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How do you use the Fibonacci sequence in the real world?
the bunnies :)
Who created the golden ratio?
The exact first date of use is unknown, but one of the earliest uses was by Plato in the 400s BC. The connection of phi to Pascal's triangle was made when Leonardo Fibonacci created his Fibonacci sequence.
When did Fibonacci relate to the Decimal System.?
Decimal numbers were in use in Europe well before the time of Fibonacci so he would have "related" to them when he started to count!
What do we use the golden ratio also known as phi for?
The main use for the golden ratio is its aesthetic appeal - in art and architecture. Rectangles with the golden ratio as their aspect appeal to the human mind (for some reason). So various aspects of the Parthenon in Athens, for example, have dimensions whose ratio is phi. Phi is closely related to the Fibonacci sequence: the ratio of successive terms of the sequence approaches phi and so, just like the Fibonacci sequence, phi appears in many natural situations. However, there is no particular application based on phi.
Are the first two numbers in the Fibonacci Series 0 and 1 or 1 and 1?
Different authors use different conventions for indexing the Fibonacci sequence (n.b., "sequence" not "series"). For example, in Cameron's Combinatorics, he defines F1=1, F2=2. The most common choice, used for example in Sloane's Online Encyclopedia of Integer Sequences (http://www.research.att.com/~njas/sequences/), is to define thezeroth Fibonacci number to be 0 and the first to be 1; thus the second is also 1. With this choice, a number of formulas become simpler and we have this particularly nice number-theoretic result: if m divides n, then the mth Fibonacci number divides the nth Fibonacci number.
