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Flofloflo
Member
Joined: 07 Nov 2007
Posts: 120
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 Posted: 01 Apr 2008 10:18:34 am Post subject: |
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Hello,
AAAAHHHH!! I am having an OMFG moment here!
Turns out I put some wrong results in the table.... And that was not an april's fool's joke! I'd say 'Praise the lord' if I where a believer! But I'll just say 'JUPPIIIEEEE'
I am busy on a report on PI, and right now in particular with square roots.....
I am trying to solve: √(1+√(x+√1(+√(x......
Using my calculator I found these results:
X = input
S = output
X . . S . . . .S/X
2 . . 7 . . . .3+1/2
3 . . 61 . . . 20+1/3
4 . . 221 . . .55+1/4
5 . . 571 . . .114+1/5
6 . . 1219 . . 203+1/6
7 . . 2297 . . 328+1/7
8 . . 3836 . . 479+4/8
9 . . 6232 . . 692+4/9
10. . 9594 . . 959+4/10
Now if you look at these fractions at M, you gotta admit it looks peculiar!
For a few seconds I thought I had a formula:
X^4-2x^2-x+1=S
But it only works for X = 2,3,4,5, 6 and 7....
Still, it leaves me thinking..... The nice fractions change, and all of a sudden, the formula also stops working!
I bet I could find a formula for the next list of numbers, but without a doubt it'll change again once x=14 or something..... Well, maybe not, I have yet to try it..... But can anybody shed some light on this?
Something else: If needed I can explain how I got at X^4-2X^2-X+1, but I am Dutch, and it took me half an hour to explain it vaguely in Dutch.... I don't really feel like translating all of it:P
WOW!
I just tried my ol' formula out for some other, higher numbers.... And it worked again.
This is weird, I guess it's just off for certain numbers... I gotta figure out why though!
I gotta finish the report in two days, so I hope I can finish it before then...
-Floris
Hmm... April's fools huh-_- These things are so lame-_-
Last edited by Guest on 01 Apr 2008 12:31:58 pm; edited 1 time in total |
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Weregoose
Authentic INTJ
Super Elite (Last Title)
Joined: 25 Nov 2004
Posts: 3976
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| Posted: 01 Apr 2008 12:32:13 pm Post subject: |
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This reminds me of the Pronic Numbers, which are the numbers x where x-√(x+√(x+… produces whole numbers. Seeing that these can be calculated with x²-x, we can follow suit with your equation to get S = (x²-1)²-x, which expands to the formula you found. Thus, you just must have erred in your efforts after x = 7. The pattern continues. :-)
[EDIT]
Wow, spoke one minute too soon. Good to know that the universe isn't on its head after all.
Last edited by Guest on 02 Aug 2010 02:41:59 am; edited 1 time in total |
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