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Virahanka
Virahanka (Devanagari: विरहाङ्क) was an Indian prosodist who is also known for his work on mathematics. He may have lived in the 6th century, but it is also possible that he worked as late as the 8th century. His work on prosody builds on the ''Chhanda-sutras'' of Pingala (4th century BCE), and was the basis for a 12th-century commentary by Gopala. He was the first to propose the so-called Fibonacci Sequence. See also *Indian mathematicians Indian mathematicians have made a number of contributions to mathematics that have significantly influenced scientists and mathematicians in the modern era. One of such works is Hindu numeral system which is predominantly used today and is likely ... References External links ''The So-called Fibonacci Numbers in Ancient and Medieval India'' by Parmanand Singh 8th-century Indian mathematicians Fibonacci numbers Medieval Sanskrit grammarians Ancient Indian mathematical works {{asia-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gopala (mathematician)
In mathematics, the Fibonacci sequence is a sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted . Many writers begin the sequence with 0 and 1, although some authors start it from 1 and 1 and some (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the sequence begins : 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, also known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book . 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 Fibonac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Sequence
In mathematics, the Fibonacci sequence is a Integer sequence, sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted . Many writers begin the sequence with 0 and 1, although some authors start it from 1 and 1 and some (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the sequence begins : 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, also known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book . Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the ''Fibonacci Quarterly''. Appli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Numbers
In mathematics, the Fibonacci sequence is a sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted . Many writers begin the sequence with 0 and 1, although some authors start it from 1 and 1 and some (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the sequence begins : 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, also known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book . 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 Fibon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 '. According to some historians Maharshi Pingala was the brother of Pāṇini, the famous Sanskrit grammarian, considered the first descriptive linguist''. François & Ponsonnet (2013: 184).'' Another think tank identifies him as Patanjali, the 2nd century CE scholar who authored Mahabhashya. Combinatorics The ' presents a formula to generate systematic enumerations of metres, of all possible combinations of light (''laghu'') and heavy (''guru'') syllables, for a word of ''n'' syllables, using a recursive formula, that results in a partially ordered ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indian Mathematicians
Indian mathematicians have made a number of contributions to mathematics that have significantly influenced scientists and mathematicians in the modern era. One of such works is Hindu numeral system which is predominantly used today and is likely to be used in the future. Ancient (Before 320 CE) *Shulba sutras (around 1st millenium BCE) * 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) *Nyāya Sūtras, Akṣapada Gautama(c. 600 BCE–200 CE) *Bharata Muni (200 BCE-200 CE) *Pingala (c. 3rd/2nd century BCE) * Bhadrabahu (367 – 298 BCE) * Umasvati (c. 200 CE) * Yavaneśvara, Yavaneśvara (2nd century) * Vasishtha Siddhanta, 4th century CE Classical (320 CE–520 CE) *Vasishtha Siddhanta, 4th century CE * Aryabhata (476–550 CE) * Yativrsabha (500–570) * Varahamihira (505–587 CE) * Yativṛṣabha, (6th-century CE) * Virahanka (6th cent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prosody (linguistics)
In linguistics, prosody () is the study of elements of speech, including intonation, stress, rhythm and loudness, that occur simultaneously with individual phonetic segments: vowels and consonants. Often, prosody specifically refers to such elements, known as ''suprasegmentals'', when they extend across more than one phonetic segment. Prosody reflects the nuanced emotional features of the speaker or of their utterances: their obvious or underlying emotional state, the form of utterance (statement, question, or command), the presence of irony or sarcasm, certain emphasis on words or morphemes, contrast, focus, and so on. Prosody displays elements of language that are not encoded by grammar, punctuation or choice of vocabulary. Attributes of prosody In the study of prosodic aspects of speech, it is usual to distinguish between auditory measures ( subjective impressions produced in the mind of the listener) and objective measures (physical properties of the sound wave and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
8th-century Indian Mathematicians
The 8th century is the period from 701 (represented by the Roman numerals DCCI) through 800 (DCCC) in accordance with the Julian Calendar. In the historiography of Europe the phrase the long 8th century is sometimes used to refer to the period of circa AD 660–820. The coast of North Africa and the Iberian Peninsula quickly came under Islamic Arab domination. The westward expansion of the Umayyad Empire was famously halted at the siege of Constantinople by the Byzantine Empire and the Battle of Tours by the Franks. The tide of Arab conquest came to an end in the middle of the 8th century.Roberts, J., '' History of the World'', Penguin, 1994. In Europe, late in the century, the Vikings, seafaring peoples from Scandinavia, begin raiding the coasts of Europe and the Mediterranean, and go on to found several important Monarchy, kingdoms. In Asia, the Pala Empire is founded in Bengal. The Tang dynasty reaches its pinnacle under China, Chinese Emperor Xuanzong of Tang, Emper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Medieval Sanskrit Grammarians
In the history of Europe, the Middle Ages or medieval period lasted approximately from the 5th to the late 15th centuries, similarly to the post-classical period of global history. It began with the fall of the Western Roman Empire and transitioned into the Renaissance and the Age of Discovery. The Middle Ages is the middle period of the three traditional divisions of Western history: classical antiquity, the medieval period, and the modern period. The medieval period is itself subdivided into the Early, High, and Late Middle Ages. Population decline, counterurbanisation, the collapse of centralised authority, invasions, and mass migrations of tribes, which had begun in late antiquity, continued into the Early Middle Ages. The large-scale movements of the Migration Period, including various Germanic peoples, formed new kingdoms in what remained of the Western Roman Empire. In the 7th century, North Africa and the Middle East—once part of the Byzantine Empire—came und ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
