Late Middle Ages
Madhava of Sangamagrama (c. 1340 – 1425) and his Kerala school of astronomy and mathematics developed and founded mathematical analysis. The infinite series for π was stated by him and he made use of the series expansion of to obtain an infinite series expression, now known as the Madhava-Gregory series, for . Their rational approximation of the error for the finite sum of their series are of particular interest. They manipulated the error term to derive a faster converging series for . They used the improved series to derive a rational expression, for correct up to nine decimal places, i.e. . The development of the series expansions for trigonometric functions (sine, cosine, and arc tangent) was carried out by mathematicians of the Kerala School in the 15th century CE. Their work, completed two centuries before the invention of calculus in Europe, provided what is now considered the first example of a power series (apart from geometric series).
Shēr Shāh of northern India issued silver currency bearing Islamic motifs, later imitated by the Mughal empire. The Chinese merchant Ma Huan (1413–51) noted that gold coins, known as fanam, were issued in Cochin and weighed a total of one fen and one li according to the Chinese standards. They were of fine quality and could be exchanged in China for 15 silver coins of four-li weight each.
In 1500, Nilakantha Somayaji of the Kerala school of astronomy and mathematics, in his Tantrasangraha, revised Aryabhata's elliptical model for the planets Mercury and Venus. His equation of the centre for these planets remained the most accurate until the time of Johannes Kepler in the 17th century.
The Seamless celestial globe was invented in Kashmir by Ali Kashmiri ibn Luqman in 998 AH (1589-90 CE), and twenty other such globes were later produced in Lahore and Kashmir during the Mughal Empire. Before they were rediscovered in the 1980s, it was believed by modern metallurgists to be technically impossible to produce metal globes without any seams, even with modern technology. These Mughal metallurgists pioneered the method of lost-wax casting in order to produce these globes.
It was written in the Tarikh-i Firishta (1606–1607) that the envoy of the Mongol ruler Hulegu Khan was presented with a pyrotechnics display upon his arrival in Delhi in 1258 CE. As a part of an embassy to India by Timurid leader Shah Rukh (1405–1447), 'Abd al-Razzaq mentioned naphtha-throwers mounted on elephants and a variety of pyrotechnics put on display. Firearms known as top-o-tufak also existed in the Vijayanagara Empire by as early as 1366 CE. From then on the employment of gunpowder warfare in the region was prevalent, with events such as the siege of Belgaum in 1473 CE by the Sultan Muhammad Shah Bahmani.
In A History of Greek Fire and Gunpowder, James Riddick Partington describes Indian rockets, mines and other means of gunpowder warfare:
| The Indian war rockets were formidable weapons before such rockets were used in Europe. They had bam-boo rods, a rocket-body lashed to the rod, and iron points. They were directed at the target and fired by lighting the fuse, but the trajectory was rather erratic. The use of mines and counter-mines with explosive charges of gunpowder is mentioned for the times of Akbar and Jahāngir. |
By the 16th century, Indians were manufacturing a diverse variety of firearms; large guns in particular, became visible in Tanjore, Dacca, Bijapur and Murshidabad. Guns made of bronze were recovered from Calicut (1504) and Diu (1533). Gujarāt supplied Europe saltpeter for use in gunpowder warfare during the 17th century. Bengal and Mālwa participated in saltpeter production. The Dutch, French, Portuguese, and English used Chhapra as a center of saltpeter refining.
The construction of water works and aspects of water technology in India is described in Arabic and Persian works. During medieval times, the diffusion of Indian and Persian irrigation technologies gave rise to an advanced irrigation system which bought about economic growth and also helped in the growth of material culture. The founder of the cashmere wool industry is traditionally held to be the 15th century ruler of Kashmir, Zayn-ul-Abidin, who introduced weavers from Central Asia.
The scholar Sadiq Isfahani of Jaunpur compiled an atlas of the parts of the world which he held to be 'suitable for human life'. The 32 sheet atlas—with maps oriented towards the south as was the case with Islamic works of the era—is part of a larger scholarly work compiled by Isfahani during 1647 CE. According to Joseph E. Schwartzberg (2008): 'The largest known Indian map, depicting the former Rajput capital at Amber in remarkable house-by-house detail, measures 661 × 645 cm. (260 × 254 in., or approximately 22 × 21 ft).'
Read more about this topic: History Of Science And Technology In The Indian Subcontinent
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