Comments on Profile Post by Elite

oooo triangular numbers <3

Oh, you graphed it? xD

The whole purpose of me coming up with this tbh, was to prove the sum of all numbers is equal to - 1/12 is invalid...But a usage of it, at least, is for example:

1 + 2 = 3 ... 1 + 2 + 3 = 6 ... 1 + 2 + 3 + 4 = 10... etc ...if you were to plug the number 4 in place of A, you would get the sum of all positive numbers preceding 4, including 4 :)

The way I found it was, I noticed the ratio of sum of numbers over the amount of numbers, was proportional, and only increased by 0.5 each time... So I just multiplied the amount of numbers by 0.5 (aka divide by 2) ... multiplied that by the amount of numbers (minus 1) ...then just added the amount of numbers to get the sum of that amount of numbers :)

I personally prefer the cubic formula. It's an absolute ridiculous thing to memorize, but it leaves everyone in awe.

I loved doing those - When i'm on computer tomorrow - I could show examples of square or cube jumping :) ...formula is only useful for programming, but there are mental math tricks, too :D

I was bored in Geometry and came up with a function to find how many blocks are in a (solid) pyramid. I may actually use it a bit with regard to beacons and smp9's love for pyramid builds.

n = height [4(n^3)-n]/3 Boy does that look messy

examples:
1 (1)
1 + 3^2 (10)
1 + 3^2 + 5^2 (35)
etc...

So if you wanted to find the amount of blocks in a pyramid and the height was four (7x7, 5x5, 3x3, 1x1) you could plug 4 into the function.

4(4^3)-4 -> 4(64)-4 -> 256-4 -> 252/3 -> 84 -> 49+25+9+1=84

That's pretty nifty :)

I love proving the Euler's formula: e^i(pi) + 1 = 0

When I first looked at it, I thought it would be pretty simple, and then I delved into the world of derivations.