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Topic: Bhaskara II

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	Bhaskaracharya
		Bhaskara was born in 1114 A.D. according to a statement he recorded in one of his own works.
		Bhaskara wrote his famous Siddhanta Siroman in the year 1150 A.D. It is divided into four parts; Lilavati (arithmetic), Bijaganita (algebra), Goladhyaya (celestial globe), and Grahaganita (mathematics of the planets).
		Bhaskara was somewhat of a poet as were many Indian mathematicians at this time.
	www.math.sfu.ca /histmath/India/12thCenturyAD/Bhaskara.html (229 words)

	Bhaskara II Encyclopedia
		Kumar Bhaskara Varman was the Maharaja of the Kamarupa kingdom in the 7th century C.E. He patronized the Buddhist traveler I Ching, though he was not a Buddhist himself.
		Bhaskara wrote an important commentary on the Shiva Sutras of Vasugupta.
		the cohort during the period [0, M]: (i) dies of cancer, (ii) dies of other causes, (iii) leaves the study, or (iv) is...
	www.hallencyclopedia.com /topic/Bhaskara_II.html (254 words)

	Bhaskara Biography \| scit_02123_package.xml
		Bhaskara, one of the greatest medieval Indian scholars, pioneered learning in a number of areas, most notably in his approximations of π.
		Director of the astronomical observatory at Ujjain, he was at the center of scientific activities in the India of his time, and his work in number systems and equations represented a level of understanding far beyond that of contemporary Europeans.
		Bhaskara is known variously as Bhaskara II, Atscharja Bhaskara, Bhaskaracharya, and Bhaskara the Learned.
	www.bookrags.com /biography/bhaskara-scit-02123 (386 words)

	did you know?
		There is a story which says that Bhaskara put to use all his astrological knowledge to find out an auspicious moment for her marriage, and on the marriage day had a water-clock fixed up as to hit the exact time favourable for her happy marriage, but his efforts were foiled by the child-bride herself.
		Bhaskara's treatment of the mathematics of the zero is remarkable for the undoubted realisation that any quantity divided by zero is infinity (termed Khahara or Khahara having zero as divisor) and for the implied concept of the infinitestimal.
		Bhaskara calculated the equinoctial shadow at any place and the new corrections to be applied to the calculation of the time of sunrise.
	www.infinityfoundation.com /mandala/t_dy/t_dy_Q13.htm (1909 words)

	8 V. Bhaskaracharya II
		8 V. Bhaskaracharya II Bhaskaracharya, or Bhaskara II, is regarded almost without question as the greatest Hindu mathematician of all time and his contribution to not just Indian, but world mathematics is undeniable.
		Evidence suggests Bhaskara was fully acquainted with the principle of differential calculus, and that his researches were in no way inferior to Newton's, asides the fact that it seems he did not understand the utility of his researches, and thus historians of mathematics generally neglect his outstanding achievement, which is extremely regrettable.
		Bhaskara also goes deeper into the 'differential calculus' and suggests the differential coefficient vanishes at an extremum value of the function, indicating knowledge of the concept of 'infinitesimals'
	www-groups.dcs.st-and.ac.uk /~history/Projects/Pearce/Chapters/Ch8_5.html (763 words)

	Bhaskara I - Wikipedia, the free encyclopedia
		Bhaskara is considered as the most important scholar of the Aryabhata's astronomical school.
		Bhaskara's probably most important mathematical contribution concerns the representation of numbers in a positional system.
		Presumably, Bhaskara did not invent it, but he was the first having no compunctions to use the Brahmi numerals in a scientific contribution in Sanskrit.
	en.wikipedia.org /wiki/Bhaskara_I (762 words)

	8 V. Bhaskaracharya II
		8 V. Bhaskaracharya II Bhaskaracharya, or Bhaskara II, is regarded almost without question as the greatest Hindu mathematician of all time and his contribution to not just Indian, but world mathematics is undeniable.
		Evidence suggests Bhaskara was fully acquainted with the principle of differential calculus, and that his researches were in no way inferior to Newton's, asides the fact that it seems he did not understand the utility of his researches, and thus historians of mathematics generally neglect his outstanding achievement, which is extremely regrettable.
		Bhaskara also goes deeper into the 'differential calculus' and suggests the differential coefficient vanishes at an extremum value of the function, indicating knowledge of the concept of 'infinitesimals'
	turnbull.mcs.st-and.ac.uk /~history/Projects/Pearce/Chapters/Ch8_5.html (763 words)

	Pell's equation
		Bhaskara II now knows (but he gives no proof) that when m is chosen so that am + b is divisible by k then m
		Next Bhaskara II knows that there are infinitely many m such that am + b is divisible by k.
		Bhaskara II knows (almost certainly by experience rather than by having a proof) that the process will end after a finite number of steps.
	www-gap.dcs.st-and.ac.uk /~history/HistTopics/Pell.html (2173 words)

	Part.7
		The main mathematicians of the tenth century in India were Aryabhata II and Vijayanandi, both adding to the understanding of sine tables and trigonometry to support their astronomical calculations.
		Following Bhaskara II there was over 200 years before any other major contributions to mathematics were made on the Indian subcontinent.
		In fact for a long time it was thought that Bhaskara II represented the end of mathematical developments in the Indian subcontinent until modern times.
	www.alumbo.com /article/10027-Part-7 (946 words)

	Schneier on Security: World War II Statistics-and-Security Story
		This also works with estimating Saddams WMD's as dividing by 0 usually works in your favour...
		The answer is either infinite (Bhaskara II) or "undefined" meaning you can use the "over-estimating (intellegence) method"....
		If you prefer to receive Bruce Schneier's comments on security as a monthly e-mail digest, subscribe to Schneier on Security's sister publication, Crypto-Gram.
	www.schneier.com /blog/archives/2006/08/world_war_ii_st.html (1762 words)

	TIMELINE 12th CENTURY page of ULTIMATE SCIENCE FICTION WEB GUIDE
		Bhaskara II) 1117: P'ingchow Table Talk by Chu Yu, has the first known mention in China of a compass being used for oceanic navigation.
		Book II of his Policraticus is devoted to a general discussion of omens, divination and the philosophical problems of predestination.
		Bhaskara II) 1126: Averroes (Mohammed ibn Ahmed ibn Mohammed ibn Roshd, Abu Velid) [c.1126-1198 or 1199] 1135: Maimonides (Rabbi Moses ben Maimun) [1135-1204] 1140: Johannes Hispalensis [c.1140] 8 Sep 1157: Birth of Alexander Neckham in St.Albans, England.
	www.magicdragon.com /UltimateSF/timeline12.html (5788 words)

	Metanexus Institute
		Bhaskara was an eminent mathematician of India who lived in the 12th century.
		Since there had been another astronomer of that name earlier, this one is referred to, in a royal sort of way, as Bhaskara II.
		Bhaskara II also wrote on astronomy: on planetary conjunctions with stars, on solar orbits and lunar phases, and even on the radius of the sun's path.
	www.metanexus.net /metanexus_online/show_article2.asp?ID=5180 (1409 words)

	timelinescience - 1101 to 1200
		The first mention in Chinese literature of a compass being used for navigation at sea and, between 1150-59, the Chinese also develop the first rockets.
		Bhaskara II, an Indian mathematician, modifies a 5th century idea from Sanskrit writings to describe a wheel which he claims will run indefinitely - an early perpetual motion machine.
		Modern science tells us that such machines are impossible since they conflict with laws which describe the behaviour of energy.
	www.timelinescience.org /years/1200.htm (334 words)

	Math-History Timeline
		Bhaskara is also known as Bhaskara II or as Bhaskaracharya (meaning "Bhaskara the Teacher").
		Bhaskara is considered to represent the peak of mathematical knowledge in the 12th century.
		King Henry II had appointed Becket to the top post of the Church believing that he was appointing someone he could control.
	www.math.wichita.edu /~richardson/timeline.html (9728 words)

	Diaspora (Site not responding. Last check: 2007-11-03)
		1000 CE by a grant from Bhaskara Ravivarman II of Kerala, to Joseph Rabban, the leader of the exceedingly ancient Malabari Jewish community.
		The grant was engraved on a set of copper plates, extant to this day, which forms a charter of royal privileges for Kerala's Jews.
		In response to anti-Jewish persecution by Shah Kobad, spurred on by the Mazdak movement, Mar Zutra II rebelled against the Persian government and established an independent state around the town of Makhoza, with himself as head of state and a high council composed of rabbis.
	ellone-loire.net /obsidian/Diaspora.html (5330 words)

	Indian Space Program by Subhajit Ghosh
		Orders and instructions were transmitted to the experimental 360 kg satellite Aryabhata from the control station at Sriharikota.
		Bhaskara-I was the second Indian satellite and Bhaskara-II the third which were launched from the same soviet cosmodrome mainly for observations on the earth.
		With the successful launch of SLV-3 on 18th July 1980 when a 35 kg satellite called Rohini I was placed in LEO, India became only the seventh nation in the world to achieve space orbit capability.
	www.boloji.com /computing/012.htm (1461 words)

	Desicritics.org: Say, Lovely Woman, The Number of Bees: Bhaskara's Lilavati
		There's an earlier Bhaskara, also famous, so Lilavati's Bhaskara is sometimes referred to as Bhaskara II or Bhaksaracharya.
		In Bhaskara's time, 'shyness'-- at least in Sanskrit poetics-- was as much a performance, as say, cock fighting.
		Beautiful A. Bhaskara in the role of a 12th century 'Agrawal classes' textbook writer is LoL.
	desicritics.org /2006/09/02/163714.php (1603 words)

	The Date of Mahabharata Based on the Indian Astronomical Works (Site not responding. Last check: 2007-11-03)
		For critical study, the commentaries of Bhaskara I, Somesvara and Suryadeva Yajvan are considered, so that their view prevalent during their period could be understood.
		Therefore, Bhaskara and Someswara had known the significance of the association of Bharat War with the starting of the Kaliyuga.
		This is repeated in Brahma-sputha-Siddhanta (i.4), Maha-Siddhanta of Aryabhata II (i.5), Siddhanta-sekhara (i.10), Siddhanta-siromani of Bhaskara II (I.i.15).
	www.hindunet.org /saraswati/colloquium/astronomy01.htm (4315 words)

	Math History - Middle Ages
		Gerbert of Aurillac (later Pope Sylvester II) reintroduces the abacus into Europe.
		Bhaskara II (sometimes known as Bhaskaracharya) writes Lilavati (The Beautiful) on arithmetic and geometry, and Bijaganita (Seed Arithmetic), on algebra.
		Adelard of Bath produces two or three translations of Euclid's Elements from Arabic.
	lahabra.seniorhigh.net /pages/teachers/pages/math/timeline/MmiddleAges.html (856 words)

	Chowk : Ideas & Identities of India Pakistan
		Of course it does not work since if it were introduced as Bhaskara II suggests then 0 times infinity must be equal to every number n, so all numbers are equal.
		And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it about.
		It is significant that Fibonacci is not bold enough to treat 0 in the same way as the other numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 since he speaks of the "sign" zero while the other symbols he speaks of as numbers.
	www.chowk.com /show_interactor_page.cgi?membername=fawadnajam (13191 words)

	História da Matemática na Índia - Bhaskara II
		Bhaskara II Bhaskara nasceu em 1114, na Índia, numa terra chamada Vijalavida (da qual se desconhece a localização) e morreu, provavelmente, em 1193, aos 79 anos.
		Foi este tradutor que introduziu a história de que Lilavati era o nome da filha de Bhaskara.
		De acordo com essa história, a partir do seu horóscopo, Bhaskara tinha previsto o dia e a hora propícia para o casamento da sua filha.
	www.malhatlantica.pt /mathis/India/BhaskaraII.htm (437 words)

	Storytelling Science: Aryabhata and Diophantus' son
		Many months later, you are eating appam with a friend from Kerala, when he shows you an old palm leaf, about half a meter by ten cm, across which are fine engravings in ancient Malayalam.
		These methods were unknown in the west, and this very equation was posed as a problem in 1657 by the French mathematician Pierre de Fermat - however, its solution was found only seventy years later by Euler.
		Meanwhile, many centuries ago, the solution to this equation was recorded by Bhaskara II (1150AD), using a modified version of Brahmagupta's method (no wonder it is difficult; the lowest values are x = 226153980 and y = 1766319049).
	www.cse.iitk.ac.in /~amit/story/19_aryabhata.html (1017 words)

	winners
		This will give n, from which m can be found out using (ii).
		Then m = ab, and n is given by (ii).
		Brahmagupta's Chakravala method, though simplified by Bhaskara, is too laborious to describe here.
	www.angelfire.com /ak/ashoksandhya/winners2.html (1874 words)

	Sulbasutra Geometry
		In this period, geometry took somewhat of a backseat to the pursuit of astronomy and algebra.
		This method is well known in later Indian mathematics as the ‘fish’ method due to its shape.
		ii) The construction of a square with a given side results in a beautiful geometrical pattern.
	www.math.ubc.ca /~cass/courses/m309-01a/kong/sulbasutra_geometry.htm (2156 words)

	The Hindu : India and space laws: A millennium perspective
		During the Eighties, the space programme moved closer to realising the goal of self- reliant use of space technology for national development.
		With the launching of Bhaskara II, SLV-3, APPLE in the early Eighties, the programme entered the operational stage to provide space services in communications, metereology and remote sensing and development of launch vehicles.
		The INSAT-1 series of communication satellites and the IRS series of remote sensing satellites were operationalised for well- defined applications.
	www.hinduonnet.com /thehindu/2000/03/09/stories/08090008.htm (1772 words)

	BHARAT RAKSHAK MONITOR: Volume 3(5)
		The program has evolved (i) from the experimental remote sensing satellites, Bhaskara-I and II to the world’s most advanced IRS class satellites and (ii) from the experimental APPLE (Ariane Passenger Payload Experiment) communications satellite to the advanced Insat-2 series of satellites.
		This evolution, as we will see, has not been easy and was beset with frequent problems that were overcome with sheer grit and determination.
		Useful ocean and land surface data were received from Bhaskara-I, but the cameras malfunctioned.
	www.bharat-rakshak.com /MONITOR/ISSUE3-5/sarma.html (5091 words)

	Biographies - Asia-Pacific Remote Sensing 2006 - Call for Papers - Calls for Papers - Conferences - SPIE Web (Site not responding. Last check: 2007-11-03)
		He has been involved in the development of electro-optical imaging sensors of progressively increasing complexity starting from a moderate one kilometer spatial resolution BHASKARA TV payload (1979) to ONE meter high resolution TES payload (2001).
		He has worked on development of airborne imaging spectrometers such as a 4-channel Advanced Linear Imaging Self-Scanning Sensor (ALISS) and also a 142-channel hyper-spectral imaging spectrometer (AIMS).He was actively involved in development of Ocean Color Monitor payload flown on Oceansat-1.
		Navalgund has played an important role in the definition of Indian Earth Observation Systems and in the formulation and execution of most of the major remote sensing applications programmes undertaken in the country right from the experimental Bhaskara satellite mission in 1979 to the operational IRS series of satellites.
	spie.org /Conferences/Calls/06/ae/index.cfm?fuseaction=bios (4400 words)

	Proof: demonstration from all angles \| csmonitor.com
		It helps to describe the space around us and is essential not only in construction but also, in modified form, in equations of thermodynamics and general relativity.
		The Hindu mathematician Bhaskara II constructed a proof using a simple diagram - and instead of an explanation wrote a single word of instruction: "See!"
		And in his memoirs, novelist George MacDonald Fraser writes of proving it to a war-weary but delighted comrade, tracing outlines in the sand with a bayonet, in a break during the fighting against the Japanese in World War II.
	www.csmonitor.com /2006/0725/p09s02-coop.html (864 words)

	Science > Math > Algebra
		Indian mathematician, Aryabhattthe (476 AD) found whole total solutions to linear eqautions by a method same to the modern 1.
		Bhaskara II (1114 AD), world health organization wrote bijaganita (algebrthe), was a 1st to recognize that a caring total has Two square roots.
		A Hindus recognized that quadratic equations use at times 2 roots, & involved negative also when irrational roots.
	algebra.generalanswers.org (670 words)

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