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Pātīgaṇita
Pātīgaṇita is the term used in pre-modern Indian mathematical literature to denote the area of mathematics dealing with arithmetic and mensuration. The term is a compound word formed by combining the words ''pātī'' and ''gaṇita''. The former is a non-Sanskrit word meaning a "board" and the latter is a Sanskrit word meaning "science of calculation". Thus the term ''pātīgaṇita'' literally means the science of calculations which requires a board (on which dust or sand is spread out) for performing the calculations, or "board-computation" in short. The usage of the term became popular among authors of Indian mathematical works about the beginning of the seventh century CE. It may be noted that Brahmagupta (c. 598 – c. 668 CE) has not used this term. Instead, he uses the term ''dhūlīkarma'' (''dhūlī'' is the Sanskrit term for dust). The terminology ''pātīgaṇita''may be contrasted with "bījagaṇita" which denotes the area of mathematics referred to as algebr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brahmagupta
Brahmagupta ( – ) was an Indian Indian mathematics, mathematician and Indian astronomy, astronomer. He is the author of two early works on mathematics and astronomy: the ''Brāhmasphuṭasiddhānta'' (BSS, "correctly established Siddhanta, doctrine of Brahma", dated 628), a theoretical treatise, and the ''Khandakhadyaka'' ("edible bite", dated 665), a more practical text. In 628 CE, Brahmagupta first described gravity as an attractive force, and used the term "gurutvākarṣaṇam (गुरुत्वाकर्षणम्)" in Sanskrit to describe it. He is also credited with the first clear description of the quadratic formula (the solution of the quadratic equation)Bradley, Michael. ''The Birth of Mathematics: Ancient Times to 1300'', p. 86 (Infobase Publishing 2006) in his main work, the ''Brāhma-sphuṭa-siddhānta''. Life and career Brahmagupta, according to his own statement, was born in 598 CE. Born in ''Bhillamāla'' in Gurjaradesa (modern Bhinmal in Rajasthan, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sridhara
Śrīdhara or Śrīdharācārya (8th–9th century) was an Indian mathematician, known for two extant treatises about arithmetic and practical mathematics, ''Pāṭīgaṇita'' and ''Pāṭīgaṇita-sāra'', and a now-lost treatise about algebra, ''Bījagaṇita''. Life Very little is known about Śrīdhara's life beyond mentions of his mathematical work by later mathematicians and the content of his extant treatises, which do not contain biographical details such as his parents, teachers, or birthplace. Various scholars have suggested he came from the Bengal region or from South India. Based on example problems in his works mentioning Shiva, and a dedication in ''Pāṭīgaṇita-sāra'', he was probably a Shaivism, Shaivite Hindu. He was mentioned by Bhāskara II (12th century), and made apparent reference to Brahmagupta (7th century). Govindasvāmin (9th century) quoted a passage also found in ''Pāṭīgaṇita-sāra'', and overlapping material is found in the work of Mah ... [...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] |
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] |
Ganita Kaumudi
''Ganita Kaumudi'' () is a treatise on mathematics written by Indian mathematician Narayana Pandita in 1356. It was an arithmetical treatise alongside the other algebraic treatise called "Bijganita Vatamsa" by Narayana Pandit. Contents Gaṇita Kaumudī contains about 475 verses of ''sūtra'' (rules) and 395 verses of ''udāharaṇa'' (examples). It is divided into 14 chapters (''vyavahāra''):M. D. Srinivas, ''Mathematics In India'', Lecture 27. 1. Prakīrṇaka-vyavahāra Weights and measures, length, area, volume, etc. It describes addition, subtraction, multiplication, division, square, square root, cube and cube root. The problems of linear and quadratic equations described here are more complex than in earlier works.M. S. Sriram, ''Mathematics in India'', Lecture 25. 63 rules and 82 examples 2. Miśraka-vyavahāra Mathematics pertaining to daily life: “mixture of materials, interest on a principal, payment in instalments, mixing gold objects with different purities ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Narayana Pandita (mathematician)
Nārāyaṇa Paṇḍita () (1340–1400) was an Indian mathematician. Plofker writes that his texts were the most significant Sanskrit mathematics treatises after those of Bhaskara II, other than the Kerala school. He wrote the '' Ganita Kaumudi'' (lit. "Moonlight of mathematics") in 1356 about mathematical operations. The work anticipated many developments in combinatorics. Life and Works About his life, the most that is known is that: Narayana Pandit wrote two works, an arithmetical treatise called ''Ganita Kaumudi'' and an algebraic treatise called ''Bijaganita Vatamsa''. Narayana is also thought to be the author of an elaborate commentary of Bhaskara II's Lilavati, titled ''Karmapradipika'' (or ''Karma-Paddhati''). Although the ''Karmapradipika'' contains little original work, it contains seven different methods for squaring numbers, a contribution that is wholly original to the author, as well as contributions to algebra and magic squares. Narayana's other major work ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Govindasvāmi
Govindasvāmi (or Govindasvāmin, Govindaswami) (c. 800 – c. 860) was an Indian mathematical astronomer most famous for his ''Bhashya'', a commentary on the ''Mahābhāskarīya'' of Bhāskara I, written around 830. The commentary contains many examples illustrating the use of a Sanskrit place-value system and the construction of a sine table. His works have been quoted extensively by Sankaranarayana (fl. 869), Udayadivakara (fl. 1073) and Nilakantha Somayaji (c. 1444-1544). Sankaranarayana was the director of the observatory founded in Mahodayapuram, the capital of the Chera kingdom, and is believed to be the student of Govindasvami. In his book, Sankaranarayana gives explanations to the insightful questions of the king Ravi Varma, then ruler of Mahodayapuram and from these references the period of Sankaranarayana is known. His work ''Govindakriti'' was a sequel to Āryabhaṭīya and is lost. Other works attributed to Govindasvami include''Govinda-paddhati'' (on astro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Āryabhaṭa II
Āryabhaṭa (c. 920 – c. 1000) was an Indian mathematician and astronomer, and the author of the ''Maha-Siddhanta''. The numeral II is given to him to distinguish him from the earlier and more influential Āryabhaṭa I. Scholars are unsure of when exactly he was born, though David Pingree dates of his main publications between 950–1100. The manuscripts of his ''Maha-Siddhanta'' have been discovered from Gujarat, Rajasthan, Uttar Pradesh, and Bengal, so he probably lived in northern India. Maha Siddhanta Aryabhata wrote ''Maha-Siddhanta'', also known as ''Arya-siddhanta'', Sanskrit language work containing 18 chapters. It summarizes a lost work attributed to Parashara, and is probably based on Shridhara's work. The initial twelve chapters deal with topics related to mathematical astronomy and cover the topics that Indian mathematicians of that period had already worked on. The various topics that have been included in these twelve chapters are: the longitudes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Śrīpati
Śrīpati ( – 1066), also transliterated as Shri-pati, was an Indian astronomer, astrologer and mathematician. His major works include ''Dhīkotida-karana'' (1039), a work of twenty verses on solar eclipse, solar and lunar eclipses; ''Dhruva-mānasa'' (written in 1056), a work of 105 verses on calculating planetary longitudes, eclipses and planetary Astronomical transit, transits; ''Siddhānta-śekhara'' a major work on astronomy in 19 chapters; and ''Gaṇita-tilaka'', an incomplete arithmetical treatise in 125 verses based on a work by Shridhara. Biography Śrīpati was born in Rohinikhand in present-day Maharashtra, and lived during (–1066. His father was Naga-deva (sometimes written as Namadeva) and his grandfather was Kesava. Śrīpati followed the teachings of Lalla, and wrote on astrology, astronomy and mathematics. He was mainly focused on astrology, and his work on astronomy was aimed at supporting his research on astrology; his work on mathematics, in turn, was aim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internet Archive
The Internet Archive is an American 501(c)(3) organization, non-profit organization founded in 1996 by Brewster Kahle that runs a digital library website, archive.org. It provides free access to collections of digitized media including websites, Application software, software applications, music, audiovisual, and print materials. The Archive also advocates a Information wants to be free, free and open Internet. Its mission is committing to provide "universal access to all knowledge". The Internet Archive allows the public to upload and download digital material to its data cluster, but the bulk of its data is collected automatically by its web crawlers, which work to preserve as much of the public web as possible. Its web archiving, web archive, the Wayback Machine, contains hundreds of billions of web captures. The Archive also oversees numerous Internet Archive#Book collections, book digitization projects, collectively one of the world's largest book digitization efforts. ... [...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] |
