DislikedYou know Y i have it in my user name and for fib, its a Reciprocal ( 1/x ) of fib # 1.27 .Ignored
Start at zero and add one, then continue to add the previous number to form a sequence...0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, …
Now you divide any two adjacent numbers to get the magical golden ratio number of 1.618; the higher up the sequence you go, the more accurate the golden ratio. For example, 5/3 = 1.66, but 610/377 = 1.618037 - freaky huh!
Now to find any fib level, we divide different (non-adjacent) numbers, higher up in the sequence to get more accurate numbers:-
For example, pick ANY two numbers
55 / 233 = 0.236
89 / 610 = 0.1459
34/55 = 0.61818
34/89 = 0.3820
etc, etc
What you'll notice from above, is that you there is no natural fib level for anything higher than 61.8%. So to find fib levels of 76.4%, we subtract the natural fib level of 23.6% from 100% = 76.4%.
To get a 78.6% fib level, it is the square root of 61.8%, so is subjective, but whatever floats your boat.
I then thought of analysing instances of these numbers within the golden ratio, to see if there are any patterns. Here's the first part from this page:
QuoteDisliked1.61803398874989484820458683436563811772030917980576286213544862270526046281890
244970720720418939113748475408807538689175212663386222353693179318006076672635
443338908659593958290563832266131992829026788067520876689250171169620703222104
321626954862629631361443814975870122034080588795445474924618569536486444924104
432077134494704956584678850987433944221254487706647809158846074998871240076521
7057517978834166256249407589069704000281210427621771117778053...
Fib level......Number........Count
14.6%........146............. 49
23.6%........236..............44
38.2%........382..............58
50%...........500..............37
61.8%........618..............47
76.4%........764..............62
78.6%........786..............48
88.6%........886..............50
Extensions
100%.........100..............46
114%.........114..............38
127%.........127..............60
141%.........141..............53
etc, etc
So we can see that 76.4% is indeed relevant, but I'm stubborn so will now use the average of 76.4 and 78.6; my new fib level = 77.5%.
HTH
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