[Math] Triangles in Equations?

[LiveSsenkrad]

Bleh I did create my post that I wanted, but the post never got through and I was too lazy to retype and post it again. I'll post it again just now, under General Discussion =]

Number triangles? Pythagoras is my theory..

So I was playing around with some square numbers, and I created a sequence, that when looked at in a spreadsheet (will be included) it creates triangles out of numbers.

I'll first try to explain what I did, and by try, I really mean try, because in my head it makes perfect sense =]

So in Column A I created a simple sequence that is double numbers counting: 11; 22; 33; 44; 55 ... 150150.

In Column B I simply squared the numbers in Column A.

In Column C I did something different, I removed the 1ths and 10ths from Column B, why I did this is something I'd rather not go into now.

In Column D I simply squared the single number of the double numbers, e.g.: 150150 is 150^2, 99 is 9^2.

In Column E I subtracted Column D with Column C, and got the absolute value of it.

Column F to Column EY I subtracted the previous Column's number above it, and next to it, e.g.: F11 =ABS(E11-E10).

Now when you take a look at the numbers it forms right-angled triangles everywhere, of all shapes and sizes! Even more peculiar is that the seemingly binary also has triangles in them, just look at the 0's! I want to know why this happens.

Attachments:

Excel File with triangles

Example of triangles:

 

[Jaujarahje]

The screenshot just looks like you used Paint or Photoshop to put triangles in.
I have no idea why it does this, my only guess is some kind of glitch/error?

 

[13lade619]

upload the file here.. (attachment)

 

[thewrongvine]

A better question is why wouldn't it happen.

~Hai-Bye-Vine~

 

[Jindo]

A better question is why wouldn't it happen.

~Hai-Bye-Vine~

If you don't have a helpful answer then please refrain from posting.

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I'm currently trying to replicate this although I've been unsuccessful so far, if you could attach the file it would help greatly.

 

[sqrage]

If you don't have a helpful answer then please refrain from posting.

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I'm currently trying to replicate this although I've been unsuccessful so far, if you could attach the file it would help greatly.

http://www.4shared.com/file/mlgsSt70/WHATTHEHELL.html

He did upload it.

 

[13lade619]

attach here? I cant access 4shared

 

[Jindo]

He did upload it.

Woops, I saw the 4shared link and assumed it was the same as the image

EDIT: My version of Excel doesn't even want to open this correctly.

 

[thewrongvine]

My answer was serious.
If you can't find out why something happens, usually another way is to find out why it doesn't happen.

Test your theory.

That's the most-filled excel file I've ever seen. May I ask where you started with these equations? Especially with row 10 and up, why the jump?

~Hai-Bye-Vine~

 

[Dave312]

That's the most-filled excel file I've ever seen.

That is pretty pathetic. I've worked with spreadsheets with over 500,000 lines. At that amount, excel has a habit of crashing every few minutes. I had to write another program to analyse the data for me because I wasn't getting anywhere with excel.

The reason for the triangles is nothing to do with the numbers you have used but rather how you have arranged your formula's. From the image below, the green box is equal to the difference between the two values in the red box. So your formula is set out in a triangular shape and because it is just the differences, eventually you will get smaller numbers being grouped together.

I then tested my theory by changing all the numbers in column A to a value starting at 1 and incrementing each line by +1 (1, 2, 3, 4, ... etc). Below is the result I get and you can still see all the triangles.

 

[LiveSsenkrad]

Dave seems to be the only guy here that could post something constructive, no offence. So by doing the subtraction in that way creates the triangles?


Heh it's still hard for me to comprehend that subtracting it like that will create triangles in peculiar patterns.

 

[Dave312]

Because you are subtracting in a triangular pattern, small numbers tend to group together in triangular shapes, thus resulting in triangles.

This does remind me of the Sierpinski Triangle (below) which can "modify" a random number and when done many times and the results graphed, you end up with a triangle built of an infinite number of triangles (similar to what you have created).