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The x5 sets

🔗Stearns <stearns@xxxxxxx.xxxx>

1/25/1999 12:00:15 PM

x5 sets
____________________________________________________

1x5
(1)d � O � F = 1/0
(5)d � O � F = 3/2

1 + 3 4
------- = ---- 6(d)
0 + 2 2

The 1x5 pentad is a non-apical set (i.e., one where [n]tad>[n]d � O � F)
that draws its step structure from an inverted f�Ff�FF. The 'formula' I use
to determine fourth space would be:

FF
F -------
d ---- Ff
f

Or:

2(iw)
3 --------
5 ---- 1(ih)
2(iw)

where "i" is inversion and wwhww is hhwhh @: 0 1 2 4 5 6. As a multiple of
one (1 � 5/5 � 1), a 1x[n-tad] can only define the borders the 0=h Ps, all
n-tET�s after 1x5/5x1 have a hhwhh pentad.

1 5x1
2
3
4
1x5�

1 2 3 4 5
[6]�

____________________________________________________

2x5
(2)d � O � F = 1/1
(5)d � O � F = 3/2

1 + 3 4
------- = ---- 7(d)
1 + 2 3

The 2x5 pentad is also a non-apical set (as [5]tad>[7]d � O � F):

3(iww�h)
5 ---------------
2(iw�h)

whwwh=hwhhw: 0 1 3 4 5 7

2 5
4 7 5x2
6 9�
8
2x5

2 4 1 3 5
7 9 6 8 10

Es@ 1, 3, and 5
Ps@ 2, 4, 6, 8, and 10
Is@ 7 and 9
____________________________________________________

3x5
(3)d � O � F = 2/1
(5)d � O � F = 3/2

2 + 3 5
------- = ---- 8(d)
1 + 2 3

The 3x5 pentad is an apical set where the n-tad equals the nF of nd � O � F.

3(ww�h)
5 --------------
2(w�h)

0w2h3w5w7h8

3 5
6 8 10
9 11 13 5x3
12 14�
3x5

3 1 4 2 5
8 6 9 7 10
13 11 14 12 15

Es @ 1, 4, 2, 7, 5 and 10
Ps @ 3, 6, 9, 12, and 15
Is @ 8, 13, 11 and 14
____________________________________________________

4x5
(4)d � O � F = 2/2
(5)d � O � F = 3/2

2 + 3 5
------- = ---- 9(d)
2 + 2 4

The 4x5 pentad is also an apical set (as [5]tad = [9]d � O � F):

2w
3 --------
5 ---- 1h
2w

0w2w4h5w7w9

0. (ww)h(ww)
2. whwww
4. h(ww)(ww)
5. (ww)(ww)h
7. wwwhw
9. (ww)h(ww)

4 5
8 9 10
12 13 14 15
16 17 18 19 5x4
4x5�

4 3 2 1 5
9 8 7 6 10
14 13 12 11 15
19 18 17 16 20

Es @ 3, 2, 1, 5, 7, 6, 10, 11, and 15
Ps @ 4, 8, 12, 16, and 20
Is @ 9, 14, 13, 19, 18, and 17

w=2 h=1
0 2 4 5 7 9
0 267 533 667 933 1200

w=3 h=2
0 3 6 8 11 14
0 257 514 686 943 1200

w=4 h=3
0 4 8 11 15 19
0 253 505 695 947 1200

w=5 h=4 0 5 10 14 19 24
w=6 h=5 0 6 12 17 23 29
w=7 h=6 0 7 14 20 27 34
...

w=3 h=1
0 3 6 7 10 13
0 277 554 646 923 1200

w=4 h=2
0 4 8 10 14 18
0 267 533 667 933 1200

w=5 h=3 0 5 10 13 18 23
w=6 h=4 0 6 12 16 22 28
w=7 h=5 0 7 14 19 26 33
...

w=4 h=1
0 4 8 9 13 17
0 282 565 635 918 1200

w=5 h=2 0 5 10 12 17 22
w=6 h=3 0 6 12 15 21 27
w=7 h=4 0 7 14 18 25 32
...

w=5 h=1 0 5 10 11 16 21
w=6 h=2 0 6 12 14 20 26
w=7 h=3 0 7 14 17 24 31
...

w=6 h=1 0 6 12 13 19 25
w=7 h=2 0 7 14 16 23 30
w=8 h=3 0 8 16 19 27 35
...

Dan

🔗alves@xxxxx.xx.xxx.xxxxxxxxxxxxxxx)

1/25/1999 12:06:02 PM

This character
>(1)d � O � F = 1/0
^
appears as a rectangle on my system. Is there a way to express your
formulas using just the 7-bit ascii standard?

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)607-7600 (fax) ^
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