Hola
 
I was making my own shell measurement system and probing the different
methods
that came to my mind and was able to use, when I thought about measuring
the
different whorls of the same shell; I used one shell that I am trying to
identify and I measure each of the ten whorls from tip to sutura, except
the
last that is the total length of the shell; my methods are not very
precise but
were enough to suspect that those lenghts follow the golden rule.
The golden rule is an old (Greeks at least) known relation of numbers;
here it
can be stated as:
If you know the length of the first n whorls then you can calculate the
length
of the n+1 first whorls by multiplying by the number 1,618; also, if you
know
the lenght of the first n whorls then you can calculate the length of
the first
n-1 whorls dividing by 1,618 (or multiplying by 0,618).
 
The total length was 14,2mm, and using this approach the other lengths
could
be:
(14,2  ;  8,8  ;  5,4  ;  3,4  ;  2,1  ; 1,3  ;  0,8  ;  0,5  ;  0,3  ;
0,2)
I used in the calculations all the decimals but I write here only the
first.
The observed lenghts were:
(14,2  ;  7,5  ;  5,7  ;  3,6  ;  2,3  ;  1,5  ; 1,0  ;  0,5  ;  0,3  ;
0,1)
(I used paper with lines printed each 0,2mm, I put the shell above the
paper
and I saw using the microscope and counted lines)
The only gross change is 8,8 vs 7,5 (?Why?)
 
I know that different annimals and vegetals use the golden rule (and the
Fibonacci series) for different things. ?How about molluscs?
 
I am very interested in this
Emilio.
 
Excuse me [log in to unmask], I send this mesage to you; I don4t
understad how?