Page 96 - J. C. Turner "History and Science of Knots"

The Peruvian Quipu 85

must have had a geometric visualization for arithmetics, and the also knew the
area of the circle in the figure.
As this is only one single case, we do not know if the Inca had a formula for
the relationship of a circle's diameter to its area, and hence an approximation
for 7r. If he did have, we can calculate from this case a correctness of 4.61%
for ir:
C, = (1 2 X) 27r xr = 2, 997.

-X X X 1-X 1-X

C

1 ^2 a
C 1
C C C C
3
C

Fig. 10.
We still have to take into account an error already introduced when cal-
culating the values in the table. A further error can come from the calculation
or encoding of this special case. For the values of the various errors , see [6], p.
146.
Guaman Poma 's Calculation Device
A quipu is well adapted for storing numbers in a permanent and transportable
form, but it can hardly be used as a tool for calculating, as it takes too much
time to tie and untie the knots. But as the Incas handled large numbers (of up
to five digits), they probably had a calculation device. Father Jose de Acosta,
who had lived in Peru from 1571 to 1586, wrote in his Historia Natural y Moral
de las Indias:

`To see them use another kind of quipu with maize kernels is a per-
fect joy. In order to effect a very difficult computation for which an
able calculator would require pen and ink for the various methods
of calculation , these Indians make use of their kernels. They place
one here, three somewhere else and eight I know not where. They
move one kernel here and three there and the fact is that they are
able to complete their computation without making the smallest
mistake. As a matter of fact, they are better at calculating what
each one is due to pay or give than we should be with pen and