Aryabhata
Āryabhaṭa | |
---|---|
Varahamihira |
Aryabhata (
For his explicit mention of the relativity of motion, he also qualifies as a major early physicist.[8]
Biography
Name
While there is a tendency to misspell his name as "Aryabhatta" by analogy with other names having the "
Time and place of birth
Aryabhata mentions in the Aryabhatiya that he was 23 years old 3,600 years into the Kali Yuga, but this is not to mean that the text was composed at that time. This mentioned year corresponds to 499 CE, and implies that he was born in 476.[6] Aryabhata called himself a native of Kusumapura or Pataliputra (present day Patna, Bihar).[1]
Other hypothesis
It has been claimed that the aśmaka (Sanskrit for "stone") where Aryabhata originated may be the present day Kodungallur which was the historical capital city of Thiruvanchikkulam of ancient Kerala.[11] This is based on the belief that Koṭuṅṅallūr was earlier known as Koṭum-Kal-l-ūr ("city of hard stones"); however, old records show that the city was actually Koṭum-kol-ūr ("city of strict governance"). Similarly, the fact that several commentaries on the Aryabhatiya have come from Kerala has been used to suggest that it was Aryabhata's main place of life and activity; however, many commentaries have come from outside Kerala, and the Aryasiddhanta was completely unknown in Kerala.[9] K. Chandra Hari has argued for the Kerala hypothesis on the basis of astronomical evidence.[12]
Aryabhata mentions "Lanka" on several occasions in the Aryabhatiya, but his "Lanka" is an abstraction, standing for a point on the equator at the same longitude as his
Education
It is fairly certain that, at some point, he went to Kusumapura for advanced studies and lived there for some time.
Works
Aryabhata is the author of several treatises on mathematics and astronomy, some of which are lost.
He was student of
The Arya-siddhanta, a lost work on astronomical computations, is known through the writings of Aryabhata's contemporary,
A third text, which may have survived in the
Aryabhatiya
Direct details of Aryabhata's work are known only from the Aryabhatiya. The name "Aryabhatiya" is due to later commentators. Aryabhata himself may not have given it a name. His disciple
- Gitikapada: (13 verses): large units of time—kalpa, manvantra, and yuga—which present a cosmology different from earlier texts such as Lagadha's jya), given in a single verse. The duration of the planetary revolutions during a mahayuga is given as 4.32 million years.
- Ganitapada (33 verses): covering indeterminateequations (kuṭṭaka).
- Kalakriyapada (25 verses): different units of time and a method for determining the positions of planets for a given day, calculations concerning the intercalary month (adhikamAsa), kShaya-tithis, and a seven-day week with names for the days of week.
- Golapada (50 verses): Geometric/zodiacal signs on horizon, etc. In addition, some versions cite a few colophonsadded at the end, extolling the virtues of the work, etc.
The Aryabhatiya presented a number of innovations in mathematics and astronomy in verse form, which were influential for many centuries. The extreme brevity of the text was elaborated in commentaries by his disciple Bhaskara I (Bhashya, c. 600 CE) and by Nilakantha Somayaji in his Aryabhatiya Bhasya (1465 CE).
Aryabhatiya is also well-known for his description of relativity of motion. He expressed this relativity thus: "Just as a man in a boat moving forward sees the stationary objects (on the shore) as moving backward, just so are the stationary stars seen by the people on earth as moving exactly towards the west."[8]
Mathematics
Place value system and zero
The
However, Aryabhata did not use the Brahmi numerals. Continuing the Sanskritic tradition from Vedic times, he used letters of the alphabet to denote numbers, expressing quantities, such as the table of sines in a mnemonic form.[17]
Approximation of π
Aryabhata worked on the approximation for pi (π), and may have come to the conclusion that π is irrational. In the second part of the Aryabhatiyam (gaṇitapāda 10), he writes:
caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.
"Add four to 100, multiply by eight, and then add 62,000. By this rule the circumference of a circle with a diameter of 20,000 can be approached."[18]
This implies that for a circle whose diameter is 20000, the circumference will be 62832
i.e, = = , which is accurate to two parts in one million.[19]
It is speculated that Aryabhata used the word āsanna (approaching), to mean that not only is this an approximation but that the value is incommensurable (or
After Aryabhatiya was translated into
Trigonometry
In Ganitapada 6, Aryabhata gives the area of a triangle as
- tribhujasya phalaśarīraṃ samadalakoṭī bhujārdhasaṃvargaḥ
that translates to: "for a triangle, the result of a perpendicular with the half-side is the area."[21]
Aryabhata discussed the concept of
Indeterminate equations
A problem of great interest to
- Find the number which gives 5 as the remainder when divided by 8, 4 as the remainder when divided by 9, and 1 as the remainder when divided by 7
That is, find N = 8x+5 = 9y+4 = 7z+1. It turns out that the smallest value for N is 85. In general, diophantine equations, such as this, can be notoriously difficult. They were discussed extensively in ancient Vedic text
Algebra
In Aryabhatiya, Aryabhata provided elegant results for the summation of series of squares and cubes:[24]
and
Astronomy
Aryabhata's system of astronomy was called the audAyaka system, in which days are reckoned from uday, dawn at lanka or "equator". Some of his later writings on astronomy, which apparently proposed a second model (or ardha-rAtrikA, midnight) are lost but can be partly reconstructed from the discussion in Brahmagupta's Khandakhadyaka. In some texts, he seems to ascribe the apparent motions of the heavens to the Earth's rotation. He may have believed that the planet's orbits as elliptical rather than circular.[25][26]
Motions of the Solar System
Aryabhata correctly insisted that the Earth rotates about its axis daily, and that the apparent movement of the stars is a relative motion caused by the rotation of the Earth, contrary to the then-prevailing view, that the sky rotated.[19] This is indicated in the first chapter of the Aryabhatiya, where he gives the number of rotations of the Earth in a yuga,[27] and made more explicit in his gola chapter:[28]
In the same way that someone in a boat going forward sees an unmoving [object] going backward, so [someone] on the equator sees the unmoving stars going uniformly westward. The cause of rising and setting [is that] the sphere of the stars together with the planets [apparently?] turns due west at the equator, constantly pushed by the cosmic wind.
Aryabhata described a
The positions and periods of the planets was calculated relative to uniformly moving points. In the case of Mercury and Venus, they move around the Earth at the same mean speed as the Sun. In the case of Mars, Jupiter, and Saturn, they move around the Earth at specific speeds, representing each planet's motion through the zodiac. Most historians of astronomy consider that this two-epicycle model reflects elements of pre-Ptolemaic
Eclipses
Solar and lunar eclipses were scientifically explained by Aryabhata. He states that the
Sidereal periods
Considered in modern English units of time, Aryabhata calculated the
Heliocentrism
As mentioned, Aryabhata advocated an astronomical model in which the Earth turns on its own axis. His model also gave corrections (the śīgra anomaly) for the speeds of the planets in the sky in terms of the mean speed of the Sun. Thus, it has been suggested that Aryabhata's calculations were based on an underlying
Legacy
This section needs additional citations for verification. (March 2017) |
Aryabhata's work was of great influence in the Indian astronomical tradition and influenced several neighbouring cultures through translations. The Arabic translation during the Islamic Golden Age (c. 820 CE), was particularly influential. Some of his results are cited by Al-Khwarizmi and in the 10th century Al-Biruni stated that Aryabhata's followers believed that the Earth rotated on its axis.
His definitions of
In fact, modern names "sine" and "cosine" are mistranscriptions of the words jya and kojya as introduced by Aryabhata. As mentioned, they were translated as jiba and kojiba in Arabic and then misunderstood by Gerard of Cremona while translating an Arabic geometry text to Latin. He assumed that jiba was the Arabic word jaib, which means "fold in a garment", L. sinus (c. 1150).[42]
Aryabhata's astronomical calculation methods were also very influential. Along with the trigonometric tables, they came to be widely used in the Islamic world and used to compute many Arabic astronomical tables (
Calendric calculations devised by Aryabhata and his followers have been in continuous use in India for the practical purposes of fixing the Panchangam (the Hindu calendar). In the Islamic world, they formed the basis of the Jalali calendar introduced in 1073 CE by a group of astronomers including Omar Khayyam,[43] versions of which (modified in 1925) are the national calendars in use in Iran and Afghanistan today. The dates of the Jalali calendar are based on actual solar transit, as in Aryabhata and earlier Siddhanta calendars. This type of calendar requires an ephemeris for calculating dates. Although dates were difficult to compute, seasonal errors were less in the Jalali calendar than in the Gregorian calendar.[citation needed]
Aryabhatta Knowledge University (AKU), Patna has been established by Government of Bihar for the development and management of educational infrastructure related to technical, medical, management and allied professional education in his honour. The university is governed by Bihar State University Act 2008.
India's first satellite
See also
References
- ^ a b c Bhau Daji (1865). "Brief Notes on the Age and Authenticity of the Works of Aryabhata, Varahamihira, Brahmagupta, Bhattotpala, and Bhaskaracharya". Journal of the Royal Asiatic Society of Great Britain and Ireland. pp. 392–406.
- ISBN 978-81-7359-124-2. Retrieved 15 April 2023.
- ^ O'Connor, J J; Robertson, E F. "Aryabhata the Elder". www-history.mcs.st-andrews.ac.uk. Archived from the original on 11 July 2015. Retrieved 18 July 2012.
- ISBN 978-1-61530-218-5.
- ISBN 978-81-317-1818-6.
- ^ ISBN 978-0-8176-4694-3.
- ISBN 978-1-56324-420-9.
- ^ a b S. Kak, Aryabhatiya. Encyclopedia of India, 2005
- ^ a b c d e f K. V. Sarma (2001). "Āryabhaṭa: His name, time and provenance" (PDF). Indian Journal of History of Science. 36 (4): 105–115. Archived from the original (PDF) on 31 March 2010.
- ^ a b c d e f
Ansari, S.M.R. (March 1977). "Aryabhata I, His Life and His Contributions". Bulletin of the Astronomical Society of India. 5 (1): 10–18. hdl:2248/502.
- ISBN 978-81-317-2890-1.
- ^ Radhakrishnan Kuttoor (25 June 2007), "Aryabhata lived in Ponnani?", The Hindu, archived from the original on 1 July 2007
- ISBN 978-81-208-0612-2.
- Kusumapura (Pataliutra, a village near the city of Patna) and wrote a book called Aryabhatiya.
- ^ "Get ready for solar eclipse" (PDF). National Council of Science Museums, Ministry of Culture, Government of India. Archived from the original (PDF) on 21 July 2011. Retrieved 9 December 2009.
- ^ George. Ifrah (1998). A Universal History of Numbers: From Prehistory to the Invention of the Computer. London: John Wiley & Sons.
- ^
Dutta, Bibhutibhushan; Singh, Avadhesh Narayan (1962). History of Hindu Mathematics. Asia Publishing House, Bombay. ISBN 81-86050-86-8.
- ^
Jacobs, Harold R. (2003). Geometry: Seeing, Doing, Understanding (Third ed.). New York: W.H. Freeman and Company. p. 70. ISBN 0-7167-4361-2.
- ^ a b How Aryabhata got the earth's circumference right Archived 15 January 2017 at the Wayback Machine
- ^
S. Balachandra Rao (1998) [First published 1994]. Indian Mathematics and Astronomy: Some Landmarks. Bangalore: Jnana Deep Publications. ISBN 81-7371-205-0.
- ISBN 0-471-18082-3.
Aryabhata gave the correct rule for the area of a triangle and an incorrect rule for the volume of a pyramid. (He claimed that the volume was half the height times the area of the base.)
- ^ Howard Eves (1990). An Introduction to the History of Mathematics (6 ed.). Saunders College Publishing House, New York. p. 237.
- ^ Amartya K Dutta, "Diophantine equations: The Kuttaka" Archived 2 November 2014 at the Wayback Machine, Resonance, October 2002. Also see earlier overview: Mathematics in Ancient India Archived 2 November 2014 at the Wayback Machine.
- ISBN 0-471-54397-7.
He gave more elegant rules for the sum of the squares and cubes of an initial segment of the positive integers. The sixth part of the product of three quantities consisting of the number of terms, the number of terms plus one, and twice the number of terms plus one is the sum of the squares. The square of the sum of the series is the sum of the cubes.
- MacTutor History of Mathematics archive:
"He believes that the Moon and planets shine by reflected sunlight, incredibly he believes that the orbits of the planets are ellipses."
- ^ Hayashi (2008), Aryabhata I
- ^ Aryabhatiya 1.3ab, see Plofker 2009, p. 111.
- ^ [achalAni bhAni samapashchimagAni ... – golapAda.9–10]. Translation from K. S. Shukla and K.V. Sarma, K. V. Āryabhaṭīya of Āryabhaṭa, New Delhi: Indian National Science Academy, 1976. Quoted in Plofker 2009.
- ^
ISBN 0-7141-1746-3. pp. 127–9.
- ISBN 0-387-90844-7
- ISBN 0-387-94822-8
- ISBN 978-0-7923-4066-9.
- ^ Ansari, p. 13, Table 1
- ISBN 978-81-7434-480-9
- ^ The concept of Indian heliocentrism has been advocated by B. L. van der Waerden, Das heliozentrische System in der griechischen, persischen und indischen Astronomie. Naturforschenden Gesellschaft in Zürich. Zürich:Kommissionsverlag Leeman AG, 1970.
- ^ B.L. van der Waerden, "The Heliocentric System in Greek, Persian and Hindu Astronomy", in David A. King and George Saliba, ed., From Deferent to Equant: A Volume of Studies in the History of Science in the Ancient and Medieval Near East in Honor of E. S. Kennedy, Annals of the New York Academy of Science, 500 (1987), pp. 529–534.
- ISBN 0-387-94822-8.
- ^ Noel Swerdlow, "Review: A Lost Monument of Indian Astronomy," Isis, 64 (1973): 239–243.
- Greek astronomy known in ancient India as the Paulisa Siddhantamakes no reference to such a theory.
- ^ Dennis Duke, "The Equant in India: The Mathematical Basis of Ancient Indian Planetary Models." Archive for History of Exact Sciences 59 (2005): 563–576, n. 4 "Archived copy" (PDF). Archived (PDF) from the original on 18 March 2009. Retrieved 8 February 2016.
{{cite web}}
: CS1 maint: archived copy as title (link). - ISBN 978-0-691-12067-6.
- ^ Douglas Harper (2001). "Online Etymology Dictionary". Archived from the original on 13 July 2007. Retrieved 14 July 2007.
- ^ "Omar Khayyam". The Columbia Encyclopedia (6 ed.). May 2001. Archived from the original on 17 October 2007. Retrieved 10 June 2007.
- ^ "Maths can be fun". The Hindu. 3 February 2006. Archived from the original on 1 October 2007. Retrieved 6 July 2007.
- ^ "New Microorganisms Discovered in Earth's Stratosphere". ScienceDaily. 18 March 2009. Archived from the original on 1 April 2018.
- ^ "ISRO Press Release 16 March 2009". ISRO. Archived from the original on 5 January 2012. Retrieved 24 June 2012.
Works cited
- Cooke, Roger (1997). The History of Mathematics: A Brief Course. Wiley-Interscience. ISBN 0-471-18082-3.
- ISBN 978-1-4254-8599-3.
- ISBN 0-7923-6363-9.
- Shukla, Kripa Shankar. Aryabhata: Indian Mathematician and Astronomer. New Delhi: Indian National Science Academy, 1976.
- Thurston, H. (1994). Early Astronomy. Springer-Verlag, New York. ISBN 0-387-94107-X.
External links
- 1930 English translation of The Aryabhatiya in various formats at the Internet Archive.
- O'Connor, John J.; Robertson, Edmund F., "Aryabhata", MacTutor History of Mathematics Archive, University of St Andrews
- Achar, Narahari (2007). "Āryabhaṭa I". In Thomas Hockey; et al. (eds.). The Biographical Encyclopedia of Astronomers. New York: Springer. p. 63. ISBN 978-0-387-31022-0. (PDF version)
- "Aryabhata and Diophantus' son", Hindustan Times Storytelling Science column, November 2004
- Surya Siddhanta translations