# [Math] Triangles in Equations?

##### Member
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

##### I have now changed this in the User CP
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?

#### thewrongvine

##### The Evolved Panda Commandant
A better question is why wouldn't it happen.

~Hai-Bye-Vine~

#### Jindo

##### Self
A better question is why wouldn't it happen.

~Hai-Bye-Vine~

---

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

##### is now a game developer :)
attach here? I cant access 4shared

#### Jindo

##### Self

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

##### The Evolved Panda Commandant
If you can't find out why something happens, usually another way is to find out why it doesn't happen.

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

##### Censored for your safe viewing
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.

#### Attachments

• MathTriangles.png
4.5 KB · Views: 539
• MathTriangles2.png
27.2 KB · Views: 517

##### Member
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

##### Censored for your safe viewing
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).

General chit-chat
Help Users
• No one is chatting at the moment.
• The Helper:
If you are new to the site please check out the Recipe and Food Forum https://www.thehelper.net/forums/recipes-and-food.220/
• Monovertex:
How come you're so into recipes lately? Never saw this much interest in this topic in the old days of TH.net
• Monovertex:
Hmm, how do I change my signature?
• tom_mai78101:
Signatures can be edit in your account profile. As for the old stuffs, I'm thinking it's because Blizzard is now under Microsoft, and because of Microsoft Xbox going the way it is, it's dreadful.
• The Helper:
I am not big on the recipes I am just promoting them - I use the site as a practice place promoting stuff
+2
• Monovertex:
@tom_mai78101 I must be blind. If I go on my profile I don't see any area to edit the signature; If I go to account details (settings) I don't see any signature area either.
• The Helper:
You can get there if you click the bell icon (alerts) and choose preferences from the bottom, signature will be in the menu on the left there https://www.thehelper.net/account/preferences
• The Helper:
I think I need to split the Sci/Tech news forum into 2 one for Science and one for Tech but I am hating all the moving of posts I would have to do
• The Helper:
What is up Old Mountain Shadow?
• The Helper:
Happy Thursday!
+1
• Varine:
Crazy how much 3d printing has come in the last few years. Sad that it's not as easily modifiable though
• Varine:
I bought an Ender 3 during the pandemic and tinkered with it all the time. Just bought a Sovol, not as easy. I'm trying to make it use a different nozzle because I have a fuck ton of Volcanos, and they use what is basically a modified volcano that is just a smidge longer, and almost every part on this thing needs to be redone to make it work
• Varine:
Luckily I have a 3d printer for that, I guess. But it's ridiculous. The regular volcanos are 21mm, these Sovol versions are about 23.5mm
• Varine:
So, 2.5mm longer. But the thing that measures the bed is about 1.5mm above the nozzle, so if I swap it with a volcano then I'm 1mm behind it. So cool, new bracket to swap that, but THEN the fan shroud to direct air at the part is ALSO going to be .5mm to low, and so I need to redo that, but by doing that it is a little bit off where it should be blowing and it's throwing it at the heating block instead of the part, and fuck man
• Varine:
I didn't realize they designed this entire thing to NOT be modded. I would have just got a fucking Bambu if I knew that, the whole point was I could fuck with this. And no one else makes shit for Sovol so I have to go through them, and they have... interesting pricing models. So I have a new extruder altogether that I'm taking apart and going to just design a whole new one to use my nozzles. Dumb design.
• Varine:
Can't just buy a new heatblock, you need to get a whole hotend - so block, heater cartridge, thermistor, heatbreak, and nozzle. And they put this fucking paste in there so I can't take the thermistor or cartridge out with any ease, that's 30 dollars. Or you can get the whole extrudor with the direct driver AND that heatblock for like 50, but you still can't get any of it to come apart
• Varine:
Partsbuilt has individual parts I found but they're expensive. I think I can get bits swapped around and make this work with generic shit though
• Ghan:
Heard Houston got hit pretty bad by storms last night. Hope all is well with TH.
• The Helper:
Power back on finally - all is good here no damage
+2
• V-SNES:
Happy Friday!
+1
• The Helper:
New recipe is another summer dessert Berry and Peach Cheesecake - https://www.thehelper.net/threads/recipe-berry-and-peach-cheesecake.194169/

### Members online

No members online now.