# Mathematics of the Indus-Saraswati Civilization

The Indus-Saraswati civilization, also referred to as the Harappa, is one of the earliest known urban Indian cultures. It was first identified in 1921 at Harappa in the Punjab and has since then been discovered to cover much of modern Pakistan and India. This civilization began around 6,000 BC and survived until approximately 1700 BC. The people were literate and used a written script containing around 500 characters which have yet to be fully deciphered. Much research remains to be done before a full appreciation of the mathematical achievements of this ancient civilization can be fully assessed.

Two of its most famous cities, Harappa and Mohenjo-Daro, provide evidence that construction of buildings followed a standardized measurement which was decimal in nature--which implies that mathematical ideas were developed for the purpose of construction. This civilization had an advanced brick-making technology (having invented the kiln). Bricks were used in the construction of buildings and embankments for food control.

## Decimal System

It is known that the Harappans had adopted a uniform system of weights and measures. An analysis of the weights discovered suggests that they belong to two series both being decimal in nature with each decimal number multiplied and divided by two, giving for the main series ratios of 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, and 500. Several scales for the measurement of length were also discovered during excavations. One was a decimal scale based on a unit of measurement of 1.32 inches (3.35 centimeters)^{[1]}. Ten units equal 13.2 inches^{[2]}. A similar measure based on the length of a foot is present in other parts of Asia and beyond. Another scale was discovered when a bronze rod was found which was marked in lengths of 0.367 inches. Now 100 units of this measure is 36.7 inches^{[3]}. Measurements of the ruins of the buildings which have been excavated show that these units of length were accurately (and precisely) used by the Harappans in construction.