Fibonacci numbers are 1, 1, 2, 3, 5, 8, 13, ...
You add two previous terms you get the next term.
If you put F(n) as the nth Fibonacci number,
the golden ratio (φ) is
lim(n→inf) F(n+1)/F(n)
that is because
F(n) = (φ^n-(-φ)^(-n))/(√5)
Other properties of φ
φ = (1+√(5))/2
1/φ = φ-1
φ2 = φ+1
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I'm currently doing a project on this, My project is based on the idea that if you had a group of rectangles and one of them was in the Golden ratio then they would prefer the golden ratio over the others.See related link below for more help
The ratio of dividing the larger Fibonacci number into the smaller Fibonacci number gives you the golden ratio (1.618 to 1). -------- The Golden Ratio is the number (1+sqrt(5))/2~=1.618 The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... . Skipping the first two terms, if you divide one term in this sequence by the previous term the resulting sequence converges to the Golden Ratio: 1.0000 2.0000 1.5000 1.6667 1.6000 1.6250 1.6154 1.6190 1.6176 1.6182 1.6180 Please see the link for more information.
well a synopsis of it is that a fraction is a for of splitting something in to pieces like 1\2 is half of anything. where as a ratio is just a number divided by another number. In a 100:10 form which is 100 divided by 10 and the answer is obviously 10.
The related link provides an excel template and some notes on how to calculate the sharpe ratio..pretty simple and effective.
Nominal, ordinal, interval and ratio. Please see the link.