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Chandaḥśāstra
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 cal ... [...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 specifica ... [...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 specifica ... [...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, it is possible to expand the polynomial into a sum involving terms of the form , where the exponents and are nonnegative integers with , 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 the term of is known as the binomial coefficient \tbinom or \tbinom (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 \tbinom gives the number of different combinations of elements that can be chosen from an -element set. Therefore \tbinom is often pronounced as " choose ". History Special cases of the binomial theorem were known since at least the 4th century BC when Greek mathematician Euclid ment ... [...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, it is possible to expand the polynomial into a sum involving terms of the form , where the exponents and are nonnegative integers with , 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 the term of is known as the binomial coefficient \tbinom or \tbinom (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 \tbinom gives the number of different combinations of elements that can be chosen from an -element set. Therefore \tbinom is often pronounced as " choose ". History Special cases of the binomial theorem were known since at least the 4th century BC when Greek mathematician Euclid ment ... [...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 In mathematics, Pascal's trian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metre (poetry)
In poetry, metre ( Commonwealth spelling) or meter ( American spelling; see spelling differences) is the basic rhythmic structure of a verse or lines in verse. Many traditional verse forms prescribe a specific verse metre, or a certain set of metres alternating in a particular order. The study and the actual use of metres and forms of versification are both known as prosody. (Within linguistics, " prosody" is used in a more general sense that includes not only poetic metre but also the rhythmic aspects of prose, whether formal or informal, that vary from language to language, and sometimes between poetic traditions.) Characteristics An assortment of features can be identified when classifying poetry and its metre. Qualitative versus quantitative metre The metre of most poetry of the Western world and elsewhere is based on patterns of syllables of particular types. The familiar type of metre in English-language poetry is called qualitative metre, with stressed syllables comin ... [...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), mathematician a ... [...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] |
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. 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 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. Petermann, Wilhelm Schot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Śūnyatā
''Śūnyatā'' ( sa, wikt:शून्यता#Sanskrit, शून्यता, śūnyatā; pi, suññatā) pronounced in English as (shoon-ya-ta), translated most often as ''emptiness'', ''vacuity'', and sometimes ''voidness'', is a Buddhism, Buddhist concept which has multiple meanings depending on its doctrinal context. It is either an ontological feature of reality, a meditative state, or a phenomenological analysis of experience. In Theravada, Theravāda Buddhism, ''Suññatā'' often refers to the Anatta, non-self (Pāli: ''anattā'', Sanskrit: ''anātman'') nature of the Skandha, five aggregates of experience and the Āyatana, six sense spheres. ''Suññatā'' is also often used to refer to a Buddhist meditation, meditative state or experience. In Mahayana, Mahāyāna Buddhism, ''śūnyatā'' 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 awar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sanskrit
Sanskrit (; attributively , ; nominally , , ) is a classical language belonging to the Indo-Aryan branch of the Indo-European languages. It arose in South Asia after its predecessor languages had diffused there from the northwest in the late 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 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 impact on the languages of South Asia, Southeast Asia and East Asia, especially in their formal and learned vocabularies. Sanskrit generally connotes several Old Indo-Aryan language varieties. The most archaic of these is the Vedic Sanskrit found in the Rig Veda, a colle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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