Very interesting, Linda. 1.61803 looks familiar, but I can't quite recognize
it. No, it's not
^.5
1.60944
--Kip Murray
Sent from my iPad
> On Feb 23, 2014, at 2:16 AM, "Linda Alvord" <[email protected]> wrote:
>
> ]A=:>:i.8
>
> 1 2 3 4 5 6 7 8
>
> +/A
>
> 36
>
> A+/A
>
> 2 3 4 5 6 7 8 9
> 3 4 5 6 7 8 9 10
> 4 5 6 7 8 9 10 11
> 5 6 7 8 9 10 11 12
> 6 7 8 9 10 11 12 13
> 7 8 9 10 11 12 13 14
> 8 9 10 11 12 13 14 15
> 9 10 11 12 13 14 15 16
>
> +\A
>
> 1 0 0 0 0 0 0 0
> 1 2 0 0 0 0 0 0
> 1 2 3 0 0 0 0 0
> 1 2 3 4 0 0 0 0
> 1 2 3 4 5 0 0 0
> 1 2 3 4 5 6 0 0
> 1 2 3 4 5 6 7 0
> 1 2 3 4 5 6 7 8
>
> +/\A
>
> 1 3 6 10 15 21 28 36
>
> A+/\A
>
> 1 2 3 4 5 6 7 8
> 3 5 7 9 11 13 15 0
> 6 9 12 15 18 21 0 0
> 10 14 18 22 26 0 0 0
> 15 20 25 30 0 0 0 0
> 21 27 33 0 0 0 0 0
> 28 35 0 0 0 0 0 0
> 36 0 0 0 0 0 0 0
>
>
>
> ]B=:8$1
>
> 1 1 1 1 1 1 1 1
>
> +/B
>
> 8
>
> B+/B
>
> 2 2 2 2 2 2 2 2
> 2 2 2 2 2 2 2 2
> 2 2 2 2 2 2 2 2
> 2 2 2 2 2 2 2 2
> 2 2 2 2 2 2 2 2
> 2 2 2 2 2 2 2 2
> 2 2 2 2 2 2 2 2
> 2 2 2 2 2 2 2 2
>
> +\B
>
> 1 0 0 0 0 0 0 0
> 1 1 0 0 0 0 0 0
> 1 1 1 0 0 0 0 0
> 1 1 1 1 0 0 0 0
> 1 1 1 1 1 0 0 0
> 1 1 1 1 1 1 0 0
> 1 1 1 1 1 1 1 0
> 1 1 1 1 1 1 1 1
>
> +/\B
>
> 1 2 3 4 5 6 7 8
>
> B+/\B
>
> 1 1 1 1 1 1 1 1
> 1 1 1 1 1 1 1 1
> 1 1 1 1 1 1 1 1
> 1 1 1 1 1 1 1 1
> 1 1 1 1 1 1 1 1
> 1 1 1 1 1 1 1 1
> 1 1 1 1 1 1 1 1
> 1 1 1 1 1 1 1 1
>
>
>
> ]C=:8$1x
>
> 1 1 1 1 1 1 1 1
>
>
>
> (+%)/A
>
> 1.43313
>
> (+%)/B
>
> 1.61905
>
> (+%)/C
>
> 34r21
>
>
>
>
>
> (+%)/\A
>
> 1 1.5 1.42857 1.43333 1.43312 1.43313 1.43313 1.43313
>
> (+%)/\B
>
> 1 2 1.5 1.66667 1.6 1.625 1.61538 1.61905
>
> (+%)/\C
>
> 1 2 3r2 5r3 8r5 13r8 21r13 34r21
>
>
>
> f=: 13 :'(+%)/\y$1'
>
> f
>
> [: (+ %)/\ 1 $~ ]
>
>
>
> g=: 13 :'(+%)/\y$1x'
>
> g
>
> [: (+ %)/\ 1x $~ ]
>
>
>
> f 16
>
> 1 2 1.5 1.66667 1.6 1.625 1.61538 1.61905 1.61765 1.61818 1.61798 1.61806
> 1.61803 1.61804 1.61803 1.61803
>
>
>
> g 16
>
> 1 2 3r2 5r3 8r5 13r8 21r13 34r21 55r34 89r55 144r89 233r144 377r233 610r377
> 987r610 1597r987
>
>
>
> (f"0) >:i.8
>
> 1 0 0 0 0 0 0 0
> 1 2 0 0 0 0 0 0
> 1 2 1.5 0 0 0 0 0
> 1 2 1.5 1.66667 0 0 0 0
> 1 2 1.5 1.66667 1.6 0 0 0
> 1 2 1.5 1.66667 1.6 1.625 0 0
> 1 2 1.5 1.66667 1.6 1.625 1.61538 0
> 1 2 1.5 1.66667 1.6 1.625 1.61538 1.61905
>
>
>
> (g"0) >:i.8
>
> 1 0 0 0 0 0 0 0
> 1 2 0 0 0 0 0 0
> 1 2 3r2 0 0 0 0 0
> 1 2 3r2 5r3 0 0 0 0
> 1 2 3r2 5r3 8r5 0 0 0
> 1 2 3r2 5r3 8r5 13r8 0 0
> 1 2 3r2 5r3 8r5 13r8 21r13 0
> 1 2 3r2 5r3 8r5 13r8 21r13 34r21
>
>
>
> 1 +. f 8
>
> 1 1 0.5 0.333333 0.2 0.125 0.0769231 0.047619
>
>
>
> 1 +. g 8
>
> 1 1 1r2 1r3 1r5 1r8 1r13 1r21
>
>
>
> % 1 +. f 8
>
> 1 1 2 3 5 8 13 21
>
>
>
> % 1 +. g 8
>
> 1 1 2 3 5 8 13 21
>
>
>
> fib=: 13 :'%1+.(+%)/\y$1'
>
> fib
>
> [: % 1 +. [: (+ %)/\ 1 $~ ]
>
> fib 18
>
> 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584
>
>
>
> Children learn to read before writing. So we should tell tales to
> beginners. If you know this already you can read it quickly and be done.
> You are ready for more complex tales. If you are just learning to read, it
> may become a favorite "Bedtime Story" to be repeated until it is no longer
> interesting. Happy reading.
>
>
>
> Linda
>
>
>
>
>
> ----------------------------------------------------------------------
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