Śaṅkaranārāyaṇa
Encyclopedia
Śaṅkaranārāyaṇa was an India
n astronomer
and mathematician
in the court of King Sthanu Ravi Varman (844- 885 CE) of the Kulasekhara dynasty (Second Cheras)
in Kerala
. He is believed to have established the first astronomical observatory in India at Kodungallur
in Kerala
. His most famous work was the Laghubhāskarīyavivaraṇa which was a commentary on the Laghubhāskarīya of Bhaskara I which in turn is based on the work of Aryabhata I. The Laghubhāskarīyavivaraṇa was written 869 CE for the author writes in the text that it is written in the Shaka year 791 which translates to a date CE by adding 78.
Śaṅkaranārāyaṇa was a student of the astronomer and mathematician Govindasvami (c. 800 – c. 860).
in India is meager. Many astronomers patronized by kings carried out astronomical observations. The places of these observations could be called as observatories. The first extant reference to a place of observation with some instruments in India is in the treatise Laghubhāskarīyavivaraṇa authored by Śaṅkaranārāyaṇa. In this work, Śaṅkaranārāyaṇa speaks of a place with instruments in the capital city Mahodayapuram of King Sthanu Ravi Varma of the Kulasekhara
dynasty in Kerala
. Mahodayapuram has been identified with the present day Kodungallur
. The observatory was fitted with an armillary sphere which is a model of the celestial sphere
. At the directions of Śaṅkaranārāyaṇa, in every 'Kadigai' duration of 34 minutes, bells were sounded at different important centres of the town to announce correct time.
The following is a translation of the verses in Laghubhāskarīyavivaraṇa containing references to the existence of an observatory in Mahodayapura:
by = ax ± c (a, b, c integers) in integers which is then applied to astronomical problems. The Indian method involves using the Euclidean algorithm
. It is called kuttakara ("pulveriser").
The most unusual feature of the Laghubhāskarīyavivaraṇa is the use of katapayadi system
of numeration as well as the place-value Sanskrit
numerals which Laghubhāskarīyavivaraṇa frequently uses. Śaṅkaranārāyaṇa is the first author known to use katapayadi system
of numeration with this name but he did not invent it for it appears to be identical to a system invented earlier which was called varnasamjna. The numeration system called varnasamjna was invented by the astronomer Haridatta
, and it was explained by him in a text which was written in 684.
The system is based on writing numbers using the letters of the Indian alphabet:
Under this system 1 to 5 are represented by four different letters. For example 1 is represented by the letters ka, ta, pa, ya which give the system its name (ka, ta, pa, ya becomes katapaya). Then 6, 7, 8 are represented by three letters and finally nine and zero are represented by two letters.
The system was a spoken one in the sense that consonants and vowels which are not vocalised have no numerical value. The system is a place-value system with zero. In fact many different "words" could represent the same number and this was highly useful for works written in verse.
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...
n astronomer
Astronomer
An astronomer is a scientist who studies celestial bodies such as planets, stars and galaxies.Historically, astronomy was more concerned with the classification and description of phenomena in the sky, while astrophysics attempted to explain these phenomena and the differences between them using...
and mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
in the court of King Sthanu Ravi Varman (844- 885 CE) of the Kulasekhara dynasty (Second Cheras)
Kulasekhara dynasty (Second Cheras)
Kulasekhara or Later Chera dynasty was a classical Hindu dynasty founded by the saint King Kulashekhara Varman. The dynasty ruled the whole of modern Kerala state , Guddalore and some parts of Nilgiri district and Salem - Coimbatore region in southern India between 9th and 12th centuries AD...
in Kerala
Kerala
or Keralam is an Indian state located on the Malabar coast of south-west India. It was created on 1 November 1956 by the States Reorganisation Act by combining various Malayalam speaking regions....
. He is believed to have established the first astronomical observatory in India at Kodungallur
Kodungallur
Kodungallur is a municipality in Thrissur District, in the state of Kerala, India on the Malabar Coast. Kodungallur is located about 29 km northwest of Kochi city and 38 km Southwest of Thrissur, on National Highway 17 . Muziris the ancient seaport at the mouth of the Periyar River was...
in Kerala
Kerala
or Keralam is an Indian state located on the Malabar coast of south-west India. It was created on 1 November 1956 by the States Reorganisation Act by combining various Malayalam speaking regions....
. His most famous work was the Laghubhāskarīyavivaraṇa which was a commentary on the Laghubhāskarīya of Bhaskara I which in turn is based on the work of Aryabhata I. The Laghubhāskarīyavivaraṇa was written 869 CE for the author writes in the text that it is written in the Shaka year 791 which translates to a date CE by adding 78.
Śaṅkaranārāyaṇa was a student of the astronomer and mathematician Govindasvami (c. 800 – c. 860).
Śaṅkaranārāyaṇa's observatory
Information on observatoriesObservatory
An observatory is a location used for observing terrestrial or celestial events. Astronomy, climatology/meteorology, geology, oceanography and volcanology are examples of disciplines for which observatories have been constructed...
in India is meager. Many astronomers patronized by kings carried out astronomical observations. The places of these observations could be called as observatories. The first extant reference to a place of observation with some instruments in India is in the treatise Laghubhāskarīyavivaraṇa authored by Śaṅkaranārāyaṇa. In this work, Śaṅkaranārāyaṇa speaks of a place with instruments in the capital city Mahodayapuram of King Sthanu Ravi Varma of the Kulasekhara
Kulasekhara
Kulasekhara or Later Chera dynasty was a classical Hindu dynasty founded by the saint King Kulashekhara Varman. The dynasty ruled the whole of modern Kerala state , Guddalore and some parts of Nilgiri district and Salem - Coimbatore region in southern India between 9th and 12th centuries AD...
dynasty in Kerala
Kerala
or Keralam is an Indian state located on the Malabar coast of south-west India. It was created on 1 November 1956 by the States Reorganisation Act by combining various Malayalam speaking regions....
. Mahodayapuram has been identified with the present day Kodungallur
Kodungallur
Kodungallur is a municipality in Thrissur District, in the state of Kerala, India on the Malabar Coast. Kodungallur is located about 29 km northwest of Kochi city and 38 km Southwest of Thrissur, on National Highway 17 . Muziris the ancient seaport at the mouth of the Periyar River was...
. The observatory was fitted with an armillary sphere which is a model of the celestial sphere
Celestial sphere
In astronomy and navigation, the celestial sphere is an imaginary sphere of arbitrarily large radius, concentric with the Earth and rotating upon the same axis. All objects in the sky can be thought of as projected upon the celestial sphere. Projected upward from Earth's equator and poles are the...
. At the directions of Śaṅkaranārāyaṇa, in every 'Kadigai' duration of 34 minutes, bells were sounded at different important centres of the town to announce correct time.
The following is a translation of the verses in Laghubhāskarīyavivaraṇa containing references to the existence of an observatory in Mahodayapura:
- "(To the King): Oh Ravivarmadeva, now deign to tell us quickly, reading off from the armillary sphereArmillary sphereAn armillary sphere is a model of objects in the sky , consisting of a spherical framework of rings, centred on Earth, that represent lines of celestial longitude and latitude and other astronomically important features such as the ecliptic...
installed (at the observatoryObservatoryAn observatory is a location used for observing terrestrial or celestial events. Astronomy, climatology/meteorology, geology, oceanography and volcanology are examples of disciplines for which observatories have been constructed...
) in Mahodayapura, duly fitted with all the relevant circles and with the sign (-degreeDegree (angle)A degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...
-minuteMinuteA minute is a unit of measurement of time or of angle. The minute is a unit of time equal to 1/60th of an hour or 60 seconds. In the UTC time scale, a minute on rare occasions has 59 or 61 seconds; see leap second. The minute is not an SI unit; however, it is accepted for use with SI units...
) markings, the time of the rising point of the eclipticEclipticThe ecliptic is the plane of the earth's orbit around the sun. In more accurate terms, it is the intersection of the celestial sphere with the ecliptic plane, which is the geometric plane containing the mean orbit of the Earth around the Sun...
(lagna) when the SunSunThe Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
is at 10° in the Sign of CapricornCapricornusCapricornus is one of the constellations of the zodiac; it is often called Capricorn, especially when referring to the corresponding astrological sign. Its name is Latin for "horned male goat" or "goat horn", and it is commonly represented in the form of a sea-goat: a mythical creature that is half...
, and also when the SunSunThe Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
is at the end of the Sign LibraLibra (constellation)Libra is a constellation of the zodiac. Its name is Latin for weighing scales, and its symbol is . It is fairly faint, with no first magnitude stars, and lies between Virgo to the west and Scorpius to the east.-Notable features:]...
, which I have noted."
Mathematical achievements
Laghubhāskarīyavivaraṇa covers the standard mathematical methods of Aryabhata I such as the solution of the indeterminate equationIndeterminate equation
An indeterminate equation, in mathematics, is an equation for which there is an infinite set of solutions; for example, 2x = y is a simple indeterminate equation. Indeterminate equations cannot be directly solved from the given information...
by = ax ± c (a, b, c integers) in integers which is then applied to astronomical problems. The Indian method involves using the Euclidean algorithm
Euclidean algorithm
In mathematics, the Euclidean algorithm is an efficient method for computing the greatest common divisor of two integers, also known as the greatest common factor or highest common factor...
. It is called kuttakara ("pulveriser").
The most unusual feature of the Laghubhāskarīyavivaraṇa is the use of katapayadi system
Katapayadi system
Kaṭapayādi system of numerical notation is an ancient Indian system to depict letters to numerals for easy remembrance of numbers as words or verses...
of numeration as well as the place-value Sanskrit
Sanskrit
Sanskrit , is a historical Indo-Aryan language and the primary liturgical language of Hinduism, Jainism and Buddhism.Buddhism: besides Pali, see Buddhist Hybrid Sanskrit Today, it is listed as one of the 22 scheduled languages of India and is an official language of the state of Uttarakhand...
numerals which Laghubhāskarīyavivaraṇa frequently uses. Śaṅkaranārāyaṇa is the first author known to use katapayadi system
Katapayadi system
Kaṭapayādi system of numerical notation is an ancient Indian system to depict letters to numerals for easy remembrance of numbers as words or verses...
of numeration with this name but he did not invent it for it appears to be identical to a system invented earlier which was called varnasamjna. The numeration system called varnasamjna was invented by the astronomer Haridatta
Haridatta
Haridatta was an astronomer-mathematician of Kerala, India, who is believed to be the promulgator of the Parahita system of astronomical computations. This system of computations is widely popular in Kerala and Tamil Nadu. According to legends, Haridatta promulgated the Parahita system on the...
, and it was explained by him in a text which was written in 684.
The system is based on writing numbers using the letters of the Indian alphabet:
- ... the numerical attribution of syllables corresponds to the following rule, according to the regular order of succession of the letters of the Indian alphabet: the first nine letters represent the numbers 1 to 9 while the tenth corresponds to zero; the following nine letters also receive the values 1 to 9 whilst the following letter has the value zero; the next five represent the first five units; and the last eight represent the numbers 1 to 8.
Under this system 1 to 5 are represented by four different letters. For example 1 is represented by the letters ka, ta, pa, ya which give the system its name (ka, ta, pa, ya becomes katapaya). Then 6, 7, 8 are represented by three letters and finally nine and zero are represented by two letters.
The system was a spoken one in the sense that consonants and vowels which are not vocalised have no numerical value. The system is a place-value system with zero. In fact many different "words" could represent the same number and this was highly useful for works written in verse.
See also
- Indian astronomy
- Indian mathematicsIndian mathematicsIndian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics , important contributions were made by scholars like Aryabhata, Brahmagupta, and Bhaskara II. The decimal number system in use today was first...
- Indian mathematicians
- History of mathematicsHistory of mathematicsThe area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past....