now it's true again.

Same goes for with the fractions, in essence when looking at

All we are doing is dividing that entire side of the equation, and at the same time multiplying the entire side of the equation by 4. Like this:


and at the same time


With what you are trying to do, you are dividing the same side of the equation by 8, twice. Going back to my simple example, 5+5=10,     your action would look something like this, 5+5-3-3=10. And that just can't work, if you do something to a side, you have to do the opposite to keep the equation equal.

So, what you did would look like this:

And that equation is definitely not the same as

#5 Re: Help Me ! » Creating Functions? » 2012-12-21 23:44:55

Awesome! Again thanks for your help! And I will definitely do what you suggested, I plan on devoting a lot of my time to math from here on so I'll probably be here often.

Thanks again!

#6 Re: Help Me ! » Creating Functions? » 2012-12-21 23:40:10

Okay, maybe it was easier than I thought to simplify, I think I figured it out. I just wasn't sure if I should distribute first or FOIL first. And what I ended up with was this:

And it seems like you can divide, which seems weird, but it comes out with the right answer.



So, it seems that I can divide like that, and I simplified correctly?

#7 Re: Help Me ! » Creating Functions? » 2012-12-21 23:18:23

Yeah, I'm trying by hand, I'll get it eventually. You've given me enough help, but thank you. I do appreciate you taking your time to walk through this with me.

#8 Re: Help Me ! » Creating Functions? » 2012-12-21 23:08:18

Well, I can't figure out how to simplify this problem. But question, where does this equation that we are using come from?

#9 Re: Help Me ! » Creating Functions? » 2012-12-21 22:47:19

hmm, that's exactly the equation I entered and that's the answer it gave me; and I'm not sure how to simplify a problem with radicals in it, on my own.

#10 Re: Help Me ! » Creating Functions? » 2012-12-21 22:36:45

Not sure how to type out a fraction on the forum, but I think this is the answer:

#11 Re: Help Me ! » Creating Functions? » 2012-12-21 22:15:27

Correct, and the second sequence really starts at 1 and not at 4, etc.

#13 Re: Help Me ! » Creating Functions? » 2012-12-21 22:01:31

Yes, I completely understand the table.

#14 Re: Help Me ! » Creating Functions? » 2012-12-21 21:53:15

No, I haven't learned of Combinations yet. /sigh so much to learn lol

#15 Re: Help Me ! » Creating Functions? » 2012-12-21 21:47:45

I'm not sure I know what you mean in your last post.

#17 Re: Help Me ! » Creating Functions? » 2012-12-21 21:27:35

I actually do this with patterns already, naturally, I just had no idea how to apply those patterns, or if they could even really be applied to do anything.

#18 Re: Help Me ! » Creating Functions? » 2012-12-21 21:13:34

Now that's interesting, when I was trying to work out a formula that didn't involve a recurrence, I actually worked out these first two patterns and were trying to figure a way to use them both, but ultimately couldn't.

{1,5,14,30,55,91,140,204,285,385}

{4,9,16,25,36,49,64,81,100}


And actually, I don't remember what I had done, but I had come to a pattern that went up by 4 constantly. I was working on the computer though and didn't save my notes.

#19 Re: Introductions » I came to the conclusion... » 2012-12-21 21:11:10

Hi Bob! wave

It would seem that my structure in my assertion was wrong, throwing off data.  More correct is my conclusion is: "that joining this forum is a Nash Equilibrium."

And here are my assumptions given my estimated values of what joining would have on our species as a whole.


 
                 General Population
               |               |               |
________|_Joining|__Not___|
               |           5  |             1|
               |               |               |
  Joining   |               |               |
________|_5_____|_3______|
               |           3  |             1|
Not         |               |               |
               |               |               |
________|_1_____|_1______|

Joining, from my calculation(maybe I have overestimated what the values truly are) Joining is in one's best interest as advancements in mathematics can only go to bettering the human species as a whole; mathematics, in my humble opinion, is the building blocks to life.  up

#20 Re: Help Me ! » Creating Functions? » 2012-12-21 20:30:37

I know that I'm capable, it's just that I'm 24 almost 25, and I haven't taken any math since I was 16 and even then in High School I never applied myself. It's a shame really, because now I'm in college and I'm taking college Algebra, which is almost sad really. I just feel like I'm really far behind, and I'm really not sure how to go about catching up quickly.

#21 Re: Help Me ! » Creating Functions? » 2012-12-21 20:17:13

I understand, this information is still very helpful to me. It's obviously showing me there is a lot I need to learn; I'm a freshman in college and I really want major in mathematics, but from your general knowledge and understanding it would seem that I'm extremely far behind and I'm not sure I can catch up. So, this helps a bit...

#22 Re: Help Me ! » Creating Functions? » 2012-12-21 20:00:51

Alright, no worries, I appreciate you taking your time out to help me - so take all the time you need.

#23 Re: Help Me ! » Creating Functions? » 2012-12-21 19:28:08

I'm ready, I'm writing this all down so I can study it and get a better grasp of it all.

#24 Re: Help Me ! » Creating Functions? » 2012-12-21 19:18:29

Okay, now that's awesome, but how did you guess the pattern was in the form of

? Is this a well known equation that I don't know?

#25 Re: Help Me ! » Creating Functions? » 2012-12-21 18:58:39

Ahh, okay, I see it now - just not completely sure what happened on the second step, but I do see that the final equation equates to the original.

Board footer

Powered by FluxBB