THE GODDAMN NUMBERS!

[teh_n00b_root]

Ive been obsessed with this all day. I think i may have discovered a new mathmatical theory. I havent found traces of this anywhere on the internet. It is already probably a theory but id like to make sure
The theory goes:

Take 2 consecutive triangle numbers

3,6 (or any it works with all of them)

3*3 (3 squared) =9
6*6 =36

the difference between theese is 27

27 = 3*3*3 (3 cubed)

So take two consecutive triangle numbers square them and find the difference and you are left with and you will have a cube number.

The strange part for me is what then is a cubed triangle? A tetrohedron? A freaky 4d shape? But Ill stop rambling.

So does anyone know if this is already a theory? Or is this still unclaimed territory?

 

[mip0]

I haven't seen it before. I could ask my teacher though, who should know.

EDIT: I assume you have noticed what number you get the cube of too (but I hope you have not 8P). If not:
1+2+3+...+n = a[sub]n[/sub]
(a[sub]n[/sub])[sup]2[/sup] - (a[sub]n-1[/sub])[sup]2[/sup] = n[sup]3[/sup]

 

[teh_n00b_root]

Mine didnt! haha

 

[teh_n00b_root]

I haven't seen it before. I could ask my teacher though, who should know.

EDIT: I assume you have noticed what number you get the cube of too (but I hope you have not 8P). If not:
1+2+3+...+n = a[sub]n[/sub]
(a[sub]n[/sub])[sup]2[/sup] - (a[sub]n-1[/sub])[sup]2[/sup] = n[sup]3[/sup]

Yeah Like i said ive been obsessing about this all day.

 

[mip0]

So I had math today and asked my teacher about this.
He hadn't heard about it before but said with a sentimental and understanding expression:
- Well of course it's been discovered.
And I believe him. It wasn't clear to me yesterday but there's a simple explanation. You couldn't find it on the web and my teacher hadn't heard about it because it isn't a big discovery enough too be named after someone or have it's own little part in the math books.
Sorry 8|

 

[Binerexis]

If it was something that worked with differences of ALL triangle numbers then it'd be worth something of note.

 

[Contun]

Ughhn...

Ma' Brain Hurts....