3rd and 10th centuries CE. The people of the Indus Valley Civilization manufactured bricks whose dimensions were mathematical thought from ancient to modern times pdf the proportion 4:2:1, considered favourable for the stability of a brick structure.

The inhabitants of Indus civilisation also tried to standardise measurement of length to a high degree of accuracy. Bricks manufactured in ancient Mohenjo-daro often had dimensions that were integral multiples of this unit of length. With three-fourths Puruṣa went up: one-fourth of him again was here. The altars were required to be constructed of five layers of burnt brick, with the further condition that each layer consist of 200 bricks and that no two adjacent layers have congruent arrangements of bricks. Pythagorean theorem for the sides of a square: “The rope which is stretched across the diagonal of a square produces an area double the size of the original square.

The rope stretched along the length of the diagonal of a rectangle makes an area which the vertical and horizontal sides make together. The formula is accurate up to five decimal places, the true value being 1. Since these tablets predate the Sulbasutras period by several centuries, taking into account the contextual appearance of some of the triples, it is reasonable to expect that similar understanding would have been there in India. Since, unfortunately, no other contemporaneous sources have been found it may never be possible to settle this issue satisfactorily. 10th-century commentary on it by Halāyudha has.

In the middle ones put the sum of the digits in the two squares above each. Jain texts on mathematical topics were composed after the 6th century BCE. Vedic period and that of the “classical period. A significant historical contribution of Jain mathematicians lay in their freeing Indian mathematics from its religious and ritualistic constraints. Not content with a simple notion of infinity, they went on to define five different types of infinity: the infinite in one direction, the infinite in two directions, the infinite in area, the infinite everywhere, and the infinite perpetually.

More than a millennium later, their appellation became the English word “zero” after a tortuous journey of translations and transliterations from India to Europe. Memorisation and recitation was also used to transmit philosophical and literary works, as well as treatises on ritual and grammar. Modern scholars of ancient India have noted the “truly remarkable achievements of the Indian pandits who have preserved enormously bulky texts orally for millennia. Prodigious energy was expended by ancient Indian culture in ensuring that these texts were transmitted from generation to generation with inordinate fidelity. The texts were subsequently “proof-read” by comparing the different recited versions.

India, they formed the last of the exclusively oral literature. 21 bricks in each layer. The bricks were then designed to be of the shape of the constituent rectangle and the layer was created. To form the next layer, the same formula was used, but the bricks were arranged transversely. Similarly, in the second stanza, “bricks” are not explicitly mentioned, but inferred again by the feminine plural form of “North-pointing.

All these inferences are made by the officiant as he recalls the formula from his memory. With the increasing complexity of mathematics and other exact sciences, both writing and computation were required. Consequently, many mathematical works began to be written down in manuscripts that were then copied and re-copied from generation to generation. India today is estimated to have about thirty million manuscripts, the largest body of handwritten reading material anywhere in the world.