posted on Jun, 10 2016 @ 11:21 PM
While I was trying to get to sleep last night I ended up developing a mathematical formula for finding the differences between any two numbers that
share the same power. It ends up being pretty hilariously convoluted for reaching a relatively simple goal.
Where y is the difference.
Where b is how large the gap is. (E.g. between 5 and 10, the gap is 5, 3 and 4, the gap is 1.)
Where c is the power.
The basic first form is: y=(x+b)^c - x^c
As an example, if you wanted to create a graph showing the differences between a cubed number, and a cubed number that has a base three larger than
itself, it would be:
y=(x+3)^3 - x^3
y=(x+3)(x+3)(x+3) - x^3
y=(x+3)(x^2 +6x +9) - x^3
y= x^3 + 6x^2 + 3x^2 + 18x + 9x + 27 - x^3
y= 9x^2 + 27x + 27
Now that you have the graph, if you want to know the difference between, say, 18^3 and 21^3, you plug 18 into the equation, and you get:
y=(9)(18)(18) + (27)(18) + 27
And checking it...
21^3 = 9261
18^3 = 5832
9261-5832 = 3429.
So, yes, it works. It should theoretically work for any power and difference. Only issue is that if you want it for something like x^21 and 173
steps ahead, the formula is going to be loooong.