21. Heron's Formula And Brahmagupta's Generalization Heron s Formula and brahmagupta s Generalization. It s tempting to think that brahmaguptamight have just imagined the equation based on its formal symmetry. http://www.mathpages.com/home/kmath196.htm

Heron's Formula and Brahmagupta's Generalization Let a,b,c be the sides of a triangle, and let A be the area of the triangle. Heron's formula states that A^2 = s(s-a)(s-b)(s-c), where s = (a+b+c)/2. The actual origin of this formula is somewhat obscure historically, and it may well have been known for centuries prior to Heron. For example, some people think it was known to Archimedes. However, the first definite reference we have to this formula is Heron's. His proof of this result is extremely circuitious, and it seems clear that it must have been found by an entirely different thought process, and then "dressed up" in the usual synthetic form that the classical Greeks preferred for their presentations. Here's a much more straightforward derivation. Consider the general triangle with edge lengths a,b,c shown below Heron's Formula For Tetrahedrons Return to MathPages Main Menu

22. Brahmagupta - Mathematics And The Liberal Arts brahmagupta Mathematics and the Liberal Arts. The work of brahmaguptashould be relevant, but is not currently available in English. http://math.truman.edu/~thammond/history/Brahmagupta.html

Brahmagupta - Mathematics and the Liberal Arts To expand search, see India . Laterally related topics: The Hindu-Arabic Numerals Bhaskara Mahaviracarya Varahamihira ... The Tamil of South India , and The Sulvasutras The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines. The notes in these pages are intended as much to evoke ideas as to indicate what the books and articles are about. They are not intended as reviews. However, some items have been reviewed in Mathematical Reviews , published by The American Mathematical Society. When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation. Subscribing institutions can access the more recent MR reviews online through MathSciNet Biggs, N. L. The roots of combinatorics. Historia Math.

23. Comments On Brahmagupta Comments on brahmagupta Comments http://math.truman.edu/cgi-bin/thammond/makebibcomment.pl?code=General&cat=Brahm

24. Brahmagupta Translate this page brahmagupta (ou Brahamagupta), indien, 598-660 (?). Dans son livre, VictorJ. Katz cite un cas traité par brahmagupta n 10 137 et n 0 60. http://www.sciences-en-ligne.com/momo/chronomath/chrono1/Brahmagupta.html

BRAHMAGUPTA (ou Brahamagupta) , indien, 598-660 indien Aryabhata Rolle : arabes Arabes Al-Khwarizmi babyloniennes et grecques . Son apparition en Inde En Inde, d'une province à l'autre, les notations différaient et évoluèrent sur plusieurs siècles Inconnue jusqu'au 16è siècle, la civilisation Maya, découverte par les espagnols au sud de l'actuel Mexique, usait d'un système de numération positionnel de base 20 présentant un symbole spécifique pour désigner l'absence d'une puissance de 20 dans la décomposition d'un nombre et que l'on peut interpréter comme un "zéro". Résolution d'équations diophantiennes Diophante et Aryabhata x = ny (lorsque n est entier) Pell Bhaskara Notons que le concept de congruence Gauss Brahamagupta dans son Bhrama Sphuta Siddhanta n et n chinoises lunaisons Dans son livre Victor J. Katz cite un cas n Gauss et les congruences : Une belle formule pour l'aire d'un quadrilatère inscriptible On doit à Brahamagupta inscriptible , c'est à dire dont les sommets sont sur un même cercle (quadruplet de points cocycliques), en fonction de la mesure de ses côtés : Cette formule généralise celle d' Boece Khwarizmi

25. Brahmagupta brahmagupta encyclopedia article about brahmagupta. Free access encyclopedia article about brahmagupta. brahmagupta in Free online Englishdictionary, thesaurus and encyclopedia. Provides brahmagupta. Word http://www.fact-index.com/b/br/brahmagupta.html

Main Page See live article Alphabetical index Brahmagupta Brahmagupta ) was an Indian mathematician and astronomer . 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 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. The major divergence is that Brahmagupta attempted to define division by zero , which is left undefined in modern mathematics. His definition is not terribly useful; for instance, he states that 0/0 = 0, which would be a handicap to discussion of removable singularities in calculus See also Brahmagupta's formula Brahmagupta's identity External links MacTutor History of Mathematics article on Brahmagupta This article is a stub. You can help Wikipedia by fixing it. This article is from Wikipedia . All text is available under the terms of the GNU Free Documentation License

26. Brahmagupta's Identity - Encyclopedia Article About Brahmagupta's Identity. Free encyclopedia article about brahmagupta s identity. brahmagupta s identity in Freeonline English dictionary, thesaurus and encyclopedia. brahmagupta s identity. http://encyclopedia.thefreedictionary.com/Brahmagupta's identity

Dictionaries: General Computing Medical Legal Encyclopedia Brahmagupta's identity Word: Word Starts with Ends with Definition In mathematics Mathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of 'figures and numbers'. In the formalist view, it is the investigation of axiomatically defined abstract structures using logic and mathematical notation; other views are described in Philosophy of mathematics. Mathematics might be seen as a simple extension of spoken and written languages, with an extremely precisely defined vocabulary and grammar, for the purpose of describing and exploring physical and conceptual relationships. Click the link for more information. 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. Specifically: The identity holds in any commutative ring In Ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation obeys the commutative law. This means that if a and b are any elements of the ring, and if the multiplication operation is written as

27. - Great Books - brahmagupta (598668), brahmagupta wrote important works on mathematicsand astronomy. In particular he wrote Brahmasphutasiddhanta http://www.malaspina.com/site/person_240.asp

Brahmagupta Brahmagupta wrote important works on mathematics and astronomy. In particular he wrote Brahmasphutasiddhanta (The Opening of the Universe), in 628. The work was written in 25 chapters and Brahmagupta tells us in the text that he wrote it at Bhillamala which today is the city of Bhinmal. This was the capital of the lands ruled by the Gurjara dynasty. Brahmagupta became the head of the astronomical observatory at Ujjain which was the foremost mathematical centre of ancient India at this time. Outstanding mathematicians such as Varahamihira had worked there and built up a strong school of mathematical astronomy. 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. [ Adapted from MacTutor The Great Books Indian Mathematics This web page is part of a biographical database on Great Ideas . These are living ideas that have shaped, defined and directed world culture for over 2,500 years. The Great Ideas are radical, and often misunderstood and distorted by popular simplifications. Understanding a

28. PlanetMath: Brahmagupta's Formula brahmagupta s formula, (Theorem). If a cyclic quadrilateral has sides then itsarea is given by. Attachments proof of brahmagupta s formula (Proof) by giri. http://planetmath.org/encyclopedia/BrahmaguptasFormula.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... Random Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Corrections talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information Docs Classification News Legalese ... TODO List Brahmagupta's formula (Theorem) If a cyclic quadrilateral has sides then its area is given by where Note that if Heron's formula is recovered. "Brahmagupta's formula" is owned by drini view preamble View style: HTML with images page images TeX source See Also: cyclic quadrilateral Heron's formula Keywords: Area, Quadrilateral, Cyclic Attachments: proof of Brahmagupta's formula (Proof) by giri Cross-references: Heron's formula sides cyclic quadrilateral There is 1 reference to this object. This is version 3 of Brahmagupta's formula , born on 2001-10-06, modified 2001-10-31. Object id is 153, canonical name is BrahmaguptasFormula. Accessed 2395 times total. Classification: AMS MSC (Geometry :: General reference works ) Pending Errata and Addenda None.

29. PlanetMath: Proof Of Brahmagupta's Formula parent proof of brahmagupta s formula, (Proof). We shall we get. proof of brahmagupta s formula is owned by giri. (view preamble). http://planetmath.org/encyclopedia/ProofOfBrahmaguptasFormula.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... Random Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Corrections talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information Docs Classification News Legalese ... TODO List proof of Brahmagupta's formula (Proof) We shall prove that the area of a cyclic quadrilateral with sides is given by where Area of the cyclic quadrilateral = Area of Area of But since is a cyclic quadrilateral, Hence Therefore area now is Applying cosines law for and and equating the expressions for side we have Substituting (since angles and are suppplementary) and rearranging, we have substituting this in the equation for area, which is of the form and hence can be written in the form as Introducing Taking square root , we get "proof of Brahmagupta's formula" is owned by giri view preamble View style: HTML with images page images TeX source This object's parent Cross-references: square root cosines law sides cyclic quadrilateral This is version 3 of proof of Brahmagupta's formula , born on 2002-11-14, modified 2002-11-14.

30. Brahmagupta. The Columbia Encyclopedia, Sixth Edition. 2001 The Columbia Encyclopedia, Sixth Edition. 2001. brahmagupta. (brä´´mg p´t ) (KEY) , c.598–c.660, Indian mathematician and astronomer. http://www.bartleby.com/65/br/Brahmagu.html

Select Search All Bartleby.com All Reference Columbia Encyclopedia World History Encyclopedia Cultural Literacy World Factbook Columbia Gazetteer American Heritage Coll. Dictionary Roget's Thesauri Roget's II: Thesaurus Roget's Int'l Thesaurus Quotations Bartlett's Quotations Columbia Quotations Simpson's Quotations Respectfully Quoted English Usage Modern Usage American English Fowler's King's English Strunk's Style Mencken's Language Cambridge History The King James Bible Oxford Shakespeare Gray's Anatomy Farmer's Cookbook Post's Etiquette Bulfinch's Mythology Frazer's Golden Bough All Verse Anthologies Dickinson, E. Eliot, T.S. Frost, R. Hopkins, G.M. Keats, J. Lawrence, D.H. Masters, E.L. Sandburg, C. Sassoon, S. Whitman, W. Wordsworth, W. Yeats, W.B. All Nonfiction Harvard Classics American Essays Einstein's Relativity Grant, U.S. Roosevelt, T. Wells's History Presidential Inaugurals All Fiction Shelf of Fiction Ghost Stories Short Stories Shaw, G.B. Stein, G. Stevenson, R.L. Wells, H.G. Reference Columbia Encyclopedia PREVIOUS NEXT ... BIBLIOGRAPHIC RECORD The Columbia Encyclopedia, Sixth Edition. Brahmagupta g KEY Brahma-sphuta-siddhanta [improved system of Brahma], a standard work on astronomy containing two chapters on mathematics that were translated into English by H. T. Colebrooke in

31. Brahmagupta From HistoryCenter.net brahmagupta. brahmagupta was the most accomplished of the ancient Indian astronomers.His great work The Opening of the Universe is written in verse form. http://www.historycenter.net/science-detail1.asp?ID=25&TimeZone=3

32. Brahmagupta brahmagupta (English). Search for brahmagupta in NRICH PLUS maths.org Google. Definition level 2. An Indian mathematician, who lived from 598 to 665. http://thesaurus.maths.org/mmkb/entry.html?action=entryByConcept&id=1149&langcod

33. Brahmagupta brahmagupta (English). Suchen nach brahmagupta in NRICH PLUS maths.org Google. Definition Niveau 2. An Indian mathematician, who lived from 598 to 665. http://thesaurus.maths.org/mmkb/entry.html?action=entryByConcept&id=1149&msglang

34. Brahmagupta brahmagupta. 598AD 670AD. http://www.virtualology.com/virtualpubliclibrary/hallofeducation/Mathematics/bra

You are in: Virtual Public Library Hall of Education Mathematics Brahmagupta Brahmagupta Start your search on Brahmagupta Other educational search engines: Ask Jeeves for Kids Britannica.com CyberSleuth Kids Education World ... Yahooligans Unauthorized Site: This site and its contents are not affiliated, connected, associated with or authorized by the individual, family, friends, or trademarked entities utilizing any part or the subject’s entire name. Any official or affiliated sites that are related to this subject will be hyper linked below upon submission and Virtualology's review. 2000 by Virtualology TM . All rights reserved. Virtualology TM Search: About Us e-mail us Now Available in Paperback President Who? Forgotten Founders Click Here Editing Sponsor Editing Sponsors review and select all student work for publishing. To learn more about our editing sponsor program click here. Published Students Primary Secondary College Graduate ... Technical

35. 8 III. Brahmagupta, And The Influence On Arabia 8 III. brahmagupta, and the influence on Arabia. (See chapter 8.6). Geometrybrahmagupta stands in high esteem for his contributions to this topic. http://www-history.mcs.st-andrews.ac.uk/history/Projects/Pearce/Chapters/Ch8_3.h

Indian Mathematics MacTutor Index Previous page (8 II. Aryabhata and his commentators) Contents Next page (8 IV. Mathematics over the next 400 years (700AD-1100AD)) 8 III. Brahmagupta, and the influence on Arabia Brahmagupta was born in 598 AD, possibly in Ujjain (possibly a native of Sind) and was the most influential and celebrated mathematician of the Ujjain school. It is important here to note that one must not ignore contributions made by Varahamihira , who was an influential figure at the same Ujjain school during the 6 th century. He is thought to have lived from 505 AD till 587 AD and made only fairly small contributions to the field of mathematics, he is described by Ifrah as: ...One of the most famous astrologers in Indian history. [EFR/JJO'C18, P 1] However he increased the stature of the Ujjain school while working there, a legacy that was to last for a long period, and although his contributions to mathematics were small they were of some importance. They included several trigonometric formulas, improvement of Aryabhata 's sine tables, and derivation of the

36. Brahmagupta's Formula brahmagupta s formula provides the area A of a cyclic quadrilateral (ie, a simplequadrilateral that is inscribed in a circle) with sides of length a, b, c http://mcraefamily.com/MathHelp/GeometryCyclicQuadrilateralBrahmagupta.htm

Brahmagupta's formula provides the area A of a cyclic quadrilateral (i.e., a simple quadrilateral that is inscribed in a circle) with sides of length a, b, c, and d as A = sqrt((s-a)(s-b)(s-c)(s-d)), where s is the semiperimeter (a+b+c+d)/2 If the quadrilateral ABCD is a rectangle, then s=a+b, so A=sqrt((b)(a)(b)(a))=ab, so the formula is true. In any cyclic quadrilateral, you can see that opposite angles are supplemental by drawing a diagonal, AC. Angle D subtends the arc ABC, so the measure of angle D is half the measure of arc ABC. Angle B subtends the arc ADC, so the measure of angle B is half the measure of arc ADC. The sum of the measures of arcs ABC and ADC is 360º, so the sum of the measures of angles B and D is 180º. Now, since the quadrilateral is not a rectangle, you can find two sides that aren't parallel. WNLOG, extend AB and DC until they meet at P: Angles BAD and BCD are supplementary, as are angles BAD and PAD, so angle BCD is equal to angle PAD. So triangles PBC and PDA are similar. The ratio of their sides is b/d, so the ratio of their areas is b^2/d^2. Let A be the area of the quadrilateral, and let T be the area of triangle PBC.

37. Identidad De Brahmagupta - Ciencia.net - Noticias Científicas brahmagupta . El http://www.ciencia.net/VerArticulo/Identidad-de-Brahmagupta?idArticulo=dsfjuhvna

38. Identidad De Brahmagupta Translate this page Identidad de brahmagupta (c) (c) ciencia.net. http//www.ciencia.net//VerArticulo/Identidad-de-brahmagupta?idArticulo=dsfjuhvnanmk3a61hmqdxx. http://www.ciencia.net/enciclo_imprimir.jsp?id=dsfjuhvnanmk3a61hmqdxx

39. Science Jokes:Brahmagupta brahmagupta. brahmagupta (c.598c. 665), Hindu mathematician and astronomer.he wrote the oldest known work with the cipher zero. http://www.xs4all.nl/~jcdverha/scijokes/Brahmagupta.html

Index Comments and Contributions Index Jokes with Famous Scientists Brahmagupta Brahmagupta (c.598-c. 665), Hindu mathematician and astronomer. he wrote the oldest known work with the cipher zero. Index Comments and Contributions Index Jokes with Famous Scientists Definition of a mathematician Index Comments and Contributions

40. Brahmagupta I brahmagupta I. The First Problem Set. Roy Lisker, 2002. brahmagupta The priceof brahmagupta I is $15. Send check, cash or money order to Roy http://www.fermentmagazine.org/Publicity/Science/brahma1.html

Brahmagupta I The First Problem Set Roy Lisker, 2002 Brahmagupta 1 is the first of a series of books of mathematics problems, largely invented by its author. It contains 17 problems at the level of graduate students and advanced undergraduates in mathematics. It is the author's hope that some of these problems are challenging to mathematicians in general. Brahmagupta (598-665 C.E.) was an outstanding mathematician and astronomer of 7th Century India. All solutions are written out in full. Problems: Convex figures Zeta-Function series problems Algebraic Integers on the Unit Circle A Topology on Permutation Space A relationship between tangent and radius vector Parametrizing a graph by arc-length and curvature A curious infinite product Some Fibonacci Series problems An iterated sum-product A double summation problem Everywhere and Nowhere convergent series A metric Knot Theory problem Basic representations of Unity Combinatorics of semi-groups Non-standard logic1 Non-standard logic 2 Self-inverting analytic functions. The price of "Brahmagupta I " is $15 Send check, cash or money order to:

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z

Page 2     21-40 of 86    Back | 1  | 2  | 3  | 4  | 5  | Next 20