|
Bījapallava
Bījapallava (or Bījapallavaṃ) is a commentary in Sanskrit of Bhaskara II's Bījagaṇita composed by the 16th-17th century astrologer-mathematician Kṛṣṇa Daivajña. This work is also known by several other names: ''Kalpālatāvatāra'', ''Bījānkura'' and ''Nāvāakura''. A manuscript of the work, copied in 1601, has survived to the present day indicating that the work must have been composed earlier than 1601. The ''Bījapallava'' commentary is written in prose. Commentaries composed in prose, since they are not constrained by considerations of conforming to a particular meter, generally contain more information, more detailed explanations and often original material not found in the work on which the commentary is written. ''Bījapallava'' also follows this general pattern. T. Hayashi, a Japanese historian of Indian mathematics, in his forward to the critical edition of ''Bījapallava'', writes: :". . . he ṛṣṇa Daivajñagoes on to discuss the mathematical cont ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kṛṣṇa Daivajña
Kṛṣṇa Daivajña was a 16th-17th century Indian astrologer-astronomer-mathematician from Varanasi patronized by the Mughal Emperors, Mughal Emperor Jahangir. As a mathematician Kṛṣṇa Daivajña is best known for his elaborate commentary on Bhaskara II's (c. 1114–1185) ''Bijaganita, Bījagaṇita'' and, as an astrologer, his fame rested on his commentary on Śrīpati's (c. 1019 – 1066) ''Jātakapaddhati''. These commentaries contain not only detailed explanations of the text being commented upon, but also the rationales of the various rules and often additional original material. (p. iii-vi) He has also composed an original work by name ''Chādakanirṇaya'' dealing with eclipses. Kṛṣṇa Daivajña's family originally lived in Dadhigrama in the Vidarbha region; his father moved his family to Varanasi and took residence there. Kṛṣṇa Daivajña's father was Ballāla and his grandfather was Trimalla. He had five brothers of whom Ranganātha was known for his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bijaganita
''Bijaganita'' ( iːd͡ʒəgəɳit̪ᵊ, -ɪt̪ᵊ IAST: ') was treatise on algebra by the Indian mathematician Bhāskara II. It is the second volume of his main work '' Siddhānta Shiromani (''"Crown of treatises") alongside '' Lilāvati'', ''Grahaganita'' and ''Golādhyāya''. Meaning The title of the work, , which literally translates to "mathematics () using seeds ()", is one of the two main branches of mediaeval Indian mathematics, the other being , or "mathematics using algorithms". derives its name from the fact that "it employs algebraic equations () which are compared to seeds () of plants since they have the potentiality to generate solutions to mathematical problems." Contents The book is divided into six parts, mainly indeterminate equations, quadratic equations, simple equations, surds. The contents are: * Introduction * On Simple Equations * On Quadratic Equations * On Equations involving indeterminate Questions of the 1st Degree * On Equations involving inde ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bhāskara II
Bhāskara II ('; 1114–1185), also known as Bhāskarāchārya (), was an Indian people, Indian polymath, Indian mathematicians, mathematician, astronomer and engineer. From verses in his main work, Siddhānta Śiromaṇi, it can be inferred that he was born in 1114 in Vijjadavida (Vijjalavida) and living in the Satpura mountain ranges of Western Ghats, believed to be the town of Patana in Chalisgaon, located in present-day Khandesh region of Maharashtra by scholars. In a temple in Maharashtra, an inscription supposedly created by his grandson Changadeva, lists Bhaskaracharya's ancestral lineage for several generations before him as well as two generations after him. Henry Thomas Colebrooke, Henry Colebrooke who was the first European to translate (1817) Bhaskaracharya II's mathematical classics refers to the family as Maharashtrian Brahmins residing on the banks of the Godavari River, Godavari. Born in a Hindu Deshastha Brahmin family of scholars, mathematicians and astrono ... [...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] |
Henry Thomas Colebrooke
Henry Thomas Colebrooke FRS FRSE FLS (15 June 1765 – 10 March 1837) was an English orientalist and botanist. He has been described as "the first great Sanskrit scholar in Europe". Biography Henry Thomas Colebrooke was born on 15 June 1765. His parents were Sir George Colebrooke, 2nd Baronet, MP for Arundel and Chairman of the East India Company from 1769, and Mary Gaynor, daughter and heir of Patrick Gaynor of Antigua. He was educated at home, and from the age of twelve to sixteen he lived in France. In 1782 Colebrooke was appointed through his father's influence to a writership with the East India Company in Calcutta. In 1786 and three years later he was appointed assistant collector in the revenue department at Tirhut. He wrote ''Remarks on the Husbandry and Commerce of Bengal'', which was privately published in 1795, by which time he had transferred to Purnia. This opposed the East India Company's monopoly on Indian trade, advocating instead for free trade be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Līlāvatī
''Līlāvatī'' is a treatise by Indian mathematician Bhāskara II on mathematics, written in 1150 AD. It is the first volume of his main work, the ''Siddhānta Shiromani'', alongside the ''Bijaganita'', the ''Grahaganita'' and the ''Golādhyāya''. Name Bhaskara II's book on arithmetic is the subject of interesting legends that assert that it was written for his daughter, Lilavati. As the story goes, the author had studied Lilavati's horoscope and predicted that she would remain both childless and unmarried. To avoid this fate, he ascertained an auspicious moment for his daughter's wedding. To alert his daughter at the correct time, he placed a cup with a small hole at the bottom of a vessel filled with water, arranged so that the cup would sink at the beginning of the propitious hour. He put the device in a room with a warning to Lilavati to not go near it. In her curiosity, though, she went to look at the device. A pearl from her bridal dress accidentally dropped into it, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Line
A number line is a graphical representation of a straight line that serves as spatial representation of numbers, usually graduated like a ruler with a particular origin point representing the number zero and evenly spaced marks in either direction representing integers, imagined to extend infinitely. The association between numbers and points on the line links arithmetical operations on numbers to geometric relations between points, and provides a conceptual framework for learning mathematics. In elementary mathematics, the number line is initially used to teach addition and subtraction of integers, especially involving negative numbers. As students progress, more kinds of numbers can be placed on the line, including fractions, decimal fractions, square roots, and transcendental numbers such as the circle constant : Every point of the number line corresponds to a unique real number, and every real number to a unique point. Using a number line, numerical concepts can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kuṭṭaka
Kuṭṭaka is an algorithm for finding integer solutions of linear Diophantine equations. A linear Diophantine equation is an equation of the form ''ax'' + ''by'' = ''c'' where ''x'' and ''y'' are unknown quantities and ''a'', ''b'', and ''c'' are known quantities with integer values. The algorithm was originally invented by the Indian astronomer-mathematician Āryabhaṭa (476–550 CE) and is described very briefly in his Āryabhaṭīya. Āryabhaṭa did not give the algorithm the name ''Kuṭṭaka'', and his description of the method was mostly obscure and incomprehensible. It was Bhāskara I (c. 600 – c. 680) who gave a detailed description of the algorithm with several examples from astronomy in his ''Āryabhatiyabhāṣya'', who gave the algorithm the name ''Kuṭṭaka''. In Sanskrit, the word Kuṭṭaka means ''pulverization'' (reducing to powder), and it indicates the nature of the algorithm. The algorithm in essence is a process where the coefficients in a given lin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diophantine Equation
''Diophantine'' means pertaining to the ancient Greek mathematician Diophantus. A number of concepts bear this name: *Diophantine approximation In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria. The first problem was to know how well a real number can be approximated ... * Diophantine equation * Diophantine quintuple * Diophantine set {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Equation
In mathematics, a quadratic equation () is an equation that can be rearranged in standard form as ax^2 + bx + c = 0\,, where the variable (mathematics), variable represents an unknown number, and , , and represent known numbers, where . (If and then the equation is linear equation, linear, not quadratic.) The numbers , , and are the ''coefficients'' of the equation and may be distinguished by respectively calling them, the ''quadratic coefficient'', the ''linear coefficient'' and the ''constant coefficient'' or ''free term''. The values of that satisfy the equation are called ''solution (mathematics), solutions'' of the equation, and ''zero of a function, roots'' or ''zero of a function, zeros'' of the quadratic function on its left-hand side. A quadratic equation has at most two solutions. If there is only one solution, one says that it is a double root. If all the coefficients are real numbers, there are either two real solutions, or a single real double root, or two comple ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indian Mathematics
Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhata, Brahmagupta, Bhaskara II, Varāhamihira, and Madhava of Sangamagrama, Madhava. The Decimal, decimal number system in use today: "The measure of the genius of Indian civilisation, to which we owe our modern (number) system, is all the greater in that it was the only one in all history to have achieved this triumph. Some cultures succeeded, earlier than the Indian, in discovering one or at best two of the characteristics of this intellectual feat. But none of them managed to bring together into a complete and coherent system the necessary and sufficient conditions for a number-system with the same potential as our own." was first recorded in Indian mathematics. Indian mathematicians made early contributions to the study of the concept of 0 (number), ze ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
