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 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.