Indian Mathematics: Mathematics in Indus Valley Civilization (Harappa Civilization)
India is home to one of the oldest civilizations in this world. The Mesopotamian, Egyptian and Indus valley civilization make the three early cradles of civilization in the old world. We will start the Indian Mathematics series by going over the mathematical accomplishments of the Indus Valley Civilization.
The Indus valley civilization existed over almost all of the modern day Pakistan, North Western and Western India. The civilization flourished between 3300 BCE to about 1700 BCE and peaked between 2600 to 1900 BCE. This civilization was spread along a vast area of one million square kilometers and included more than 1000 settlements with about 600 settlements on India and about 400 settlements in Pakistan. It is believed that the Indus valley civilization was the biggest civilization amongst its contemporaries, which included the Egyptian and Mesopotamian civilizations.
Unlike the other civilization very little is known about Indus valley civilization because we are yet to understand the script they used. However material evidence indicates that it was a highly urbanized civilization with a sophisticated knowledge of mathematics for its time. The well-developed urban layouts, watertight walls, elaborate drainage systems, large granaries and the dock of Lothal, all are evidences indicating a sophisticated civilization with detailed knowledge of engineering and therefore mathematics.
Indus valley civilization placed huge emphasis on precision. This is evident from the fact that the urban layout of the cities of this civilization is very organized with perpendicular roads intersecting each other and nicely uniform house structures made with precisely shaped bricks. All the bricks used in the structures of Indus valley civilization have a absolute ratio of 4:2:1 for the length width and height. Even today, in brick technology, this ratio is considered the best for optimal bonding of bricks.
Indus valley civilization is the first to develop standard measurements of lengths and weights. Archeologists have excavated numerous scales and instruments for measuring lengths at multiple sites of this civilization. Similarly 500 plumb-bobs of same size and weight have been uncovered at multiple urban centers of this civilization.
Indus valley civilization was also very particular about using the ratios and used a series of binary and decimal ratios, that is ratios of 1, 2, 4, 8, 16, 32, 64 which were binary and ratios of 10, 20, 40, 160, 200, 300, 640, 1600, 8000 and 12800. The existence of such a graduated system of accurately marked weights and lengths shows indicates highly developed trade and commerce in Harappan society. Such measures of units were in use in India until the standard SI system of measures were adopted internationally.
During the excavation of the great bath in Mohenjo-Daro the Mohenjo-Daro was found which has nine equally spaced parallel lines 6.7056mm apart. The accuracy on the distances between these parallel lines is very high with a mean error of only 0.075mm. One of the lines is marked with a hollow circle, and the sixth line from this line is marked with a solid circular dot. The distance between these two lines is 33.54mm and is called an Indus inch, which is 1.32inches. The traditional unit of gaz used in India until recently is 25 Indus inches, indicating how these units have been in use in India for such a long time. Moreover the standard unit of measure in Mesopotamia, the sushi, is exactly half of Indus inch indicating close connection between these two civilizations.
In the modern times people are highly fascinated with the ancient Egyptian civilization for its grandiose pyramids and temples. For the Mesopotamian civilization the fascination is with their clay tablets on which were written the code of Hammurabi and the ancient epic of Gilgamesh. If we had to talk of something similarly fascinating for the Indus valley civilization then it would be their precision and organization. Indus valley civilization was a highly organized civilization with a highly organized urban planning and standardized methods for measuring lengths and weights.
Here we conclude our first chapter on Indian mathematics, stay tuned as we will cover more topics on the accomplishments of ancient India is arts, science and mathematics.
