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Pingala
Acharya Pingala ('; c. 3rd2nd century BCE) was an ancient Indian poet and mathematician, and the author of the ' (also called the ''Pingala-sutras''), the earliest known treatise on Sanskrit prosody. The ' is a work of eight chapters in the late Sūtra style, not fully comprehensible without a commentary. It has been dated to the last few centuries BCE. In the 10th century CE, Halayudha wrote a commentary elaborating on the '. Pingala Maharshi was also said to be the brother of Pāṇini, the famous Sanskrit grammarian, considered the first descriptive linguist''. François & Ponsonnet (2013: 184).'' Combinatorics The ' presents the first known description of a binary numeral system in connection with the systematic enumeration of metres with fixed patterns of short and long syllables. Pingala's discussion of the combinatorics of metre corresponds to the binomial theorem. Halāyudha's 10th-century commentary on the ' includes a presentation of this theorem in what is now ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sanskrit Prosody
Sanskrit prosody or Chandas refers to one of the six Vedangas, or limbs of Vedic studies.James Lochtefeld (2002), "Chandas" in The Illustrated Encyclopedia of Hinduism, Vol. 1: A-M, Rosen Publishing, , page 140 It is the study of poetic metres and verse in Sanskrit. This field of study was central to the composition of the Vedas, the scriptural canons of Hinduism, so central that some later Hindu and Buddhist texts refer to the Vedas as ''Chandas''. The Chandas, as developed by the Vedic schools, were organized around seven major metres, and each had its own rhythm, movements and aesthetics. Sanskrit metres include those based on a fixed number of syllables per verse, and those based on fixed number of morae per verse. Extant ancient manuals on Chandas include Pingala's ''Chandah Sutra'', while an example of a medieval Sanskrit prosody manual is Kedara Bhatta's ''Vrittaratnakara''. The most exhaustive compilations of Sanskrit prosody describe over 600 metres. This is a sub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chandas
Sanskrit prosody or Chandas refers to one of the six Vedangas, or limbs of Vedic studies.James Lochtefeld (2002), "Chandas" in The Illustrated Encyclopedia of Hinduism, Vol. 1: A-M, Rosen Publishing, , page 140 It is the study of poetic metres and verse in Sanskrit. This field of study was central to the composition of the Vedas, the scriptural canons of Hinduism, so central that some later Hindu and Buddhist texts refer to the Vedas as ''Chandas''. The Chandas, as developed by the Vedic schools, were organized around seven major metres, and each had its own rhythm, movements and aesthetics. Sanskrit metres include those based on a fixed number of syllables per verse, and those based on fixed number of morae per verse. Extant ancient manuals on Chandas include Pingala's ''Chandah Sutra'', while an example of a medieval Sanskrit prosody manual is Kedara Bhatta's ''Vrittaratnakara''. The most exhaustive compilations of Sanskrit prosody describe over 600 metres. This is a subst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indian Mathematics
Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhata, Brahmagupta, Bhaskara II, and Varāhamihira. The decimal number system in use today: "The measure of the genius of Indian civilisation, to which we owe our modern (number) system, is all the greater in that it was the only one in all history to have achieved this triumph. Some cultures succeeded, earlier than the Indian, in discovering one or at best two of the characteristics of this intellectual feat. But none of them managed to bring together into a complete and coherent system the necessary and sufficient conditions for a number-system with the same potential as our own." was first recorded in Indian mathematics. Indian mathematicians made early contributions to the study of the concept of zero as a number,: "...our decimal system, which (by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Number
In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the first few values in the sequence are: :0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. The Fibonacci numbers were first described in Indian mathematics, as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths. They are named after the Italian mathematician Leonardo of Pisa, later known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book '' Liber Abaci''. Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the '' Fibonacci Quarterly''. Applications of Fibonacci numbers includ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Numbers
In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the first few values in the sequence are: :0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. The Fibonacci numbers were first described in Indian mathematics, as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths. They are named after the Italian mathematician Leonardo of Pisa, later known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book ''Liber Abaci''. Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the '' Fibonacci Quarterly''. Applications of Fibonacci numbers include ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Number
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" ( zero) and "1" (one). The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because of the simplicity of the language and the noise immunity in physical implementation. History The modern binary number system was studied in Europe in the 16th and 17th centuries by Thomas Harriot, Juan Caramuel y Lobkowitz, and Gottfried Leibniz. However, systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, and India. Leibniz was spec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Numeral System
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" ( zero) and "1" (one). The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because of the simplicity of the language and the noise immunity in physical implementation. History The modern binary number system was studied in Europe in the 16th and 17th centuries by Thomas Harriot, Juan Caramuel y Lobkowitz, and Gottfried Leibniz. However, systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, and India. Leibniz was spec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pascal's Triangle
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in India, Persia, China, Germany, and Italy. The rows of Pascal's triangle are conventionally enumerated starting with row n = 0 at the top (the 0th row). The entries in each row are numbered from the left beginning with k = 0 and are usually staggered relative to the numbers in the adjacent rows. The triangle may be constructed in the following manner: In row 0 (the topmost row), there is a unique nonzero entry 1. Each entry of each subsequent row is constructed by adding the number above and to the left with the number above and to the right, treating blank entries as 0. For example, the initial number of row 1 (or any other row) is 1 (the sum of 0 and 1), whereas the numbers 1 and 3 i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pāṇini
, era = ;;6th–5th century BCE , region = Indian philosophy , main_interests = Grammar, linguistics , notable_works = ' ( Classical Sanskrit) , influenced= , notable_ideas=Descriptive linguistics (Devanagari: पाणिनि, ) was a Sanskrit philologist, grammarian, and revered scholar in ancient India, variously dated between the 6th and 4th century BCE. Since the discovery and publication of his work by European scholars in the nineteenth century, Pāṇini has been considered the "first descriptive linguist", François & Ponsonnet (2013: 184). and even labelled as “the father of linguistics”. Pāṇini's grammar was influential on such foundational linguists as Ferdinand de Saussure and Leonard Bloomfield. Legacy Pāṇini is known for his text '' Aṣṭādhyāyī'', a sutra-style treatise on Sanskrit grammar, 3,996 verses or rules on linguistics, syntax and semantics in "eight chapters" which is the foundational text of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Halayudha
Halayudha (Sanskrit: हलायुध) was a 10th-century Indian mathematician who wrote the ',Maurice Winternitz, ''History of Indian Literature'', Vol. III a commentary on Pingala's ''Chandaḥśāstra''. The latter contains a clear description of Pascal's triangle (called ''meru-prastāra''). Biography Halayudha originally resided at the Rashtrakuta capital Manyakheta, where he wrote under the patronage of emperor Krishna III. His ''Kavi-Rahasya'' eulogizes Krishna III. Later, he migrated to Ujjain in the Paramara kingdom. There, he composed ''Mṛta-Sañjīvanī'' in honour of the Paramara king Munja. Works Halayudha composed the following works: * ''Kavi-Rahasya'', a book on poetics * ''Mṛta-Sañjīvanī'', a commentary on Pingala's ''Chandaḥ-śāstra'' * ''Abhidhana-ratna-mala'', a lexicon * ''Halāyudha Kośa'', a dictionary * He seems to be the first person who came out with the idea of what is today called Pascal's triangle, which he called the staircase ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maurya Period
The Maurya Empire, or the Mauryan Empire, was a geographically extensive Iron Age historical power in the Indian subcontinent based in Magadha, having been founded by Chandragupta Maurya in 322 BCE, and existing in loose-knit fashion until 185 BCE. Quote: "Magadha power came to extend over the main cities and communication routes of the Ganges basin. Then, under Chandragupta Maurya (c.321–297 bce), and subsequently Ashoka his grandson, Pataliputra became the centre of the loose-knit Mauryan 'Empire' which during Ashoka's reign (c.268–232 bce) briefly had a presence throughout the main urban centres and arteries of the subcontinent, except for the extreme south." The Maurya Empire was centralized by the conquest of the Indo-Gangetic Plain, and its capital city was located at Pataliputra (modern Patna). Outside this imperial center, the empire's geographical extent was dependent on the loyalty of military commanders who controlled the armed cities sprinkling it. During Asho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indian Mathematicians
chronology of Indian mathematicians spans from the Indus Valley civilisation and the Vedas to Modern India. Indian mathematicians have made a number of contributions to mathematics that have significantly influenced scientists and mathematicians in the modern era. Hindu-Arabic numerals predominantly used today and likely into the future. Ancient * Baudhayana sutras (fl. c. 900 BCE) *Yajnavalkya (700 BCE) * Manava (fl. 750–650 BCE) * Apastamba Dharmasutra (c. 600 BCE) *''Pāṇini'' (c. 520–460 BCE) * Kātyāyana (fl. c. 300 BCE) * Akspada Gautama(c. 600 BCE–200 CE) *Bharata Muni (200 BCE-200 CE) * Pingala (c. 3rd/2nd century BCE) Classical Post-Vedic Sanskrit to Pala period mathematicians (2nd century BCE to 11th century CE) Medieval Period (1200–1800) Kerala School of Mathematics and Astronomy * Madhava of Sangamagrama * Parameshvara (1360–1455), discovered drk-ganita, a mode of astronomy based on observations * Nilakantha Somayaji (1444–1545), mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
