Identifying and Expressing Patterns

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I can identify patterns really well. I can explain them using pictures, usually stacking numbers on top of each other or, taking slices/boxes of numbers and putting them in different parts to make the pattern work. I can't express myself at all in terms of a mathematical equation.

eg.

fibonacci sequence

1, 1, 2, 3, 5, 8, 13, ...

the way i understand this takes me two seconds, it's like flipping pages in a book to make a pyramid...

the equation to describe the nth fibonacci number took me like 5 hours to write down
n = (n -1) + (n -2)

anyone have tips on translating pictures into formulas lol?

I usually visualize solutions before formulas but usually I don't have big problem translating them into formulas. Basically you need to know geometry and some discrete math.

I'll make you an example, when I was 10 I argued with my teacher that many "prodige" of the past will be normal people nowaday because what they discovered was really simple and now you need far more effort to find new things. So she gave us a work saying that (Gauss?) solved it at our age:

What is the sum of the first n numbers? It takes me around 10 minute to solve it and the teacher said "You already known that" but she was lieing. Actually it was simple:

Summing n numbers mean doing a square triangle:

1) X
2) XX
3) XXX
4) XXXX
...

If each number take 1 block then I can apply the formula to compute the are of a square triangle = base x height /2 so it was (n^2) / 2 this was only approximately true because my triangle was discrete so I need to add up "half square" for each step = n/2 so finally the solution was n^2 / 2 + n/2. Normally it's written like n(n+1)/2.

Also the fibonacci "solution" you wrote is only the implicit function (like saying that the solution to 1,2,3,4,5 is n=n+1 instead of n(n+1)/2) the explicit solution is far more complicated
http://users.tellurian.com/hsejar/maths/fibonacci/