AS192/KH0210

Original Author: Marcia & Robert Ascher
Museum: American Museum of Natural History, NY
Museum Number: 41.2/6701
Provenance: Unknown
Region: Ica 		Total Number of Cords: 13
Number of Ascher Cord Colors: 4
Similar Khipu:  Previous (UR161)  Next (UR223)
Catalog: AS192
Khipu Notes: Khipu Notes

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Khipu Notes

Ascher Databook Notes:
  1. AS190-AS197 were purchased by the Museum in 1969 from Louis Slavitz. Their provenance is near Callengo, lea Valley. They are compared following AS191.
  2. Pendant 1 is a sum cord for the group since the value on it and on its 3 subsidiaries all can be obtained by summing other pendant values in the group.
    \[ P_{1} = \sum\limits_{i=3}^{10} P_{i} \]
    \[ P_{1s1} = \sum\limits_{i=3}^{6} P_{i} \]
    \[ P_{1s2} = \sum\limits_{i=3}^{5} P_{i} \]
    \[ P_{1}s_{3} = \sum\limits_{i=3}^{5} (P_{i} + P_{12-i}) \]
  3. An unusual number of perfect squares are values on the cords:

    P1 s1 = 49 = 72
    P1 s3 = 64 = 82
    P3 = 16 = 42
    P10 = 36 = 62

  4. In keeping with observations 2 and 3, additional perfect squares can be found by summing cord values. The number of them and their patterned appearance seem to be more than chance.

    1. Separating the 9 pendants (P2-P10) into subgroups of 1, 3, 1, 3, 1 pendants each and calling them:

      Yi i=(1,...,5) (i. e., Y1 = P2; Y2 = P3 + P4 + P5; Y3 = P6; Y4 = P7 + P8 + P9; Y5 =P 10)

      The following hold:

      1. Y1 + Y3 + Y5 = 92
        Y2 + Y4 = 82

      2. Y4 = 52
        Y5 = 62
        Y2 + Y3 = 72
        Y2 + Y4 = 82
        Y2 + Y4 + Y5 = 102
      3. \[ Y_{2}+Y_{3} = \sum\limits_{i=3}^{6} P_{i} = {7}^{2} \]
        \[ \sum\limits_{i=3}^{6} (P_{i})^{2} = {25}^{2} \]
      4. The values on P1 and its subsidiaries can also be expressed in terms of these subgroups:

        P1 = Y2 + Y3 + Y4 + Y5
        P1 s1 = Y2 + Y3
        P1 s2 = Y2
        P1 s3 = Y2 + Y4

    2. An alternate separation into subgroups of 3, 1, 1, 1, 3 pendants such that:

      Y1=P2+P3+P4
      Y2=P5
      Y3=P6
      Y4=P7
      Y5=P8+P9+P10

      gives:

      Y1+Y3+Y5=112

    3. Finally, the sum cord P1 and its subsidiaries can be viewed in terms of squares.

      P1 =52 + 62 + 72
      P1 s3 =82
      P1 - P1 s1 =52 + 62 P1 s3-P1 s2 = 52

      or

      P1 - P1 s1 + P1 s2 = 62 + 82 =102
      P1 s3 - P1 s2 + P1 s1 = 52 + 72
      P1 - P1 s1+P1 s2 - P1 s3 = 62
      -(P1 s3 - P1 s2 + P1 s1) + P1 = 62