Re: is there a connection between the fibonacci series and the mobius strip?

Hi, Christophere.

I am afraid the connection you have found is a very simple and 
straightforward mathematical one. You are looking at the Fibonacci 
sequence in modulo 10 arithmetic. each number depends on the two that 
go immediately before it. If ever the sequence reaches the numbers 
(10-t0) and (10-t1), then the next number in the sequence will be (20 - t0 - 
t1) = (10 - t2), and so on. It must continue 10-t2, 10-t3, 10-t4, and so on. 
The only question is whether you ever reach the point where you get the 
complements of the 0,1 that starts the sequence appearing as 
successive terms.

You can check this by working with another digital base, say modulo 12. 
The sequence goes

0,1,1,2,3,5,8,1,9,10,7,5,0,5,5,10,3,1,4,5,9,2,11,1,0,1

This time, we have not reached the complement numbers 0,11, but the 
starting numbers 0,1 instead. The sequence will repeat without ever 
reaching the complements.

Trying modulo 7

0,1,1,2,3,5,1,6,0,6

we reach the complement numbers very quickly. This particular Moebius 
strip would only have 16 numbers on it in 8 pairs.

a similar thing happens with repeating decimals:

1/17 is .05882352941176470588... etc.

Note how the second set of 8 numbers are the complement of the first 
(adding to 9).

1/19 is .0526315789473684210526... etc.

with sets of 9 numbers complementing each other.


The Moebius strip has no real significance, other than being a neat and 
convenient way to display the complementarity in halves of a continuing 
and repeating sequence.