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	Brahmagupta at AllExperts
		The Brahmasphutasiddhanta, written circa 628 CE, is the earliest known text to treat zero as a number in its own right.
		It goes well beyond that, however, stating rules for arithmetic on negative numbers and zero which are quite close to the modern understanding.
		The Famous King Khalif Abbasid Al Mansoor (712-775) founded Baghdad, which is situated on the banks of the Tigris, and made it a center of learning.
	en.allexperts.com /e/b/br/brahmagupta.htm (528 words)

	Brahmagupta. Who is Brahmagupta? What is Brahmagupta? Where is Brahmagupta? Definition of Brahmagupta. Meaning of ...
		He was the head of the astronomical observatory at Ujjain, and during his tenure there wrote two texts on mathematics and astronomy: the Brahmasphutasiddhanta in 628, and the Khandakhadyaka in 665.
		The Brahmasphutasiddhanta is the earliest known text other than the Mayan number system to treat zero as a number in its own right.
		It goes well beyond that, however, stating rules for arithmetic on negative numbers and zero which are quite close to the modern understanding.
	www.knowledgerush.com /kr/encyclopedia/Brahmagupta (159 words)

	Vidyapatha :: Indian Scientists : India's Largest Portal on Educational Information
		Brahmagupta was born at Bhillamala (Bhinmal), in Gujarat, in 598 A.D. He became court astronomer to I King Vyaghramukha of the Chapa dynasty.
		Of his two treatises, Brahmasphutasiddhanta and Karanakhandakhadyaka, the first is the more famous.
		Brahmasphutasiddhanta also contains chapters on arithmetic and algebra.
	www.vidyapatha.com /scientists/brahmagupta.php (363 words)

	History of astronomy - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-10-22)
		In 500 AD, Aryabhata presented a mathematical system that took the earth to spin on its axis and considered the motions of the planets with respect to the sun.
		Brahmagupta (598-668) was the head of the astronomical observatory at Ujjain and during his tenure there wrote a text on astronomy, the Brahmasphutasiddhanta in 628.
		Bhaskara (1114-1185) was the head of the astronomical observatory at Ujjain, continuing the mathematical tradition of Brahmagupta.
	encyclopedia.worldsearch.com /history_of_astronomy.htm (1870 words)

	Brahmagupta biography
		In addition to the Brahmasphutasiddhanta Brahmagupta wrote a second work on mathematics and astronomy which is the Khandakhadyaka written in 665 when he was 67 years old.
		The Brahmasphutasiddhanta contains twenty-five chapters but the first ten of these chapters seem to form what many historians believe was a first version of Brahmagupta's work and some manuscripts exist which contain only these chapters.
		In the Brahmasphutasiddhanta Brahmagupta gave remarkable formulae for the area of a cyclic quadrilateral and for the lengths of the diagonals in terms of the sides.
	www-history.mcs.st-andrews.ac.uk /Biographies/Brahmagupta.html (1408 words)

	Brahmagupta's Formula Brahmagupta's Identity (Site not responding. Last check: 2007-10-22)
		It goes well beyond that, however, stating rules for arithmetic on negative number s and zero which are quite close to the modern understanding.
		He was the head of the astronomical observatory at Ujjain, and during his tenure there wrote two texts on mathematics and astronomy: the Brahmasphutasiddhanta in 628, and the Khandakhad
		Brahmagupta's identity Analytic number theory In mathematics, Brahmagupta's identity says that the product of two numbers, each of which is a sum of two squares, is itself a sum of two squares.
	www.masterliness.com /a/Brahmagupta.htm (451 words)

	The Horoscope of Baghdad
		He mentions a study made by Billard of the Indian material, where the result represents "not the exact date at which any particular deviation vanishes, but rather the date at which the sum of squares of selected deviations is minimum".
		In the case of the Brahmasphutasiddhanta (A.D.628), Billiard concludes that A.D. 562.8 "might be regarded as the date which represents overall the origin of the sidereal coordinates".
		But Mercier shows that an exact calculation using the Brahmasphutasiddhanta would put the zero point in A.D. 580, making it clear that the position of the Sun in the Kwarizmian Tables is not derived from it.
	www.expreso.co.cr /centaurs/posts/mundane/baghdad.html (3364 words)

	[No title]
		In addition, he wrote important works on mathematics and astronomy and his understanding of the number systems went far beyond that of others of the period.
		He is most famous for his book Brahmasphutasiddhanta, a twenty-five chapter work with the first ten dealing with astronomy and the remaining fifteen chapters devoted to mathematics.
		In this work, Brahmagupta defined zero as the result of subtracting a number from itself.
	www.intermath-uga.gatech.edu /tweb/augusta-nums/dlowe/BRAHMAGUPTA.doc (178 words)

	Brahmasphutasiddhanta: The Sindhi Roots of Modern Astronomy
		In connection with Ddiyaarii, I mentioned that the art of navigation is believed by historians to have been invented in Sindh.
		They consisted of text and tables called zij, after a Pahlavi (old scholarly Persian) word meaning "cord" or "thread" and, by extension, "the warp of a fabric." Around 771 [AD] an Indian political mission arrived from Sind[h] to the court of al-Mansur, the caliph of Baghdad.
		The group included a scholar versed in astronomy who brought along the famous Brahmasphutasiddhanta.
	yangtze.cs.uiuc.edu /~jamali/sindh/sindh-l/archive/her/msg00889.html (290 words)

	brahmasphutasiddhanta (Site not responding. Last check: 2007-10-22)
		Brahmasphutasiddhanta: The Sindhi Roots of Modern Astronomy To : SINDH-L@LISTSERV.UIUC.EDU Subject : Brahmasphutasiddhanta: The Sindhi Roots of Modern Astronomy From : Gul Agha andlt; agha@CS.UIUC.EDU andgt; Date : Sat...
		This book, which the Indian scholar presented from, was likely Brahmasphutasiddhanta (The Opening of the Universe) which was written in 628 CE by the Indian mathematician Brahmagupta...
		(4) Translation of Brahmasphutasiddhanta of Brahmagupta : This Research Project was undertaken by Mrs.
	brahmasphutasiddhanta.networklive.org (280 words)

	Ujjain travel guide
		In the 4th century CE, Ujjain was the traditional capital of King Chandragupta II, also known as Vikramaditya, at whose court the nine poets known as the navaratna (nine jewels) of Sanskrit literature are said to have flourished.
		d: Brahmagupta, whose book Brahmasphutasiddhanta was responsible for spreading the use of zero, negative numbers and the positional number system to Arabia and Cambodia; Varahamihira, who was the f many areas of mathematics.
		Ujjain was invaded by the forces of the Delhi Sultanate led by Iltutmish in 1235, suffering widespread destruction and systematic desecration of temples.
	www.world66.com /asia/southasia/india/madhyapradesh/ujjain (1006 words)

	Division by zero Summary
		But in the case of zero, repeated subtraction of zero will never yield a remainder less than zero, so dividing by zero is not defined.
		The Brahmasphutasiddhanta of Brahmagupta is the earliest known text to treat zero as a number in its own right and to define operations involving zero.
		The author failed, however, in his attempt to explain division by zero – his definition can be easily proven to lead to algebraic absurdities.
	www.bookrags.com /Division_by_zero (2000 words)

	Nullity - Objectivism Online Forum
		No, I think it's worse than that, since this is hiding contradictions or redefinitions, and lying about the utility.
		First off, the problem is almost 1400 years old, not 1200, having been treated in the Brahmasphutasiddhanta.
		Second, this stupid symbol of his is not a real number.
	forum.objectivismonline.net /index.php?showtopic=8208 (574 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		Now in [1] (where a longer quote is given) Ifrah tries to determine which Indian work is referred to.
		He concludes that the work was most likely to have been Brahmagupta's Brahmasphutasiddhanta (The Opening of the Universe) which was written in 628.
		Irrespective of whether Ifrah is right, since all Indian texts after Aryabhata I's Aryabhatiya used the Indian number system of the nine signs, certainly from this time the Arabs had a translation into Arabic of a text written in the Indian number system.
	www.indybay.org /newsitems/2003/08/29/16387361_content.html (1666 words)

	Brahmagupta Summary
		His Brahmasphutasiddhanta (628), translated as The Opening of the Universe, defined zero as the result obtained when a number is subtracted from itself—by far the best definition of zero up to that time.
		If there is a person to be assigned the most important discovery in all of mathematics, finding of zero, that would be Brahmagupta.
		The Brahmasphutasiddhanta, written circa 628 AD, is the earliest known text to treat zero as a number in its own right.
	www.bookrags.com /Brahmagupta (1551 words)

	0 (number) information - Search.com (Site not responding. Last check: 2007-10-22)
		Zero may or may not be counted as a natural number, depending on the definition of natural numbers.
		Mathematical operations involving zero were first described by Brahmasphutasiddhanta in the 7th century.
		In set theory, the number zero is the cardinality of the empty set: if one does not have any apples, then one has zero apples.
	c10-ss-1-lb.cnet.com /reference/0_(number) (4107 words)

	Astronomy in Ancient India - Crystalinks
		This is an extremely accurate ratio of a fundamental astronomical ratio (1,582,237,500/57,753,336 = 27.3964693572), and is perhaps the oldest astronomical constant calculated to such accuracy.Brahmagupta (598-668) was the head of the astronomical observatory at Ujjain and during his tenure there wrote a text on astronomy, the Brahmasphutasiddhanta in 628.
		Thus we can see that what ancient Indian astronomers say comes close to the heliocentric theory of gravitation, which was a thousand years later articulated by Copernicus and Galileo inviting severe reactions from the clergy in Rome.
		He was the earliest to use algebra to solve astronomical problems.
	www.crystalinks.com /indiastronomy.html (2904 words)

	test (Site not responding. Last check: 2007-10-22)
		During the 7th century this was the most important centre of mathematical learning in India.
		We have two of his books the Khandakhadyaka written later in his life and the extraordinary Brahmasphutasiddhanta written in around 628.
		This book discusses astronomy, but for the first time it looks at how we can study astronomy using algebra.
	www.mathsyear2000.org /timeline/test-mathinfo.php?m=brahmagupta (222 words)

	Number
		An isolated use of their initial, N, was used in a table of Roman numerals by Bede or a colleague about 725, a true zero symbol.
		An early documented use of the zero by Brahmagupta (in the Brahmasphutasiddhanta) dates to 628.
		He treated zero as a number and discussed operations involving it, including division.
	articles.gourt.com /en/number (3720 words)

	Arabic numerals
		Now in [1] (where a longer quote is given) Ifrah tries to determine which Indian work is referred to.
		He concludes that the work was most likely to have been Brahmagupta 's Brahmasphutasiddhanta (The Opening of the Universe) which was written in 628.
		Irrespective of whether Ifrah is right, since all Indian texts after Aryabhata I 's Aryabhatiya used the Indian number system of the nine signs, certainly from this time the Arabs had a translation into Arabic of a text written in the Indian number system.
	www-gap.dcs.st-and.ac.uk /~history/HistTopics/Arabic_numerals.html (2205 words)

	[No title]
		Tallet null, slik vi bruker det i dag, ble første gang innført av den indiske matematikeren og astronomen Brahmagupta.
		I storverket 'Brahmasphutasiddhanta' fra år 628 setter han opp en rekke regler for hvordan man regner med både null og negative tall - regler som er i bruk den dag i dag.
		Før Brahmagupta fantes det riktignok også et symbol for ingenting i flere kulturer.
	www.illustrertvitenskap.com /Crosslink.jsp?d=169&a=1217&id=9607_6 (206 words)

	Perpetuum Mobile: Early concepts and classical machines
		The first description of a perpetual motion machine was found to be made by the Indian mathematician and astronomer Brahmagupta in 624.
		In his Brahmasphutasiddhanta, he describes a perpetual motion device: "Make a wheel of light timber, with uniformly hollow spokes at equal intervals.
		Fill each spoke up to half with mercury and seal its opening situated in the rim.
	www.hp-gramatke.net /perpetuum/english/page0020.htm (1466 words)

	BRAHMAGUPTA
		Brahmagupta wrote important works on mathematics and astrology.
		The first was Brahmasphutasiddhanta (The Opening of the Universe), written in 628 AD.
		Brahmagupta's second work was called Khandakhadyaka, written at age 67.
	www.algana.co.uk /FamousNames/B/Brahmagupta.htm (152 words)

	The Z Files, Holistic ( Psychic Sciences ) & Astrology Free Ezine (Site not responding. Last check: 2007-10-22)
		Another great astronomer-mathematician Aryabhata wrote treatises on Spherical Astronomy and Spherical Trignometry in his magnum opus Aryabhateeyam.
		It is said that Arabs acquired a knowledge of maths and astronomy only after Brahmagupta's Brahmasphutasiddhanta was translated into Arabic (As Sind Hind)!
		Albert Einstein rightly remarked " We owe a lot to the Indians who taught us how to count without which no worthwhile discovery could have been made " !
	www.astrologiavedica.com /html/zfiles10.htm (804 words)

	::::::::::::::::::::::::::::Himalayan Research:::::::::::::::::::::::
		About 45 NGOs and 88 non-formal education centres were covered for the survey.
		Translation of Brahmasphutasiddhanta of Brahmagupta : This Research Project was undertaken by Mrs.
		Sushma Zadoo on with critical analysis, notes and introduction as approved by the Indian National Science Academy under the auspices of Himalayan Research and Cultrual Foundation.
	www.himalayanresearch.org /projects.php (930 words)

	IMC India - Vedic Astrology (Site not responding. Last check: 2007-10-22)
		It is said that Arabs acquired a knowledge of maths and
		astronomy only after Brahmagupta's Brahmasphutasiddhanta was translated into
		Albert Einstein rightly remarked " We owe a lot to
	india.indymedia.org /en/2002/03/984.shtml (637 words)

	Wicca Pagan Discussion Board (Site not responding. Last check: 2007-10-22)
		It is said that Arabs acquired a knowledge of maths and
		astronomy only after Brahmagupta's Brahmasphutasiddhanta was translated into
		Albert Einstein rightly remarked `` We owe a lot to
	www.newagecities.com /neighborhoods/wiccapagan/Discussion.asp?ID=1383 (665 words)

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