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

i first thought of this about a year ago, which is part of a larger theory i am 
exploring. then i recently took the repeating sixty final digits and wrote them 
on a mobius strip at equal intervals so it looked like an unending series of 
digits. i found that digits aligning on either side add up to ten every time. 
while i am this for contemplating a metaphysical connection, i need to know if 
there is a simple, legitimate mathematical connection first, in case this is 
just a lucky coincidence. 

essentially:
011235831459437077415617853819
099875279651673033695493257291 (0112358...)
------------------------------
000000000000000000000000000000 (zeros, if single last-digit is used again.)


a philosophical theory hinges on the precipice here... ;) thanks.

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