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Bhaskara Ii: more detail

Bhaskara II
People From Bijapur: Bhaskara Ii, Basava, Aluru Venkata Rao, Basappa Danappa Jatti, Venkanna H. Naik, Ramesh Jigajinagi, Sunil Kumar Desai
Expounding the Mathematical Seed. Vol. 2: The Supplements: A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya (Science Networks. Historical Studies) by Agathe Keller, 2006-04-28
1114 Births: Bhaskara Ii, Fujiwara No Shunzei, Henry, Earl of Northumbria, Mor O'toole, Queen of Leinster, Al-Suhayli
Indian Astronomers: Subrahmanyan Chandrasekhar, Aryabhata, Bhaskara Ii, Nilakantha Somayaji, Venkatraman Radhakrishnan, Jyesthadeva, Vasistha
1185 Deaths: Andronikos I Komnenos, Afonso I of Portugal, Pope Lucius Iii, Baldwin Iv of Jerusalem, Bhaskara Ii, Ibn Tufail, Emperor Antoku
12th-Century Mathematicians: Omar Khayyám, Adelard of Bath, Abraham Bar Hiyya, Al-Khazini, Bhaskara Ii, Sharaf Al-Din Al-usi
Indian Mathematics: Swami Bharati Krishna Tirtha's Vedic Mathematics, Bhaskara Ii, Tantrasamgraha, Shulba Sutras, Aryabhata's Sine Table
12th-Century Scientists: 12th-Century Mathematicians, Omar Khayyám, Adelard of Bath, Abraham Bar Hiyya, Al-Khazini, Bhaskara Ii
Bhaskara I and His Works: Part II: Maha-Bhaskariya by Kripa Shankar Shukla (Ed. & Trs. ), 1960-01-01

lists with details

Accounting Historians Journal, The: From Accounting To Negative Numbers: A Signa
7In Colebrooke 1973, Brahmagupta is spelled as Brahmegupta and bhaskara iias Bhiscara. But here we shall adhere to what seem to be the more common
http://www.findarticles.com/p/articles/mi_qa3657/is_199812/ai_n8810036/pg_4

Extractions: Academy of Marketing Science Review Accounting Historians Journal, The Accounting History AgExporter ... View all titles in this topic Hot New Articles by Topic Automotive Sports Top Articles Ever by Topic Automotive Sports From accounting to negative numbers: A signal contribution of medieval India to mathematics Accounting Historians Journal, The Dec 1998 by Mattessich, Richard The Arabs, and through them Leonardo da Pisa, might have transmitted to the West some knowledge about negative quantities; but the subsequent circumstances (greater "logical scruples" of European mathematicians and a more foundational-deductive orientation than the pragmatic one of their Indian counterparts [cf., Kline, 1980, pp. 110-112]), indicate that neither the Arabs nor Leonardo da Pisa succeeded in conveying the need for legitimizing negative numbers, though they did transmit such Indian achievements as the decimal place-order system and a symbol for zero.*5
SCIAMVS: Volume 3
of the Lilavati of bhaskara ii ..193 Title Page in PDF File (50KB). Information for Authors .
http://www.sciamvs.org/vol_03.html
ESWARA Activities
bhaskara ii (1150),. 6. Circumradius of a cyclic quadrilateral. Lhuiller(1782),.Parameswara(1360),. The contributions of Brhamagupta and Bhaskara in
http://www.eswaraindia.org/l-a.htm

Extractions: Bangalore Abstract Pregnancy is one of the greatest events in a woman's life. The artistry, the amazing accuracy and the awesome detail associated with the little life inside the womb can only be experienced by a mother. With the concept of small families all over the world, pregnancy has become not only very precious but also full of apprehension and fear. Yoga therapy is fast advancing as an effective tool in many physical and psychological disorders. There is enough proof available of the beneficial effects of yoga on the mind and body of the human beings. Many scientists have investigated the changes that take place in the human system at all levels by the practice of yoga and holistic living in the recent past all over the world. Swami Vivekananda Yoga Anusandhana Samsthana (sVYASA), Bangalore , has evolved a simple and useful module of basic yoga practice for mothers-to-be and extensive research is going on in one of the local super speciality referral maternity hospitals.
QUERIES ON ORIENTAL SOURCES IN RECREATIONAL MATHEMATICS By David Singmaster
in the Chiu Chang Suan Ching (c150), in Sridhara (c900) and bhaskara ii (1150) . Bhaskara gives an easy problem with crossed ladders in a street.
http://anduin.eldar.org/~problemi/singmast/mideastr.html

Extractions: Computing, Information Systems and Mathematics 87 Rodenhurst Road South Bank University London, SW4 8AF, England London, SE1 0AA, England Tel/fax: 0181-674 3676 Tel: 0171-815 7411 Fax: 0171-815 7499 E-mail: ZINGMAST@VAX.SBU.AC.UK last Web revision:December 22, 1998 Mario Velucchi's Web Index visitors since Dec. 22, 1998 Web page processed by Web Master - Mario Velucchi velucchi@bigfoot.com Mario Velucchi / Via Emilia, 106 / I-56121 Pisa - Italy
CHRONOLOGY OF RECREATIONAL MATHEMATICS By David Singmaster
1150 bhaskara ii Lilivati Bijaganita. 1150 ibn Ezra. Various works, includinga poem about chess. Late 12C Gretti s Saga mentions Fox and Geese.
http://anduin.eldar.org/~problemi/singmast/recchron.html

Extractions: Computing, Information Systems and Mathematics 87 Rodenhurst Road South Bank University London, SW4 8AF, England London, SE1 0AA, England Tel/fax: 0181-674 3676 Tel: 0171-815 7411 Fax: 0171-815 7499 E-mail: ZINGMAST@VAX.SBU.AC.UK last Web revision:December 22, 1998 Mario Velucchi's Web Index visitors since Dec. 22, 1998 Web page processed by Web Master - Mario Velucchi velucchi@bigfoot.com Mario Velucchi / Via Emilia, 106 / I-56121 Pisa - Italy
SDKindex
bhaskara ii 1 big contradicitions to the BigBang 1 The Big Bang Hoax History of the Big-Bang More Problems With The Big-Bang by David Berlinski
http://zyx.org/SDKindex.htm
Formulas Of Euclid And Archimedes Activity
Exercise 6 is from the Lilavati, written by the Indian mathematician and astronomer,bhaskara ii, in about 1150 CE. 6. (Plofker, 23) In a lake with flocks
http://newton.uor.edu/facultyfolder/beery/math115/day4.htm

Extractions: [Todays class: Maya arithmetic, especially subtraction (use toothpicks and small candies-or pencil and paper), review of Pythagorean Theorem and its converse, Puzzle Proofs of Pythagorean Theorem activity, Proofs of Pythagorean Theorem via area and algebra (see Pythagorean Theorem activity), Historical applications of Pythagorean Theorem Mathematics 115 Homework Assignment #4 Due Monday, January 14, 2002 Prof. Beery's office hours this week Thursday 1/ 10 10:30 a.m.-12:30 p.m. 4-5 p.m. Friday 1/11 1:30 - 3:30 p.m. Monday 1/14 10:30 a.m.-12:30 p.m. 4-5 p.m. and by appointment, Hentschke 203D, x3118 Tutorial session : Sunday, Jan. 13, 4 - 5 p.m. , Hentschke 204 (Jody Cochrane) Read : "No Stone Unturned (Early Southern California math artifacts?)" "Kernel revealing history of humans in the New World " "Mayan Arithmetic" (you may skip Section 4, Division) "Mayan Head Variant Numerals"
Newsletter 46, March 2001
bhaskara ii in his famous Lilavati (12th century) gives the wrong rule (a x 0) = a.His commentator Ganesa (1545) remarks that the rule comes by cancelling
http://www.hpm-americas.org/nl46/nl46art2.html

Extractions: International Study Group on the Relations Between HISTORY and PEDAGOGY of MATHEMATICS NEWSLETTER No. 46, March 2001 An Affiliate of the International Commission on Mathematical Instruction History makes a man wise is a common saying. By studying history we can know the errors and mistakes committed in the past and save ourselves from repeating them. According to P. S. Jones "One use of the history of mathematics is to reveal to students come of the conceptual difficulties and errors which have impeded progress". G. A. Miller even says "The teachers of mathematics may frequently gain more from a clear exposition of failures than from such an exposition of successes on the part of the eminent mathematicians of the past". In this brief note we mention the mistakes, gathered from a few earlier works, in connection with some arithmetical operations involving the number zero (now denoted by the hole "0"). 1. The great Indian mathematician Brahmagupta (7th century AD) was the first to give explicitly in his Brahmasphuta-Siddhanta (chapter XVIII), the various rules involving zero (in arithmetical operations) but they also include his statement that "zero divided by zero is zero". That is, ÷ = which is not true in general.
Newsletter 44, November 2000: History And Culture In Mathematics Education
bhaskara ii in his famous Lilavati (12th century) gives the wrong rule (a x 0)/0 =a His commentator Ganesa (1545) remarks that the rule comes by cancelling
http://www.hpm-americas.org/nl47/nl47apologies.html

Extractions: International Study Group on the Relations Between HISTORY and PEDAGOGY of MATHEMATICS NEWSLETTER An Affiliate of the International Commission on Mathematical Instruction: No. 47, July 2001 My apologies, but in the last HPM Newsletter there were two mistakes that I failed to notice before sending it to distributors. These were both in the article The Dangerous Hole of Zero Firstly I forgot to acknowledge the author. It was Professor R. C. Gupta from India who submitted the article, and my sincere apologies to him and all the HPM Newsletter readers for this oversight. Secondly in example 4 the wrong rule was misprinted. The correct paragraph is shown here. 4. Bhaskara II in his famous Lilavati th century) gives the wrong rule ( a x a
Vedic Sources Of The Vedic Mathematics - Article
The interpolator is Ksepaka.79 bhaskara ii succeeded in evolving a very simpleand elegant method by means of which one can derive an auxiliary equation
http://vedicmaths.org/Free Resources/Articles/kansara/kansara.asp

Extractions: This article appeared in the Indian Journal Sambodhi Vol. XXIII, 2000 and is reproduced here with permission. Diacritical marks have not been copied, nor have the few Sanskrit/Hindu lines of text. This article has been scanned into text and though we have done our best there may still be a few errors. For the full text please see the Journal version. VEDIC SOURCES OF THE 'VEDIC MATHEMATICS' Dr. N. M. Kansara Director, Akshardham Centre for Applied Research in Social Harmony (AARSH), Akshardham, Gandhinagar - (382 020) Jagadguru Shankaracharya Swami Shri Bharati Krishna Tirthaji Maharaja of Govardhan Peeth Matha, Puri, wrote or dictated a book entitled `Vedic Mathematics' based on 29 Sutras, of which 16 deal with the general case, while the rest 13 treat the special cases. The declaration of the Sutras as "Vedic" or as belonging to the Vedas, particularly to the Atharvaveda, and his claim that "the Sutras (aphorisms) apply to and cover each and every part of each and every chapter of each and every branch of mathematics including arithmetic, algebra, geometry plane and solid, trigonometry - plane and spherical, conics - geometrical and analytical, astronomy, calculus - differential and integral etc., etc.", and that "there is no part of mathematics, pure or applied, which is beyond their jurisdiction" has raised a controversy amongst the mathematicians of India, some of whom have questioned the Vedicity of the Sutras on the ground of their language, and the level of mathematics it deals with. It is endeavoured here to deal with the problem in all possible aspects, and examine the validity or otherwise of the claim.
Sulbasutra Geometry
522 CE), Bramhagupta (628 CE) and bhaskara ii (b. 1114 CE). In this period,geometry took somewhat of a backseat to the pursuit of astronomy and algebra.
http://www.math.ubc.ca/~cass/courses/m309-01a/kong/sulbasutra_geometry.htm

Extractions: Math 309 April 2001 The basis and inspiration for the whole of Indian mathematics is geometry. The beginnings of algebra can be traced to the constructional geometry of the Vedic priests preserved in the Sulbasutras , a manual of geometrical constructions from the 5 th to the 8 th centuries. Earlier remnants of geometrical knowledge of the Indus Valley Civilisation can be found in excavations at Harappa and Mohenjo-daro where there is evidence of circle-drawing instruments from as early as 2500 B.C.E. (Amma 1) Early geometry of the Sulbasutras was based on religious needs with regards to the construction of altars such as agnicitis, vedis, mandapas etc. that are required for sacrificial ritual (Kulkarni 19, Amma 3). The history of Indian geometry can be divided into three distinct periods: pre-Aryan, such as excavated in Indus Valley. Vedic or Sulbasutra post-Christian. Evidence of the pre-Aryan period includes well-planned towns and geometric designs including circles, squares and triangles. A link between this and the Vedic period can be found in the motif of a rectangle with the four sides curved inwards resembling a stretched hide; in the former period it can be seen as a decorative pattern while in the later period it is seen in the shape of the sacrificial altars or vedi . The vedi as well as the fireplaces or agni had such exact measurements and geometric shapes that they were codified and became the Sulbasutras . However, it is not known from how far back such knowledge originated as the sacrificial act is as old as the Vedas or older (Amma 5).
Quadratic Equation -- Facts, Info, And Encyclopedia Article
The rule is (as quoted by bhaskara ii) Multiply both sides of the equation bya known quantity equal to four times the coefficient of the square of the
http://www.absoluteastronomy.com/encyclopedia/q/qu/quadratic_equation.htm

Extractions: In (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics , a quadratic equation is a (A mathematical expression that is the sum of a number of terms) polynomial (A mathematical statement that two expressions are equal) equation of the second (A specific identifiable position in a continuum or series or especially in a process) degree . The generalized form is A quadratic equation with (An old small silver Spanish coin) real or ((psychoanalysis) a combination of emotions and impulses that have been rejected from awareness but still influence a person's behavior) complex coefficients has two complex roots (i.e., solutions for x when y = 0) usually denoted as and , although the two roots may be equal. These roots can be computed using the quadratic formula Note that the highest exponent is twice the value of the exponent of the middle term. This equation may be resolved directly or with a simple substitution, using the methods that are available for the quadratic, such as factoring (also called factorising), the quadratic formula, or completing the square.
The Culture Of Science
spanning as it did the times from Aryabhata to bhaskara ii Aryabhata, in hisbook Aryabhateeya makes the statement that essentially means that the Earth
http://www.iucaa.ernet.in/~scipop/ebooks/articles/cultureofscience.htm

Extractions: Email - jvn@iucaa.ernet.in C.D. Deshmukh Memorial Lecture at the India International Centre, Delhi Ladies and Gentlemen, It is a great honour to be invited to deliver this prestigious lecture in the memory of the late C.D. Deshmukh, especially at the India international Centre that was C.D.s creation and one of his most beloved projects. I feel somewhat inhibited to fulfil my assignment today, since from my childhood I had looked upon C.D. Deshmukh as a towering personality. I have memories of his visit to our house back in early nineteen fifties, when I was in secondary school. My parents asked me on that occasion to recite some Sanskrit shlokas . I did so with some trepidation since I had heard about how great a scholar C.D. was in Sanskrit. I also recall feeling very happy when the 'Guest of Honour' complimented me on my Sanskrit pronunciation. On that occasion he had come from a function at the Women's College of the Banaras Hindu University. The university is often referred to as B.H.U. and C.D. used this fact in one of his typical witty remarks. He told the women students - as students of the B.H.U. were 'Bhu-kanyas' and as such they should emulate the ideal of
Th Topic: Infinity And Infinitesimal
Quote bhaskara ii (1150) in a/0 there is no alteration, as no change takesplace in the infinite and immutable God »dattB_1935
http://www.thesa.com/th/th-78-73-175-th-196-230-59.htm

Extractions: continuous Quote : when instances approach each other continually and eventually merge, the consequences or outcomes must do so also; e.g., parabola is an ellipse Quote : rule of continuity no change takes place by leaps and bounds Quote : in every parcel of matter there is an infinity of created things Quote : the circumference of an infinite circle and a straight line are the same thing [ Quote : if moveables descend rays from a point, they form a circle of ever widening diameter; a wonderful feature of nature unsorted Quote : there is a definite beginning and the reasons for things are not infinite [ Quote : there can be no infinite regress in the production of things Quote : where there is no first term, there is no explanation at all; no infinite regress Quote : we know when we know how to explain adequately; adding factors infinitely should take endless time
Th QuoteRef: DattB_1935
243 ;;Quote bhaskara ii (1150) in a/0 there is no alteration, as no changetakes place in the infinite and immutable God
http://www.thesa.com/th/th-106-161-169-th-230-231-143.htm
Storytelling Science Aryabhata And Diophantus Son
This is Bhaskara s commentary on the ancient text Aryabhatiyam , and you find that the solution to this equation was recorded by bhaskara ii (1150AD),
http://www.cse.iitk.ac.in/~amit/story/19_aryabhata.html
Bhaskara
Translate this page On ne confondra pas ce mathématicien indien avec un autre Bhaskara ayant de Bhaskara I pour évoquer ce mathématicien homonyme, bhaskara ii désignant
http://serge.mehl.free.fr/chrono/Bhaskara.html
Transmission Of Mathematical Ideas Author 20
bhaskara ii even declares that the Rule of Three pervades the whole field ofarithmetic with its many variations, just as Visnu pervades the entire universe
http://www.iwr.uni-heidelberg.de/transmath/author20.html
The Battlefield Of Indian History
decimal places and producing an accurate table of sines; Algebra was known toAryabhata; and it is discussed in detail in bhaskara ii s Lilavati ca.
http://www.rediff.com/news/2004/aug/16rajeev.htm

Extractions: I ndian history is once again centrestage. There is in some quarters a feeling that history is the most boring of subjects, consisting of long, dry lists of dynasties and the exploits of rather barbaric kings. This, unfortunately, is a result of the way history is taught in India. For it is fake history that has been manufactured by people with vested interests with the intention of keeping Indians enslaved. History is perhaps the most important of the humanities. There is nothing quite like history that can be used in positive and negative ways to affect the affairs of men. To paraphrase George Santayana, I would say, "Those who forget their history are condemned." Condemned to forever be second-class, to forever lack self-respect, to forever suffer loss of self-image. India's loss of knowledge of its history is a double disaster, because it turns out India's history is almost unimaginably lustrous: in fact, within the first order of approximation, one could claim that India invented almost everything worth knowing in the ancient world. India was, for millennia, the Empire of the Intellect, the civilization that with astonishing creativity generated more ideas than the rest of the world put together. The denigration of Indian history is a project originally put into action by colonialist Britons, who identified, correctly, that by controlling the past they would be able to control the present as well. After Independence, a cabal of Marxists has dominated the official version of history in India, and they too want to control India's present and future. They have managed to brainwash entire generations of Indians into believing that everything that originated in India is worthless.
Bhutas : Some Reflections On Modern Scientific Concepts And Traditional Indian T
Why the astronomical tradition from Aryabhata to bhaskara ii did not continuebeyond the twelfth century? For, during those seven centuries (5001200 ad)
http://ignca.nic.in/ps_04003.htm

Extractions: Previous Page Contents of the Book Next Page Bhutas Some Reflections on Modern Scientific Concepts and Traditional Indian Thoughts Jayant V. Narlikar Against the background of some elementary knowledge about the many different streams of ancient thoughts, I have ventured to ask some questions visa-vis scientific ideas of modern times where I do know a little, perhaps just enough to gauge the extent of my ignorance. About our ancient traditions I do not even know the extent of my ignorance! So I had better begin with the modern scientific end. What does science say about the nature of matter on different physical scales? Scales of Structure A few years ago Professor Phillip Morrison had made a beautiful but short film entitled Powers of Ten. It started with a scene very common in the Western world, that of a couple picnicking in a city park. Then the camera zooms out showing the larger scale of the park, then zooms farther to show the city, then the state and so on. Each scene is followed by another with ten times larger scale. How far does this go on? Taking 1 metre as the scale we measure our local distances in ( the picnicking couple occupied an area of a few square metres), the tenfold increases in length go on till about 1026 metres that is, about a hundred million million million million metres! A few significant steps enroute to this gigantic scale are given in Table I below.

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