Oriental Mathematics (part 4)

Historical context

Archaeological excavations at Mohenjo Daro give us an indication of a very ancient civilization and a very tall culture in India, which occurred at the same time as the pyramids were built in Egypt. Later the country was occupied by the Aryan invaders who imposed the caste system, which brought a very long delay to development. These Aryan invaders developed Sanskrit literature in India. At the same time as Pythagoras began to develop his theorems and axioms in Greece, Buddha was acting in India. It is speculated that Pythagoras was in contact with Buddha and developed his most famous theorem with the Hindus.

Early Indians were exterminated around 1500 BC. This country had as policy, several small disunited principalities, which led to many invasions on its territory (Aryan, Persian, Greek, Arab and English). These invaders established themselves as the ruling class, avoiding miscegenation with the native people.

Between 3000 BC and 1500 BC there lived in India a people from the Indus River region who cultivated agriculture and lived in cities. These people were destroyed by the Aryans. Between 1500 BC and 500 BC the Aryans developed Hinduism, a combination of religion, philosophy, and social structure, which developed the basis of their civilization. Hinduism is a set of beliefs and laws based on three main ideas: worship of a large number of gods, transmigration of the soul, and the caste system that rigidly divided Indian society into four classes: Brahmana (priests), kshatriya ( warriors), vaisya (traders and artisans) and sudra (peasants).

Siddhartha Gautama (Buddha), around 500 BC rebels against this philosophy. Buddhism was a response to the chaos and turmoil of this era, finding many adherents, especially among the poor. Until it began to decline, around 500 AD. Buddhism had already spread to China, Japan, and Southeast Asia.

In 320 BC Chandragupta Mauria unified all the small Indian states and established the Maurian Empire, followed by his grandson Acoka (272-232 BC)… In 185 BC the empire once again disintegrated into small states. From the fall of the Mauritian empire to 200 AD there was a great cultural development through literature, art, science and philosophy. In 320 AD India was again unified by Chandragupta I, giving rise to the Gupta Empire, which remained until 470 AD, which is considered the classical era of India.

With the invasion of the Arabs, Islam was introduced to India, conquering parts of western India in the eighth, ninth, and tenth centuries. In 1206 Kutb ud-Din-Aibak founded the Muslim sultanate of Dehli. In 1526 Babur installs the Mughal (Turkish) empire. In the seventeenth century India was invaded by the British who exert a great tyranny against their population.

Mathematical Context

Hindu mathematics presents more historical problems than Greek mathematics, as Indian mathematicians rarely referred to their predecessors and displayed surprising independence in their mathematical work.

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India, like Egypt, had its "rope binders." Primitive geometric notions took shape in the writing known as “Sulvasutras” (string rules). This writing has three versions, the most well-known being called Apastamba. In this first version, from the same time as Pythagoras, rules are found for building right angles by means of rope trunks whose lengths form Pythagorean triads. This writing was probably influenced by Babylon since these triads are found in the cuneiform tablets. The origin and date of the Sulvasutras are uncertain, so it is not possible to relate them to the early Egyptian surveying or the Greek problem of duplicating an altar.

After this publication, the “Siddhantas” (astronomy systems) emerged. The beginning of the Gupta dynasty (290) marked a revival of Sanskrit culture and these writings may have been a product of this. Ptolemy's trigonometry was based on the functional relationship between the chords of a circle and the underlying angles it implies. For the authors of the Siddhantas, the relationship occurs between half a chord in a circle and half the angle implied in the center by the whole chord.