Mathematics of Three Civilizations
There is history to mention the mathematics of three ancient civilizations, interesting in themselves, but of little or no influence on the further course of mathematics: the MinoansMycenaeans, the Mayas and the Incas.
Their science is not that of the beginning, but belongs rather to the category of the Ancient Orient.
Mathematical symbols used in administration have been found on the ruins of the MinoanMycenaean civilization of Crete and the Greek mainland.
They belong to the scripts called Linear A and B and belong to the period of 18001200 BC.
Numbers are represented, as in Egypt (but with different symbols), by special symbols for 1, 10, 100, 1000 in an additive way.
There are also symbols for simple fractions not all unit fractions. Since the scribes did not bake the clay tablets on which they wrote, only those that were baked in the final conflagration of their cities have been preserved, so that we have adequate knowledge of the extend of the mathematical knowledge of this civilization; it may have been comparable to that of Egypt.
The Mayas of Central America, mainly in what is now Yucatan and Guatemala, established a civilization that lasted for a millennium and a half, but reached its height in the socalled classical period, about 200900 of our era.
The arithmetic of Mayas, mainly deciphered from inscribed stone monuments, some codices, and Spanish chronicles, and closely related to their astronomy, notably their calendric system, was vigesimal (it still is), represented by dots for the units up to 4, and horizontal bars for the fives up to 15.
For larger numbers they used a position system with base 20, powers of 20 being represented by the same symbol as 20, the unit symbol.
There were some modifications for calendric purposes.
This position system required a symbol for zero, often a kind of shell or half open eye sign.
This system with its calendric connections, spread to other peoples of Central America.
The Incas built a large empire in and west of the Andes of South Amreica from the middle of the thirteenth century of our era on, their capital being Cuzco.
Its vast bureaucracy, strong in administration, crafts, and engineering used for communications and information, no writing but socalled quipos.
The simplest quipo has a main cord of colored cotton or sometimes wool, from which knotted cords are suspended with the knots formed into clusters at some distance from each other.
Each cluster has a number of knots from 1 to 9, and a cluster of say, 4 followed by one of 2 and one of 8 knots represents 428.
This is therefore a position system , in which our zero is indicated by a greater distance between the knots.
The colors of the cords represent things: sheep, soldiers, etc; and the position of the cords, as well as additional cords suspended from the cords, could tell a very complicated statistical story to the scribes who could “read” the quipos.
Mathematics of Three Civilizations
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