[Jprogramming] A Tale Without End

[Linda Alvord]

   ]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