Mathematics, Astronomy, Weights & measurements and Coinage in Ancient India

Mathematics in Ancient India

  • The town planning of Harappa based on measurement and geomentry provides an evidence of existence of Mathematics.
  • The earliest book on Mathematics was SatraSutra by Baudhayan (6th century)
  • In this book there is a mention of “Pi” and Pythagorean theorem.
  • Apastanbha (2 cen BC) gives thereference of acute, obtuse and right angles.
  • There is also a mention of rotation system, decimal system and the use of Zero.

Aryabhatta role in Mathematics

  • Aryabhatta in around 499 AD wrote Aryabhatta in which the concepts of mathematics as well as astronomy were mention. It has 4 sections: 1.) Method of denoting by big Decimal numbers by alphabets 2.)Geometry, Trigonometry, Algebra 3.) Number theory and 4.) On Astronomy
  • Astronomy was called Khagol Shastra and Khagol was the famous astronomical observatory at Nalanda where Aryabhatta studied.
  • Aryabhatta stated that earth is round and rotate in its own axis.
  • He formulated area of triangle and also discovered Algebra.
  • The value of “Pi” by Aryabhatta was 3.1416 and it was much more accurate than that Greeks given.
  • Arabs called Mathematics as Hindisat or the Indian art which was learnt by them from India.

Brahmagupta (7th century)

  • He wrote Brahmagupta Siddhantha and it was the first book which mentioned Zero as a number.
  • He introduced Negative numbers and described them as Debts and Positive numbers as Furtunes.
  • Mahavir (9th century) Wrote Ganitha Sangraha about arithmetic.
  • Bhaskaracharya (12th century)
  • He wrote a book “Siddhantha Shiromani” – divided into 4 sections: 1.Leelavathi deals on Arithmetics, 2.Bej Ganitha deals on Algebra, 3.Goladhayaya about Spheres and 4.Grahaganitha deals on Planets.
  • He introduced cyclic method of Solve Algebra equation and Europeans called it as “Inverse style”
  • In Medieval India many translations were done
  • Akbar courtesan Faizi translated Bhaskaracharya’s Bejganitha.
  • Leelvathi was translated by James Taylor in 19th century to English.

Astronomy in Ancient India

  • Aryabhatta wrote Aryabhatiyam which contains 121 verses. It contains method of determining movements of Planets, Calculation of Eclipse.Astronomy

Astronomy in Medieval India

  • Feroz shah Tughlaq established an observatory at Delhi.
  • Feroz shah Bahmani established an observatory at Daulatabad.
  • Both Lunar and Solar calendars used.
  • Sawai Jai Singh II setup 5 astronomiccal observatories at Delhi, Jaipur, Varanasi, Ujjain and Mathura.

Weights and measurements in Ancient India

Measures of weight in Ancient India

  • The basic weight used in ancient India was Raktika, a bright red seed from the gunja.
  • 1 raktika = 0.118 grams.
  • 5 ratikas = 1 masa,
  • 16 masas = 1 karsa, tolaka, or suvarna.
  • 4 karsas = 1 pala (37.76 gm)
  • 10 palas = 1 dharana.
  • 16 palas = 1 prastha (600 gm)
  • 16 Prastha = 1 drona (9.6 kg)

Measurements of length in Ancient India

  • 8 yava (barleycorns) = 1 angula (.75 inches)
  • 12 angulas = 1 vitasi (9 inches)
  • 2 vitastis = 1 hasta or aratni (18 inches)
  • 4 hastas = 1 danda (6 feet)
  • 2,000 dandas = 1 krosa (2.5 miles)
  • 4 krosas = 1 yojana (about 9 miles)

Measurements of time in Ancient India

  • 18 nimesas = 1 kastha (about 3.2 seconds)
  • 30 kasthas = 1 kala (about 1.6 minuets)
  • 15 kalas = 1 nadika (about 24 minuets)
  • 2 nadikas = 1 muhurta (about 48 minuets)
  • 30 muhurtas = 1 aho-ratra (about one day and night, or 24 hours)

Coinage in Ancient India

  • Early punched coins were minted around the 6th century B.C.E., and they were made up of Copper and Silver. Rarely gold coins used
  • Satamana was the largest coin and was shaped like a small bent bar. 1 satamana would weigh about 180 grains.
  • Karaspana was the basic silver punched coin and kakinis was the basic copper coin.
  • Indo-European coins were also made of gold, silver, and copper.
  • The Indo-European coins came from Rome during their expansion southward into the area of Afghanistan.
  • Silver coins, drachm and obol, were the most abundant, copper coins, their metrology is not clear, the second most abundant, and gold coins were also very rare.
  • Kusana coins were only made of gold and copper and copper coins were large.
  • Dinaras or suvarnas were based on Roman denarius and they were also double and quarter dinaras.
  • The Pre-Gupran coins were made of silver and copper and the coins were not uniform in weight or size and were made by the native king.
  • Satavahanas of the Deccan, were the first to issue lead and potin coins.
  • The Guptas also made gold coins called dinara and were made in relation to Kusana standards.
  • The Indian standard of coin was the copper coin called the karasapana, and the silver coin, rupaka, was based on the Sakas of Ujjayini.
  • The Medieval coins were also made of gold, silver, and copper.
  • The gold coins were called suvarna or tanka and were only minted in a few dynasties in the 11th century.
  • The silver coins (dramma, tanka) also conformed to this standard, and coins of 3/4, ½, and ¼ dramma are attested.
  • Silver Tanka and Copper Jital coins issued by Illutumish (1210 – 36)
  • Mohammed bin Tughluq issued Token currency.
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