The 11:11 phenomenon and the Fibonacci series... math weirdness

I was sitting here this morning with my thoughts and a cup of coffee (my therapist and her dolls tell me it's ok )... and I was pondering the Fibonacci sequence.

For those who don't know, the Fibonacci sequence is as thus: 0,1,1,2,3,5,8,13,21,34,55... each term is the sum of the two previous terms. This sequence can be found throughout nature... and it has some heavy implications in math, geometry, art... yes, even art. The average between any two terms starting with the numbers 3 and 5 approach, or become nearly equal to the Golden Mean or Golden Ratio... 1.618033~ for instance:

5/3= 1.666 8/5= 1.6 13/8= 1.625 1597/987= 1.618034

The Golden Ratio can be found throughout art, architecture, music, etc...

So, I'm sitting here, and I get a text... at 11:11. I shrug it off... then I wondered. What would happen if you substituted 11:11 for the 1,1 in the sequence. It looks like this: 0,11,11,22,33,55,88,143,231...

The first thing that I noticed was that the two intersect at the 11th term of the Fibonacci sequence: 55

Weirder still was when I lined the two up at the 11th term, and noticed the unsigned difference between the two... that is the 3rd line of numbers... notice something?

0
0
1
2
3
5.....0....5
8.....11...3
13....11...2
21....22...1
34....33...1
55....55...0
89....88...1
144...143..1
233...231..2
377...374..3
610...605..5
987...979..8
1597.1584.13

At the 11th term of the Fibonacci sequence the difference between the two, term for term is the Fibonacci sequence...

I'm sure there is a mathemetologist on here that can explain this... I just thought the synchronicity starting at the 11th term of the Fibonacci series and the 11,11 Fibonacci series was at least worthy of noting

I don't know what you spike your coffee with, but I'd like a cup please.

I am really impressed with your calculations and discovery! And I don't have a clue as to what you're talking about!

S&F !

We live in a weird world...

Weird thinking is how I navigate

a reply to: madmac5150
Does your calculation work with other Fibonacci primes?

originally posted by: Boscov
a reply to: madmac5150
Does your calculation work with other Fibonacci primes?

Haven't tried... honestly still mulling this one. Weirdness takes time...

I have a spreadsheet somewhere that auto calculates it... gotta find it...

a reply to: madmac5150

Nice!!!! Odd coincidence. :-)

Can it go backwards?

a reply to: madmac5150

This could be something known as a Pisano Period, although I'm not entirely sure. Maths aren't my strongest suit. Here's a Numberphile video about Pisano Periods:

You might have discovered a Pisano Period that's train is, well, equal to the Fibonacci Sequence. Maybe. Again, not my strongest suit, so I could also be wrong about this.

~ Wandering Scribe

a reply to: madmac5150

I like it (take a very close look at my avatar that will explain the bias) my question is why the offset of 5 to begin the count ? also if you applied the logic exactly the pattern in the first column should be 0, 1, 1, 2, 3 then 5 , the second column if you applied the same logic should begin with 00, 11, 11, 22, then 33.

I like what you discovered I just don't follow the reasoning for the offset and how you began the counts in the columns which are counter to proper fibonacci sequence, but those numbers are considered master numbers starting at 11 and following the sequence through to like 144, sorry but anyhow you got me looking at this man, I thought subnetting ip addresses all day was a pain.

But you may have discovered something useful if anything because of the patterns you found, you might have accidentally unlocked some unknown pattern that could make you very rich ? if you follow the master numbers, it was given to you at 11:11, Good Luck!

a reply to: madmac5150

I don't know what you're talking about either. But if Dr. Mad says it's true, then it must be true. I failed at maths.

a reply to: phinubian

I didn't offset with 5 as a starting point, rather, I lined them up where they intersected... 55. The 11th term, which is one of the things I found that was unexpected... by me, anyway. Again, I am not a mathmetologist...

Oddly enough, I glanced at my post count...It stands at 1111. Weird.

a reply to: madmac5150

Ok I see your logic now it somewhat makes more sense I will buy that ! you should start a forum area called brainteasers.

a reply to: madmac5150

Fibonnaci sequence can be seen by a matrix recurrence equation

V(n) = M * V(n-1)

where V(n) is a column vector of [X_n; X_n-1]
and M = [1 1; 1 0];

Standard fibonnaci is

V(n) = M^n * [1; 1]

you are looking at V(n) = M^n * [11; 11]
except that the indexing is off by 4 or 5

so you're looking at the difference between the series.

M^n * [1; 1] - M^(n-5) * [11; 11]


take out M^n-5 so you get M^(n-5) * (M^5[1;1] - [11;11])

as n gets larger the effect of the stuff in the parentheses goes down (as it has no dependence on M), and you're dominated by the same multiplication by M which makes Fibonnacci sequences, just delayed by a few n.

What is the stuff in the parentheses, it is [2; -3]. It turns out that M^5 * that is [1;1], and therefore you start out back at the standard fibonnaci sequence.

The positive eigenvalue of M is of course phi, the golden ratio 1/2(sqrt(5)+1)

a reply to: madmac5150

I suggest we go halves on a lottery ticket.....you pick one up tomorrow, and when you turn it in just deduct the fifty cents I owe you and mail be the remaining millions.
We should collect it in one lump sum, I think. I don't want to plan my shopping trips around some annual pay-out.

a reply to: mbkennel

It's been years since I have messed with matrices and algebra... I think myself and others would love to see this translated to plain english

a reply to: madmac5150 I suggest we go halves on a lottery ticket.....you pick one up tomorrow, and when you turn it in just deduct the fifty cents I owe you and mail be the remaining millions. We should collect it in one lump sum, I think. I don't want to plan my shopping trips around some annual pay-out. - See more at: www.abovetopsecret.com...

I'll get right on that

I have also tried the series starting with 0,111,111 and 0,1111,1111 and could not find the same synchronicity as with Fibonacci 0,1,1,2... and 0,11,11,22... maybe the number 11 is just special like that. I don't know...