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Yep, a little confused. I see that
I'm just not sure where that equation came from, it looks a lot like the equation they found to solve the square problem.
Thank you, I really appreciate your help in this.
I would love to, because the only way I can possibly see how to is go through and manually figure them all out, which could take days if the square is a really large one lol.
Yes, they are the same pattern, they both solve the square question - but to use my equation you have to know what
is equal to, so it seems incomplete.Just noticed the math function that we could use, so sorry about the ugly looking equations before.
Yes, that's correct.
Yes, that's what I meant, not sure why I put f(x)^2 at the end, I just mean x^2.
bobbym -
Thank you for the welcome, glad to be here.
But yes the function you last stated was the one I came to, but it doesn't really solve the f(x) unless you know the f(x-1).
And, those are the processes I used in attempting to figure out how to solve the square problem. And yes, there are a lot of patterns in the problem because it deals with squaring numbers and adding them. So, I guess my real question, what would help me the most is: how did whoever came up with the function to solve how many squares are in a larger square, get to their function?
That function being, f(x)=x*(x+1)*(2x+1)/6
There has to be some sort of understanding, maybe something to do with Geometry, that I don't have for someone to come up with this function.
I came to the conclusion...
That, joining this forum was a Nash Equilibrium.
-TheRussEquilibrium
Okay hopefully this doesn't make me look incredibly stupid, but this is my problem. I'm wondering how mathematicians come up with their formulas. For an example, I ran into one of those pictures where it asks you how many squares are inside the other square - and instead of counting them I wanted to find out how to create an equation that would solve the problem. So say the square is a 4x4 square(one big square made up of 16 smaller squares. I attempted to try to figure an equation...well what I came up with was a function that would solve the problem, but only if you knew what the previous function was, as in:
f(x)=f(x-1)+f(x)^2
f(4)= f(3)+16
Well, yeah I created a function, but I can only use it if I know the f(x-1), so I haven't really solved anything. I ended up looking up the formula and the formula to actually solve the equation is:
f(x)=x*(x+1) * (2x+1) / 6
f(4)=4*(5) * (9) / 6 = 180/6 = 30
And I can't figure out for the life of me how you would come up with this equation.
I seem to try to create equations for almost anything, and I feel like I have really good ideas, but what I always come up with gets me close to something but it never gets me to that something which is extremely frustrating.
Another example of me trying to do something like this was when I was extremely bored at work so I decided to try to figure out how to convert Fahrenheit to Celsius, in which well I had no idea how to go about doing this but I came up with something that get's you fairly close to the correct answer, as long as the numbers don't get really big.(Which makes me feel like Newton compared to Einstein, which probably means it's because I don't have a large enough understanding of Mathematics.)
C= (F/2) - 16 (Which is obviously rather simple, but gets you somewhat close to the correct answer. And yes I do know the correct formula now...)
But anyways, any help/advice/ or even links to something that could help me in understanding how Mathematicians find these functions would be greatly appreciated.