Page "Abacus" Paragraph 33

The quipu of the Incas was a system of knotted cords used to record numerical data, like advanced tally sticks – but not used to perform calculations.

Calculations were carried out using a yupana ( Quechua for " counting tool "; see figure ) which was still in use after the conquest of Peru.

The working principle of a yupana is unknown, but in 2001 an explanation of the mathematical basis of these instruments was proposed by Italian mathematician Nicolino De Pasquale.

By comparing the form of several yupanas, researchers found that calculations were based using the Fibonacci sequence 1, 1, 2, 3, 5 and powers of 10, 20 and 40 as place values for the different fields in the instrument.

Using the Fibonacci sequence would keep the number of grains within any one field at minimum.