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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] |
Lucas Number
The Lucas numbers or Lucas series are an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and the closely related Fibonacci numbers. Lucas numbers and Fibonacci numbers form complementary instances of Lucas sequences. The Lucas series has the same recursive relationship as the Fibonacci sequence, where each term is the sum of the two previous terms, but with different starting values. This produces a sequence where the ratios of successive terms approach the golden ratio, and in fact the terms themselves are roundings of integer powers of the golden ratio. The sequence also has a variety of relationships with the Fibonacci numbers, like the fact that adding any two Fibonacci numbers two terms apart in the Fibonacci sequence results in the Lucas number in between. The first few Lucas numbers are : 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349 .... Defin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Squares
Fibonacci (; also , ; – ), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'), was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages". The name he is commonly called, ''Fibonacci'', was made up in 1838 by the Franco-Italian historian Guillaume Libri and is short for ('son of Bonacci'). However, even earlier in 1506 a notary of the Holy Roman Empire, Perizolo mentions Leonardo as "Lionardo Fibonacci". Fibonacci popularized the Indo–Arabic numeral system in the Western world primarily through his composition in 1202 of '' Liber Abaci'' (''Book of Calculation''). He also introduced Europe to the sequence of Fibonacci numbers, which he used as an example in ''Liber Abaci''. Biography Fibonacci was born around 1170 to Guglielmo, an Italian merchant and customs official. Guglielmo directed a trading post in Bugia (Béjaïa) in moder ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binet's Formula
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] |
Hemachandra
Hemachandra was a 12th century () Indian Jain saint, scholar, poet, mathematician, philosopher, yogi, grammarian, law theorist, historian, lexicographer, rhetorician, logician, and prosodist. Noted as a prodigy by his contemporaries, he gained the title ''kalikālasarvajña'', "the knower of all knowledge in his times" and ''father of Gujarati language''. Born as Changadeva, he was ordained in the Śvētāmbara school of Jainism in 1110 and took the name Somachandra. In 1125 he became an adviser to King Kumarapala and wrote ''Arhanniti'', a work on politics from a Jain perspective. He also produced ''Trishashti-shalaka-purusha-charita'' (“Deeds of the 63 Illustrious Men”), a Sanskrit epic poem on the history of important figures of Jainism. Later in his life, he changed his name to Hemachandra. Early life Hemachandra was born in Dhandhuka, in present-day Gujarat, on Kartika Sud Purnima (the full moon day of Kartika month). His date of birth differs according to source ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mora (linguistics)
A mora (plural ''morae'' or ''moras''; often symbolized μ) is a basic timing unit in the phonology of some spoken languages, equal to or shorter than a syllable. For example, a short syllable such as ''ba'' consists of one mora (''monomoraic''), while a long syllable such as ''baa'' consists of two (''bimoraic''); extra-long syllables with three moras (''trimoraic'') are relatively rare. Such metrics are also referred to as syllable weight. The term comes from the Latin word for "linger, delay", which was also used to translate the Greek word χρόνος : ''chrónos'' (time) in its metrical sense. Formation The general principles for assigning moras to segments are as follows (see Hayes 1989 and Hyman 1985 for detailed discussion): # A syllable onset (the first consonant or consonants of the syllable) does not represent any mora. # The syllable nucleus represents one mora in the case of a short vowel, and two morae in the case of a long vowel or diphthong. Consonants ser ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 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 ... 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] |
Academic Press
Academic Press (AP) is an academic book publisher founded in 1941. It was acquired by Harcourt, Brace & World in 1969. Reed Elsevier bought Harcourt in 2000, and Academic Press is now an imprint of Elsevier. Academic Press publishes reference books, serials and online products in the subject areas of: * Communications engineering * Economics * Environmental science * Finance * Food science and nutrition * Geophysics * Life sciences * Mathematics and statistics * Neuroscience * Physical sciences * Psychology Well-known products include the ''Methods in Enzymology'' series and encyclopedias such as ''The International Encyclopedia of Public Health'' and the ''Encyclopedia of Neuroscience''. See also * Akademische Verlagsgesellschaft (AVG) — the German predecessor, founded in 1906 by Leo Jolowicz (1868–1940), the father of Walter Jolowicz Walter may refer to: People * Walter (name), both a surname and a given name * Little Walter, American blues harmonica player ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Historia Mathematica
''Historia Mathematica: International Journal of History of Mathematics'' is an academic journal on the history of mathematics published by Elsevier. It was established by Kenneth O. May in 1971 as the free newsletter ''Notae de Historia Mathematica'', but by its sixth issue in 1974 had turned into a full journal. The International Commission on the History of Mathematics began awarding the Montucla Prize, for the best article by an early career scholar in ''Historia Mathematica'', in 2009. The award is given every four years. Editors The editors of the journal have been: * Kenneth O. May, 1974–1977 * Joseph W. Dauben, 1977–1985 * Eberhard Knobloch, 1985–1994 * David E. Rowe, 1994–1996 * Karen Hunger Parshall, 1996–2000 * Craig Fraser and Umberto Bottazzini, 2000–2004 * Craig Fraser, 2004–2007 * Benno van Dalen, 2007–2009 * June Barrow-Green and Niccolò Guicciardini, 2010–2013 * Niccolò Guicciardini and Tom Archibald, 2013-2015 * Tom Archibald and R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natya Shastra
The ''Nāṭya Śāstra'' (, ''Nāṭyaśāstra'') is a Sanskrit treatise on the performing arts. The text is attributed to sage Bharata Muni, and its first complete compilation is dated to between 200 BCE and 200 CE, but estimates vary between 500 BCE and 500 CE. The text consists of 36 chapters with a cumulative total of 6000 poetic verses describing performance arts. The subjects covered by the treatise include dramatic composition, structure of a play and the construction of a stage to host it, genres of acting, body movements, make up and costumes, role and goals of an art director, the musical scales, musical instruments and the integration of music with art performance. The ''Nāṭya Śāstra'' is notable as an ancient encyclopedic treatise on the arts, one which has influenced dance, music and literary traditions in India. It is also notable for its aesthetic "Rasa" theory, which asserts that entertainment is a desired effect of performance arts but not t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bharata Muni
Bharata Muni (Hindi: भरत मुनि) was an ancient sage who the musical treatise '' Natya Shastra'' is traditionally attributed to. The work covers ancient Indian dramaturgy and histrionics, especially Sanskrit theatre. Bharata is considered the father of Indian theatrical art forms. He is dated to between 200 BCE and 200 CE, but estimates vary between 500 BCE and 500 CE.Dace, W. (1963). "The Concept of "Rasa" in Sanskrit Dramatic Theory". Educational Theatre Journal. 15 (3): 249. The ''Nāṭya Śāstra'' is notable as an ancient encyclopedic treatise on the arts, which has influenced dance, music and literary traditions in India. It is also notable for its aesthetic "Rasa" theory, which asserts that entertainment is the desired effect of performance arts but not the primary goal and that the primary goal is to transport the individual in the audience into another parallel reality, full of wonder, where he experiences the essence of his own cons ... [...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] |
Fibonacci Sanskrit Prosody
Fibonacci (; also , ; – ), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'), was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages". The name he is commonly called, ''Fibonacci'', was made up in 1838 by the Franco-Italian historian Guillaume Libri and is short for ('son of Bonacci'). However, even earlier in 1506 a notary of the Holy Roman Empire, Perizolo mentions Leonardo as "Lionardo Fibonacci". Fibonacci popularized the Indo–Arabic numeral system in the Western world primarily through his composition in 1202 of '' Liber Abaci'' (''Book of Calculation''). He also introduced Europe to the sequence of Fibonacci numbers, which he used as an example in ''Liber Abaci''. Biography Fibonacci was born around 1170 to Guglielmo, an Italian merchant and customs official. Guglielmo directed a trading post in Bugia (Béjaïa) in moder ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
