      # Something Random I Discovered...

49 replies to this topic

### #1 ShamusHand

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Posted 02 December 2008 - 10:21 PM

I was doing my homework when I realised that 7.2 / 6 = 1.2, and 7.2 - 6 = 1.2. I found it interesting, and found that with this formula...

[ (x + 1) + 1 / (x - 1) ]

...You can find any number that can be subtracted and divided by to get the same result. So...

[ (x + 1) + 1 / (x - 1) ] - x = [ (x + 1) + 1 / (x - 1) ] / x

...the same equation divided and minus x is the same. For example...

[ (10 + 1) + 1 / (10- 1) ] - 10 = [ (10+ 1) + 1 / (10 - 1) ] / 10
[ (11) + 1 / (9) ] - 10 = [ (11) + 1 / (9) ] / 10
(11 1/9) - 10 = (11 1/9) / 10
10 / 9 = 10 / 9

...So basically...

11.111 / 10 = 1.111
11.111 - 10 = 1.111

...Just like...

7.2 / 6 = 1.2
7.2 - 6 = 1.2

...So did I find something special, or this something you learn on calculus or something? Edited by ShamusHand, 02 December 2008 - 10:32 PM.

### #2 CommonSense

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Posted 02 December 2008 - 10:28 PM

I was doing my homework when I realised that 7.2 / 6 = 1.2, and 7.2 - 6 = 1.2. I found it interesting, and found that with this formula...

[ (x + 1) + 1 / (x - 1) ]

...You can find any number that can be subtracted and divided by to get the same result. So...

[ (x + 1) + 1 / (x - 1) ] - x = [ (x + 1) + 1 / (x - 1) ] / x

...the same equation divided and minus x is the same. For example...

[ (10 + 1) + 1 / (10- 1) ] - 10 = [ (10+ 1) + 1 / (10 - 1) ] / 10
[ (11) + 1 / (9) ] - 10 = [ (11) + 1 / (9) ] / 10
(11 1/9) - 10 = (11 1/9) / 10
10 / 9 = 10 / 9

...So did I find something special, or this something you learn on calculus or something? Homework? Who does that? I have no idea if it's something you learn, but I find that interesting. I'm in the same grade. I'll check that later, unless someone else does. I have to find my calculator (no the one on Windows, even in Scientific mode, does not help. I don't like using it).

Wow I would never think of doing that. You're such an over-achiever. ### #3 ShamusHand

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Posted 02 December 2008 - 10:37 PM

Yeah... It all started with me accidentally finding that 7.2 / 6 = 1.2, and that 7.2 - 6 = 1.2.

So then I turned into fractions...

(7 1/5) / 6 = 1 1/5
(7 1/5) - 6 = 1 1/5

And I kinda noticed a pattern in the numbers, and I managed to write an equation with it that always comes up with a number that, when added or multiplied by 'x', gives the same number. And so the equation works backwards as well.

I don't know if this was product of curiosity or too much time in my hands... lol Edited by ShamusHand, 02 December 2008 - 10:38 PM.

### #4 hydroman

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Posted 02 December 2008 - 10:42 PM

Yeah... It all started with me accidentally finding that 7.2 / 6 = 1.2, and that 7.2 - 6 = 1.2.

So then I turned into fractions...

(7 1/5) / 6 = 1 1/5
(7 1/5) - 6 = 1 1/5

And I kinda noticed a pattern in the numbers, and I managed to write an equation with it that always comes up with a number that, when added or multiplied by 'x', gives the same number. And so the equation works backwards as well.

I don't know if this was product of curiosity or too much time in my hands... lol its just another coincidence. Just like 2+2 = 4 and 2*2 = 4, and 2^2 = 4.

### #5 Airflow

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Posted 02 December 2008 - 10:43 PM

I made a program that uses this formula.. I think this might actually be a new formula, I don't think anyone knows this... tell your professor or something!

### #6 ignition

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Posted 02 December 2008 - 10:45 PM

I was doing my homework when I realised that 7.2 / 6 = 1.2, and 7.2 - 6 = 1.2. I found it interesting, and found that with this formula...

[ (x + 1) + 1 / (x - 1) ]

...You can find any number that can be subtracted and divided by to get the same result. So...

[ (x + 1) + 1 / (x - 1) ] - x = [ (x + 1) + 1 / (x - 1) ] / x

...the same equation divided and minus x is the same. For example...

[ (10 + 1) + 1 / (10- 1) ] - 10 = [ (10+ 1) + 1 / (10 - 1) ] / 10
[ (11) + 1 / (9) ] - 10 = [ (11) + 1 / (9) ] / 10
(11 1/9) - 10 = (11 1/9) / 10
10 / 9 = 10 / 9

...So basically...

11.111 / 10 = 1.111
11.111 - 10 = 1.111

...Just like...

7.2 / 6 = 1.2
7.2 - 6 = 1.2

...So did I find something special, or this something you learn on calculus or something? theim, i got geometry and i dont get, i am falling with 48 i dont do homework either

### #7 CommonSense

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Posted 02 December 2008 - 10:51 PM

theim, i got geometry and i dont get, i am falling with 48 i dont do homework either

Do your homework, seriously. I do mine, but in Study Hall, Lunch, or Homeroom. Geometry was hard as hell for me too. Algebra I get, kinda. I still like basic math more than anything. ### #8 ShamusHand

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Posted 02 December 2008 - 10:52 PM

its just another coincidence. Just like 2+2 = 4 and 2*2 = 4, and 2^2 = 4.

But my coincidence has a formula, and a formula is consistent... unlike a mere coincidence, it works with every number.

If this IS new and undiscovered, I want to call it... Shamus' Theorem. Yeah!

Edited by ShamusHand, 02 December 2008 - 10:54 PM.

### #9 endrit10

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Posted 02 December 2008 - 11:00 PM

I don't know
Even if it was a theorm
Whats the use for it?

### #10 ShamusHand

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Posted 02 December 2008 - 11:01 PM

I don't know
Even if it was a theorm
Whats the use for it?

You never know... IT might get applied somewhere eventually. It might cure cancer!

### #11 CommonSense

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Posted 02 December 2008 - 11:05 PM

You never know... IT might get applied somewhere eventually. It might cure cancer!

You never know ### #12 ShamusHand

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Posted 02 December 2008 - 11:16 PM

Yeah... But I want to know if I really am the first to figure this out... I doubt it, but you never know...

### #13 CommonSense

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Posted 02 December 2008 - 11:25 PM

Yeah... But I want to know if I really am the first to figure this out... I doubt it, but you never know...

Speak to your math teacher. If he/she doesn't know or hasn't heard of it. Speak to the chairman of the subject (your teacher will know who that is). And if he doesn't he might know where to go.

### #14 Syzygy

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Posted 03 December 2008 - 12:30 AM

I don't know
Even if it was a theorm
Whats the use for it?

You never know... IT might get applied somewhere eventually. It might cure cancer!

haha, legend. ### #15 Arnabmatrix

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Posted 03 December 2008 - 02:16 AM

I dont understand what r u saying by

[ (x + 1) + 1 / (x - 1) ]

...You can find any number that can be subtracted and divided by to get the same result. So...

Say u want to find a number that gives the same result when divided by x and when x is subtracted from that...

Let, the number be y

then

y/x=y-x
=> y=xy-x^2
=> y(1-x)=-x^2
=> y=(x^2)/(x-1) -----------(1) where x != 1

Got it????

Means if u want to find a number for which [that number]/6=[that number] -6 the just replace the values in equation (1)
i.e. y=36/5=7.2 Edited by Arnabmatrix, 03 December 2008 - 02:17 AM.

### #16 pm_41

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Posted 03 December 2008 - 02:20 AM

WTF

Could you put it in n00b terms? My head hurts...

### #17 M.Sudoku

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Posted 03 December 2008 - 02:21 AM

It might cure cancer!

Great one ### #18 Alexx

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Posted 03 December 2008 - 02:25 AM

It's just a simple equation:
x/y = x-y

Solving it for x gives us:
x = xy - y²
xy-x = y²
x = y²/(y-1)
where y can be arbitrary (only exception is for y=0 and y=1) since it's only one equation and two unknowns

If we choose y=2 then x=2²/(2-1)=4
That gives us: 4/2 = 4-2 = 2

For y=6: x=36/5= 7.2 Btw, if we solve the first equation for y, it gives us:
y² - xy + x = 0
y=(x ± sqrt(x²-4x)) / 2
x is now arbitrary with only exception when 0 < x < 4.

For x=7.2, we get y=(7.2 ± 23.04)/2
y=6 or y=1.2

Check:
7.2/6 = 7.2-6 = 1.2
7.2/1.2 = 7.2-1.2 = 6

Don't get surprised by the second solution. It's explainable. Let's call it z. Now we know:
x/y = x-y = z

x/y = z gives us y = x/z
Replacing y with x/z in x-y=z gives us:
x-x/z=z, which means x/z = x-z

That's it. Just some algebra. Hope it was easy enough for most of you to understand.

PS: Can't believe I registered just to write this... lol

Edit: Just realized that Arnabmatrix posted the solution before me even though mine takes things a little bit further. lol

Edited by Alexx, 03 December 2008 - 03:51 AM.

### #19 ShamusHand

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Posted 03 December 2008 - 02:27 AM

Hmm... I didn't consider approaching it like that. Darn. That was almost too easy...

P.S.: Welcome to WinMatrix!

Edited by ShamusHand, 03 December 2008 - 02:31 AM.

### #20 zool

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Posted 03 December 2008 - 02:49 AM

hahaha.. thz is my 1st post... kinda interesting to read thz in Winmatrix...
thz kind of solution, even elementary studnt knew 'bout it...
you solve it with "simultaneous equation"... we learn thz in school...

PS: thz is my 1st post since i registered in Winmatrix couple years ago...  