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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] |
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 calle ... [...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 in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paramara
The Paramara dynasty (IAST: Paramāra) was an Indian dynasty that ruled Malwa and surrounding areas in west-central India between 9th and 14th centuries. They belonged to the Parmara clan of the Rajputs. The dynasty was established in either the 9th or 10th century, and its early rulers most probably ruled as vassals of the Rashtrakutas of Manyakheta. The earliest extant Paramara inscriptions, issued by the 10th-century ruler Siyaka, have been found in Gujarat. Around 972 CE, Siyaka sacked the Rashtrakuta capital Manyakheta, and established the Paramaras as a sovereign power. By the time of his successor Munja, the Malwa region in present-day Madhya Pradesh had become the core Paramara territory, with Dhara (now Dhar) as their capital. The dynasty reached its zenith under Munja's nephew Bhoja, whose kingdom extended from Chittor in the north to Konkan in the south, and from the Sabarmati River in the west to Vidisha in the east. The Paramara power rose and declined several ti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vakpati Munja
Munja (reigned c. 972-990s CE), also known as Vakpati II, was an Indian ruler from the Paramara dynasty, who ruled in the Malwa region. He is known for consolidating the Paramara kingdom, for patronizing poets and scholars and for achieving the military success against almost all of the neighbouring kingdoms. Munja achieved military successes against the Chahamanas, the Guhilas, the Hunas, the Kalachuris, and the ruler of Gurjara region (possibly a Chaulukya or Pratihara ruler). He also achieved some early successes against the Western Chalukya king Tailapa II, but was ultimately defeated and killed by Tailapa some time between 994 CE and 998 CE. Early life Munja succeeded Siyaka as the Paramara king, ascending the throne around 972 CE. According to ''Prabandha-Chintamani'' by the 14th century writer Merutunga, Munja was an adopted child of the king Simhadantabhatta (Siyaka). The king discovered him in a munja grassland. Since the king did not have any children of his own ... [...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] |
Paramara Kingdom
The Paramara dynasty (IAST: Paramāra) was an Indian dynasty that ruled Malwa and surrounding areas in west-central India between 9th and 14th centuries. They belonged to the Parmara clan of the Rajputs. The dynasty was established in either the 9th or 10th century, and its early rulers most probably ruled as vassals of the Rashtrakutas of Manyakheta. The earliest extant Paramara inscriptions, issued by the 10th-century ruler Siyaka, have been found in Gujarat. Around 972 CE, Siyaka sacked the Rashtrakuta capital Manyakheta, and established the Paramaras as a sovereign power. By the time of his successor Vakpati Munja, Munja, the Malwa region in present-day Madhya Pradesh had become the core Paramara territory, with Dhara (city), Dhara (now Dhar) as their capital. The dynasty reached its zenith under Munja's nephew Bhoja, whose kingdom extended from Chittorgarh Fort, Chittor in the north to Konkan in the south, and from the Sabarmati River in the west to Vidisha in the east. The ... [...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] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
India
India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the south, the Arabian Sea on the southwest, and the Bay of Bengal on the southeast, it shares land borders with Pakistan to the west; China, Nepal, and Bhutan to the north; and Bangladesh and Myanmar to the east. In the Indian Ocean, India is in the vicinity of Sri Lanka and the Maldives; its Andaman and Nicobar Islands share a maritime border with Thailand, Myanmar, and Indonesia. Modern humans arrived on the Indian subcontinent from Africa no later than 55,000 years ago., "Y-Chromosome and Mt-DNA data support the colonization of South Asia by modern humans originating in Africa. ... Coalescence dates for most non-European populations average to between 73–55 ka.", "Modern human beings—''Homo sapiens''—originated in Africa. Then, int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Close Reading
In literary criticism, close reading is the careful, sustained interpretation of a brief passage of a text. A close reading emphasizes the single and the particular over the general, effected by close attention to individual words, the syntax, the order in which the sentences unfold ideas, as well as formal structures. A truly attentive close reading means thinking about both what is being said in a passage (the content), and how it is being said (the form, i.e. the manner in which the content is presented) and leading it to possibilities for observation and insight. History Literary close reading and commentaries have extensive precedent in the exegesis of religious texts, and more broadly, hermeneutics of ancient works. For example, Pazand, a genre of middle Persian literature, refers to the ''Zend'' (literally: 'commentary'/'translation') texts that offer explanation and close reading of the Avesta, the sacred texts of Zoroastrianism. The scriptural commentaries of the Talmu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rashtrakuta
Rashtrakuta (IAST: ') (r. 753-982 CE) was a royal Indian dynasty ruling large parts of the Indian subcontinent between the sixth and 10th centuries. The earliest known Rashtrakuta inscription is a 7th-century copper plate grant detailing their rule from manapur a city in Central or West India. Other ruling Rashtrakuta clans from the same period mentioned in inscriptions were the kings of Achalapur and the rulers of Kannauj. Several controversies exist regarding the origin of these early Rashtrakutas, their native homeland and their language. The Elichpur clan was a feudatory of the Badami Chalukyas, and during the rule of Dantidurga, it overthrew Chalukya Kirtivarman II and went on to build an empire with the Gulbarga region in modern Karnataka as its base. This clan came to be known as the Rashtrakutas of Manyakheta, rising to power in South India in 753 AD. At the same time the Pala dynasty of Bengal and the Prathihara dynasty of Malwa were gaining force in eastern and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manyakheta
Malkhed originally known as Manyakheta (IAST: Mānyakheṭa, Prakrit: "Mannakheḍa"), and also known as Malkhed,Village code= 311400 Malkhed (J), Gulbarga, Karnataka is a town in Karnataka, India. It is located on the banks of Kagina river in Sedam Taluk of Kalaburagi district, around 40 km from Kalaburagi. The city reached the peak of its prosperity during the 9th and 10th centuries, serving as the capital of the expansionist Rashtrakuta dynasty, which united almost all of the Deccan. At Manyakheta, there is a historical fort whose restoration is in progress based on a proposal submitted by HKADB (Hyderabad Karnataka Area Development Board). Demographics India census, Malkheda had a population of 11,180 with 5,679 males and 5,501 females and 2,180 households. History Manyakheta rose to prominence when the capital of Rashtrakutas was moved from Mayurkhandi in Bidar district to Mānyakheṭa during the rule of Amoghavarsha I. After the fall of the Rāṣṭrakūṭa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
