AS192
Wide View 
OKR Name: 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 Benford Match: 0.847 Similar Khipu: Previous Next 
Use ⌘ + or ⌘ – to Zoom In or Out
Khipu Notes
Ascher Databook Notes:
 AS190AS197 were purchased by the Museum in 1969 from Louis Slavitz. Their provenance is near Callengo, lea Valley. They are compared following AS191.
 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.
\[ P_{1} = \sum\limits_{i=3}^{10} P_{i} \]\[ P_{1s1} = \sum\limits_{i=3}^{6} P_{i} \]\[ P_{1s2} = \sum\limits_{i=3}^{5} P_{i} \]\[ P_{1}s_{3} = \sum\limits_{i=3}^{5} (P_{i} + P_{12i}) \]  An unusual number of perfect squares are values on the cords:
P_{1} s_{1} = 49 = 7^{2}
P_{1} s_{3} = 64 = 8^{2}
P_{3} = 16 = 4^{2}
P_{10} = 36 = 6^{2}
 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.
 Separating the 9 pendants (P2P10) into subgroups of 1, 3, 1, 3, 1 pendants each and calling them:
Y_{i} i=(1,...,5) (i. e., Y_{1} = P_{2}; Y_{2} = P_{3} + P_{4} + P_{5}; Y_{3} = P_{6}; Y_{4} = P_{7} + P_{8} + P_{9}; Y_{5} =P _{10})
The following hold:

Y_{1} + Y_{3} + Y_{5} = 9^{2}
Y_{2} + Y_{4} = 8^{2}

Y_{4} = 5^{2}
Y_{5} = 6^{2}
Y_{2} + Y_{3} = 7^{2}
Y_{2} + Y_{4} = 8^{2}
Y_{2} + Y_{4} + Y_{5} = 10^{2}

\[ Y_{2}+Y_{3} = \sum\limits_{i=3}^{6} P_{i} = {7}^{2} \]\[ \sum\limits_{i=3}^{6} (P_{i})^{2} = {25}^{2} \]
 The values on P1 and its subsidiaries can also be expressed in terms of these subgroups:
P_{1} = Y_{2} + Y_{3} + Y_{4} + Y_{5}
P_{1} s_{1} = Y_{2} + Y_{3}
P_{1} s_{2} = Y_{2}
P_{1} s_{3} = Y_{2} + Y_{4}

Y_{1} + Y_{3} + Y_{5} = 9^{2}
 An alternate separation into subgroups of 3, 1, 1, 1, 3 pendants such that:
Y_{1}=P_{2}+P_{3}+P_{4}
Y_{2}=P_{5}
Y_{3}=P_{6}
Y_{4}=P_{7}
Y_{5}=P_{8}+P_{9}+P_{10}
gives:
Y_{1}+Y_{3}+Y_{5}=112
 Finally, the sum cord P1 and its subsidiaries can be viewed in terms of squares.
P_{1} =5^{2} + 6^{2} + 7^{2}
P_{1} s_{3} =8^{2}
P_{1}  P_{1} s_{1} =5^{2} + 6^{2} P_{1} s_{3}P_{1} s_{2} = 5^{2}
or
P_{1}  P_{1} s_{1} + P_{1} s_{2} = 6^{2} + 8^{2} =10^{2}
P_{1} s_{3}  P_{1} s_{2} + P_{1} s1 = 5^{2} + 7^{2}
P_{1}  P_{1} s1+P_{1} s_{2}  P_{1} s_{3} = 6^{2}
(P_{1} s_{3}  P_{1} s_{2} + P_{1} s_{1}) + P_{1} = 6^{2}
 Separating the 9 pendants (P2P10) into subgroups of 1, 3, 1, 3, 1 pendants each and calling them: