Ancient Indian Mathematics

The aim of this article is to present a short outline of early Indian mathematics. I mean to summarize the results and contributions of Indian mathematics which were made in the period from the first civilization in Indian subcontinent to the 5 century AD when classical era of Indian mathematics began. Indus valley civilization The first use of mathematics in the Indian subcontinent was in the Indus valley and dates as far back as 3000 BC [Wheeler]. The earliest known urban Indian culture was at Harappa in the Punjab and at Mohenjodaro near the Indus River. Excavations at Mohenjodaro, Harappa and the surrounding area of the Indus River discovered evidence of the use of basic mathematics. The mathematics used by the early Harappan civilization had mostly practical intent and was concerned with weights and measuring scales. Excavations present knowledge of basic geometry. This culture also produced artistic designs. On carvings there is evidence that these people could draw concentric and intersecting circles and triangles. The further using of circles in the Harappan decorative design can be found at the pictures of bullock carts, the wheels of which had perhaps a metallic band wrapped round the rim. It clearly points to the knowledge of the ratio of the length of the circumference of the circle and its diameter, and thus of the value of π. The Harappans adopted a uniform system of weights and measures [O’Connor, Robertson]. Detail analysis discovered that weights corresponding to ratios of 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, and 500 were used. The existence of a graduated system of accurately marked weights shows the development of trade and commerce in Harappan society. Some appliances for the measurement of length were discovered. Also a remarkably accurate decimal ruler known as the Mohenjodaro ruler is very interesting. Its subdivision has a maximum error of just 0.005 inches at a length of 1.32 inches. The length have been named the Indus inch. Another scale was discovered when a bronze rod was found which was marked in lengths of 0.367 inches. The accuracy with which these scales are marked is certainly surprising. And 100 units of this measure is 36.7 inches which is the measure of a stride. Measurements of the ruins of buildings which have been excavated show that these units of length were accurately used by the Harappans in construction.