 | Indian mathematics: Encyclopedia II - Indian mathematics - Harappan Mathematics 3300 BC - 1700 BC
Indian mathematics - Harappan Mathematics 3300 BC - 1700 BC
The first appearance of evidence of the use of mathematics in the Indian subcontinent was in the Indus Valley Civilization, which dates back to around 3300 BC. Excavations at Harrapa, Mohenjo-daro and the surrounding area of the Indus River, have uncovered much evidence of the use of basic mathematics. The mathematics used by this early Harrapan civilisation was very much for practical means, and was primarily concerned with weights, measuring scales and a surprisingly advanced brick technology, which utilised ratios. The ratio for brick dimensions 4:2:1 is even today considered optimal for effective bonding. [1]
The people of the Indus Valley Civilization achieved great accuracy in measuring length, mass, and time. They were the first to develop a system of uniform weights and measures. Their measurements were extremely precise. Their smallest division, which is marked on an ivory scale found in Lothal, was approximately 1.704mm, the smallest division ever recorded on a scale of the Bronze Age. Harappan engineers followed the decimal division of measurement for all practical purposes, including the measurement of mass as revealed by their hexahedron weights.
Brick sizes were in a perfect ratio of 4:2:1, and the decimal system was used. Weights were based on units of 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, and 500, with each unit weighing approximately 28 grams, similar to the English ounce or Greek uncia, and smaller objects were weighed in similar ratios with the units of 0.871.
Also, many of the weights uncovered have been produced in definite geometrical shapes (cuboid, barrel, cone, and cylinder to name a few) which present knowledge of basic geometry, including the circle.
Unique Harappan inventions include an instrument which was used to measure whole sections of the horizon and the tidal dock. The engineering skill of the Harappans was remarkable, especially in building docks after a careful study of tides, waves, and currents.
This culture also produced artistic designs of a mathematical nature and there is evidence on carvings that these people could draw concentric and intersecting circles and triangles.
Further to the use of circles in decorative design there is indication of the use of bullock carts, the wheels of which may have had a metallic band wrapped round the rim. This clearly points to the possession of knowledge of the ratio of the length of the circumference of the circle and its diameter, and thus values of π.
Also of great interest is a remarkably accurate decimal ruler known as the Mohenjo-daro ruler. Subdivisions on the ruler have a maximum error of just 0.005 inches and, at a length of 1.32 inches, have been named the Indus inch. Furthermore, a correspondence has been noted between the Indus scale and brick size. Bricks (found in various locations) were found to have dimensions that were integral multiples of the graduations of their respective scales, which suggests advanced mathematical thinking.
Some historians believe the Harappan civilization may have used a base 8 numeral system.
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