Talk:Fibonacci sequence
The main page says:
- A logarithmic spiral can be approximated as follows: start at the origin of the cartesian coordinate system, move F(1) units to the right, move F(2) units
up, move F(3) units to the left, move F(4) units down, move F(5) units to the right etc.
Is it not the case that a logarithmic spiral can be approximated just as well by moving an units at step n for any fixed a whatsoever? For example, I might move 1 unit right, 2 units up, 4 units left, 8 units down, 16 units right, etc., and get an approximation to a logarithmic spiral also? In which case, this is not a property of the Fibonacci numbers except by virtue of the fact that they happen to approximate a geometric sequence.
The main page continues:
- This is similar to the construction mentioned in the golden mean
article. Fibonacci number s often occur in nature when logarithmic spirals are built from discrete units, such as in sunflowers or in pine cones.
The pine cone thing (phyllotaxis) is related to the Fibonacci numbers, or, more precisely, to the golden ratio. The arrangements of pine cone bracts and other plant parts into Fibonacci spirals can be explained by a number of arguments; see for example pp. 408-412 of A New Kind of Science.
I am going to remove the logarithmic spiral remark from the main page unless someone corrects me soon.
Dominus 09:03, 6 Nov 2003 (UTC)