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Piṅgala
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 bin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binomial Theorem
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, the power expands into a polynomial with terms of the form , where the exponents and are nonnegative integers satisfying and the coefficient of each term is a specific positive integer depending on and . For example, for , (x+y)^4 = x^4 + 4 x^3y + 6 x^2 y^2 + 4 x y^3 + y^4. The coefficient in each term is known as the binomial coefficient or (the two have the same value). These coefficients for varying and can be arranged to form Pascal's triangle. These numbers also occur in combinatorics, where gives the number of different combinations (i.e. subsets) of elements that can be chosen from an -element set. Therefore is usually pronounced as " choose ". Statement According to the theorem, the expansion of any nonnegative integer power of the binomial is a sum of the form (x+y)^n = x^n y^0 + x^ y^1 + x^ y^ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Number
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] |
Halayudha
Halāyudha (Sanskrit: हलायुध) wrote the ', a commentary on Pingala's ''Chandaḥśāstra'', was an Indian Mathematician and poet who lived and worked in the 10th century. The '' Chandaḥśāstra'' by the Indian lyricist Piṅgala (3rd or 2nd century BC) somewhat crypically describes a method of arranging two types of syllables to form metres of various lengths and counting them; as interpreted and elaborated by Halāyudha his "method of pyramidal expansion" (''meru-prastāra'') for counting metres is equivalent to Pascal's triangle. 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'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Patanjali
Patanjali (, , ; also called Gonardiya or Gonikaputra) was the name of one or more author(s), mystic(s) and philosopher(s) in ancient India. His name is recorded as an author and compiler of a number of Sanskrit works. The greatest of these are the '' Yoga Sutras'', a classical yoga text. Estimates based on analysis of this work suggests that its author(s) may have lived between the 2nd century BCE and the 5th century CE. An author of the same name is credited with the authorship of the classic text on Sanskrit grammar named '' Mahābhāṣya'', that is firmly datable to the 2nd century BCE, and authorship of medical texts possibly dating from 8th-10th centuries CE. The two works, ''Mahābhāṣya'' and ''Yoga Sutras'', are completely different in subject matter, and Indologist Louis Renou has shown that there are significant differences in language, grammar and vocabulary. Before the time of Bhoja (11th century), no known text conflates the identity of the two authors. The ... [...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] |
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; in fact, 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, each with 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Albrecht Weber
Friedrich Albrecht Weber (; 17 February 1825 – 30 November 1901) was a Prussian-German Indologist and historian who studied the history of Jainism in India. Some older sources have the first and middle names interchanged. Biography Weber was born in Breslau, where his father Friedrich Benedict Weber was a professor of political economy. The Protestant family had roots in Schleusingen, where their ancestors had held clerical posts. Weber studied Greek, Latin and Hebrew in Thüringen. He then sought to become a historian and went to the University of Breslau. He studied Arabic under Hinrich Middeldorpf and Sanskrit under Adolf Friedrich Stenzler (1807–1887). In 1844, he spent two semester in Bonn attending classes under Christian Lassen and Johannes Gildemeister. At Stenzler's suggestion, he studied the Yajurveda, examining the ninth chapter of the Vâjasaneyi-Samhitâ from a copy in London. He also spent some time in 1845 in Berlin studying under Franz Bopp, H. J. Pe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Place Value
Place may refer to: Geography * Place (United States Census Bureau), defined as any concentration of population ** Census-designated place, a populated area lacking its own municipal government * "Place", a type of street or road name ** Often implies a dead end (street) or cul-de-sac * Place, based on the Cornish word "plas" meaning mansion * Place, a populated place, an area of human settlement ** Incorporated place (see municipal corporation Municipal corporation is the legal term for a local governing body, including (but not necessarily limited to) cities, counties, towns, townships, charter townships, villages, and boroughs. The term can also be used to describe municipally o ...), a populated area with its own municipal government * Location (geography), an area with definite or indefinite boundaries or a portion of space which has a name in an area Placenames * Placé, a commune in Pays de la Loire, Paris, France * Plače, a small settlement in Sloveni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Numbers
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically "0" (zero) and "1" (one). A ''binary number'' may also refer to a rational number that has a finite representation in the binary numeral system, that is, the quotient of an integer by a power of two. 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, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Śūnyatā
''Śūnyatā'' ( ; ; ), translated most often as "emptiness", "Emptiness, vacuity", and sometimes "voidness", or "nothingness" is an Indian philosophical concept. In Buddhism, Jainism, Hinduism, and Indian philosophy, other Indian philosophical traditions, the concept has multiple meanings depending on its doctrinal context. It is either an Ontology, ontological feature of reality, a meditative state, or a Phenomenology (philosophy), phenomenological analysis of experience. In Theravada, Theravāda Buddhism, ' often refers to the Anatta, non-self (Pāli: ', Sanskrit: ') nature of the Skandha, five aggregates of experience and the Āyatana, six sense spheres. ' is also often used to refer to a Buddhist meditation, meditative state or experience. In Mahayana, Mahāyāna Buddhism, ' refers to the tenet that "all things are empty of intrinsic existence and nature (''svabhava'')", but may also refer to the Buddha-nature teachings and primordial or empty awareness, as in Dzogchen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sanskrit
Sanskrit (; stem form ; nominal singular , ,) is a classical language belonging to the Indo-Aryan languages, Indo-Aryan branch of the Indo-European languages. It arose in northwest South Asia after its predecessor languages had Trans-cultural diffusion, diffused there from the northwest in the late Bronze Age#South Asia, Bronze Age. Sanskrit is the sacred language of Hinduism, the language of classical Hindu philosophy, and of historical texts of Buddhism and Jainism. It was a lingua franca, link language in ancient and medieval South Asia, and upon transmission of Hindu and Buddhist culture to Southeast Asia, East Asia and Central Asia in the early medieval era, it became a language of religion and high culture, and of the political elites in some of these regions. As a result, Sanskrit had a lasting effect on the languages of South Asia, Southeast Asia and East Asia, especially in their formal and learned vocabularies. Sanskrit generally connotes several Indo-Aryan languages# ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
