21. Brahmagupta's Formula For The Area Of A Cyclic Quadrilateral Problem Develop a proof for brahmagupta s Formula. Who was brahmagupta?brahmagupta s formula is provides the area A of a cyclic quadrilateral (ie, http://jwilson.coe.uga.edu/emt725/brahmagupta/brahmagupta.html

Brahmagupta's Formula Problem: Develop a proof for Brahmagupta's Formula. Who was Brahmagupta? Brahmagupta's formula is 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 where s is the semiperimeter Note: There are alternative approaches to this proof. The one outlined below is intuitive and elementary, but becomes tedious. A more elegant approach is available using trigonometry. The use of Ptolemy's theorem (the product of the diagonals equals the sum of the products of opposite sides) may provide a different investigation of the problem. If ABCD is a rectangle the formula is clear. Consider the chord AC. The angle that subtends a chord has measure that is half the measure of the intercepted arc. But the chord AC is simultaneously subtended by the angle at B and by the angle at D. There for the sum of these angles is 180 degrees. Opposite angles of a cyclic quadrilateral are supplemental. Assume the quadrilateral is not a rectangle. WNLOG, extend AB and CD until they meet at P. Label the extensions outside the circle e and f.

22. Final Project brahmagupta s Generalization then reduces to Heron s Formula. Click here for aGeometer s SketchPad file to test brahmagupta s Generalization. http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Umberger/MATH7200/HeronFormulaPr

MATH 7200 : Foundations of Geometry I University of Georgia, Fall 2000 Dr. McCrory, Instructor Final Project: Heron's Formula by Shannon Umberger Contents I. A brief history of Heron of Alexandria II. Heron's Formula , including a GSP sketch to test III. Three proofs of Heron's Formula: one algebraic, one geometric, and one trigonometric IV. Related topics: A. Brahmagupta's Generalization , including a GSP sketch to test and a proof B. An extension of Brahmagupta's Generalization, including a GSP sketch to test C. The Pythagorean Theorem , including a proof using Heron's Formula V. Resources Heron of Alexandria Not much is known about the man named Heron of Alexandria. Even his name is not definite; he has been called Heron and Hero. No one knows exactly when he lived, though it is commonly believed that he lived sometime between 150 B.C. and 250 A.D. Heron did live in the great scholarly city of Alexandria, Egypt, where many Greek mathematicians and scientists studied. Yet it is not known whether he was a Greek or actually an Egyptian with Greek training. What is sure, though, is that Heron of Alexandria was a brilliant man who gave the modern world much insight into the mathematical and physical sciences. Heron wrote so many works on mathematical and physical subjects that "it is customary to described him as an encyclopedic writer in these fields" (Eves, p. 178). Most of these works can be divided into two categories: geometric and mechanical. While approximately fourteen of his treatises have been uncovered, there are references to other lost works.

23. Malaspina Great Books - Brahmagupta (598) brahmagupta wrote important works on mathematics and astronomy. The work waswritten in 25 chapters and brahmagupta tells us in the text that he wrote http://www.malaspina.com/site/person_240.asp

Biography and Research Links: Please wait for Page to Load or Brahmagupta (598-668)

24. Heron's Formula And Brahmagupta's Generalization brahmagupta didn t actually give a formal proof of this result, It s temptingto think that brahmagupta might have just imagined the equation based on 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

25. Vidyapatha :: Indian Scientists : India's Largest Portal On Educational Informat brahmagupta was born at Bhillamala (Bhinmal), in Gujarat, in 598 AD He became court But brahmagupta always was careful. not to anger the priests. http://www.vidyapatha.com/scientists/brahmagupta.php

Vidyapatha Home About Us Indian Institutes Indian Universities ... Contact Us Channels Vidyapatha Mail Vidyapatha News Indian Scientists Vicharpatha ... Scientists Brahmagupta Previous Next Brahmagupta The mathematician who first framed the rules of operation for zero was Brahmagupta. He was also to give a solution to indeterminate equations of the type ax2+1=y2 and the founder of a branch of higher mathematics called "Numerical analysis". No wonder Bhaskara, the great mathematician, conferred on him Ithe title of Ganakachakrachudamani, the gem of the circle of mathematicians. 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. It was a corrected version of the old astronomical text, Brahmasiddhanta. It was translated into Arabic, but erroneously titled Sind Hind. For several centuries the treatise remained a standard work of reference in India and the Arab countries. Brahmasphutasiddhanta also contains chapters on arithmetic and algebra. Brahmagupta's major contribution is the rules of operation for zero. He declared that addition or subtraction of zero to or from any quantity,negative or positive, does not affect it. He also added that the product of any quantity with zero is zero and division of any quantity by zero is infinity. He,however, wrongly claimed that division of zero by zero was zero.

26. BRAHMAGUPTA brahmagupta was the most accomplished of the ancient Indian astronomers. brahmagupta introduced strict rules for calculations with Zero, http://www.hyperhistory.com/online_n2/people_n2/persons4_n2/brahma.html

BRAHMAGUPTA Indian Mathematician Brahmagupta was the most accomplished of the ancient Indian astronomers. His great work 'The Opening of the Universe' is written in verse form. Brahmagupta introduced strict rules for calculations with Zero , wrote about quadratic equations, and he wrote a table for sinus calculations. He also dealt with lunar eclipses, planetary conjunctions, and the determination of the positions of the planets. www link : From the University of St. Andrews, Scotland School of Mathematics Biography

27. Brahmagupta (ca. 598-ca. 665) -- From Eric Weisstein's World Of Scientific Biogr There, brahmagupta establishes the rule aa=0, and also considers the fractions brahmagupta distinguished twenty arithmetical operations (logistics), http://scienceworld.wolfram.com/biography/Brahmagupta.html

Branch of Science Astronomers Branch of Science Mathematicians ... Barile Brahmagupta (ca. 598-ca. 665) This entry contributed by Margherita Barile Hindu astronomer and mathematician who applied algebraic methods to astronomical problems. Brahmagupta's treatise (628; where means "concepts"), is based on a positional number system, and is the oldest known work where the zero cipher ) appears in arithmetical operations. There, Brahmagupta establishes the rule a a =0, and also considers the fractions x /0, which he sets equal to for x =0 and otherwise calls nought , a term of uncertain meaning. Brahmagupta distinguished twenty arithmetical operations ( logistics ), including the extraction of roots and the solution of proportions, and eight measurements ( determinations ). In this fine classification of mathematical procedures, he also listed four methods for multiplication, and five rules for reducing a rational expression to a single fraction. Brahmagupta's mathematics seems to be rooted in the Greek tradition, the achievements of which he improved and generalized. He established a formula for the area of cyclic quadrilaterals derived from Heron's formula and continued Diophantus' work by characterizing all the solutions of linear congruences, and by proposing the quadratic Diophantine equation which nowadays is known as

28. Brahmagupta - Mathematics And The Liberal Arts The work of brahmagupta should be relevant, but is not currently available inEnglish. The Arabs seem to have adopted their combinatorics from the Hindus. 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.

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

30. Brahmagupta (c. A.D. 598-c. 665) brahmagupta’s theorem states that in a cyclic quadrilateral (a foursided shapewhose corners lie on a circle) having perpendicular diagonals, http://www.daviddarling.info/encyclopedia/B/Brahmagupta.html

Return to The Worlds of David Darling INDEX LATEST NEWS ARCHIVE ... Z entire Web this site Brahmagupta (c. A.D. 598-c. 665) A Hindu astronomer and mathematician who became the head of the observatory at Ujjain—the foremost mathematical center of India at this time; he was the last and most accomplished of the ancient Indian astronomers. His main work, Brahmasphutasiddhanta (The Opening of the Universe), written in 628, contains some remarkably advanced ideas, including a good understanding of the mathematical role of zero , rules for manipulating both positive and negative numbers , a method for computing square roots, methods of solving linear and some quadratic equations, and rules for summing series. His contributions to astronomy were equally ahead of their time. Brahmagupta’s theorem states that in a cyclic quadrilateral (a four-sided shape whose corners lie on a circle) having perpendicular diagonals, the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side. INDIAN ASTRONOMY BACK TO TOP var site="s13space1234"

31. Brahmagupta. The Columbia Encyclopedia, Sixth Edition. 2001-05 brahmagupta. The Columbia Encyclopedia, Sixth Edition. 200105. http://www.bartleby.com/65/br/Brahmagu.html

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32. Brahmagupta - Definition Of Brahmagupta In Encyclopedia brahmagupta (?) (598668) was an Indian mathematician andastronomer. He was the head of the astronomical observatory at Ujjain, http://encyclopedia.laborlawtalk.com/Brahmagupta

Add to Favorites General Encyclopedia Legal ... Law forum Search Word: Visit our Law forums Labor Law Accidents Law Bankruptcy Law Business Law ... Tax Law ) 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 , and the Khandakhadyaka 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 Indian mathematicians External links MacTutor History of Mathematics article on Brahmagupta http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Brahmagupta.html

33. Brahmagupta Biography of brahmagupta, (598670) brahmagupta, whose father was Jisnugupta,wrote important works on mathematics and astronomy. http://zyx.org/Brahmagupta.html

Brahmagupta Born: 598 in (possibly) Ujjain, India Died: 670 in India Brahmagupta, whose father was Jisnugupta, 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. We look below at some of the remarkable ideas which Brahmagupta's two treatises contain. First let us give an overview of their contents. 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. These ten chapters are arranged in topics which are typical of Indian mathematical astronomy texts of the period. The topics covered are: mean longitudes of the planets; true longitudes of the planets; the three problems of diurnal rotation; lunar eclipses; solar eclipses; risings and settings; the moon's crescent; the moon's shadow;

34. Brahmagupta -- Facts, Info, And Encyclopedia Article brahmagupta (?) ( (Click link for more info and facts The major divergence is that brahmagupta attempted to define (Click link for http://www.absoluteastronomy.com/encyclopedia/b/br/brahmagupta.htm

Brahmagupta [Categories: 668 deaths, 598 births, Indian scientists, Ancient mathematicians, Indian mathematicians] (Click link for more info and facts about 598) (Click link for more info and facts about 668) ) was an (A republic in the Asian subcontinent in southern Asia; second most populous country in the world; achieved independence from the United Kingdom in 1947) India n (A person skilled in mathematics) mathematician and (A physicist who studies astronomy) astronomer . He was the head of the astronomical observatory at (Click link for more info and facts about Ujjain) Ujjain , and during his tenure there wrote two texts on mathematics and astronomy: the (Click link for more info and facts about Brahmasphutasiddhanta) Brahmasphutasiddhanta in (Click link for more info and facts about 628) , and the Khandakhadyaka in (Click link for more info and facts about 665) The Brahmasphutasiddhanta is the earliest known text other than the Mayan number system to treat (The quantity that registers a reading of zero on a scale) zero as a number in its own right. It goes well beyond that, however, stating rules for

35. Www.absoluteastronomy.com/encyclopedia/b/br/brahma AllRefer.com brahmagupta (Astronomy, Biography) - EncyclopediaAllRefer.com reference and encyclopedia resource provides complete informationon brahmagupta, Astronomy, Biographies. Includes related research links. http://www.absoluteastronomy.com/encyclopedia/b/br/brahmagupta

36. Brahmagupta FunBrain Site Map. Search. Encyclopedia. brahmagupta, brä mugoop tu PronunciationKey. brahmagupta , c.598–c.660, Indian mathematician and astronomer. http://www.factmonster.com/ce6/people/A0808697.html

Home U.S. People Word Wise ... Homework Center Fact Monster Favorites 2006 TFK Almanac Quiz: Charlie and the Chocolate Factory SpongeBob Lemony Snicket ... Fantasy Books Reference Desk Atlas Almanacs Dictionary Encyclopedia ... Encyclopedia Brahmagupta u u Pronunciation Key Brahmagupta 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 (1817). A shorter treatise, The Khandakhadyaka (tr. 1934), expounded the astronomical system of Aryabhata The Columbia Electronic Encyclopedia, Page Tools: Cite Print More on Brahmagupta from Fact Monster: Encyclopedia: Astronomy: Biographies - Encyclopeadia articles concerning Astronomy: Biographies. mathematics: Development of Mathematics - Development of Mathematics The earliest records of mathematics show it arising in response to ... See more Encyclopedia articles on: Astronomy: Biographies AD AD AD ADS Business Cards Link to Fact Monster Add Fact Monster search ... Privacy Brought to you by: Information Please

37. AoPS Math Forum :: View Topic - The Generalized Brahmagupta Formula what completes the proof of the generalized brahmagupta formula. A special caseis the (special, nongeneralized ) brahmagupta formula, which says that for http://www.artofproblemsolving.com/Forum/topic-15973.html

AoPS Subject Classes Math Jam Wednesday, Sept 7 at 7:30 PM ET AoPS instructors will discuss and work a problem from each of the Introduction to Number Theory and Click here for the complete Math Jam schedule Font Size: The time now is Tue Aug 30, 2005 1:33 pm All times are GMT - 7 Hours The generalized Brahmagupta formula Mark the topic unread Math Forum Olympiad Section ... Geometry Theorems and Formulas Moderators: darij grinberg Myth orl pbornsztein Page of [4 Posts] Printer View Tell a Friend View previous topic View next topic Author Message darij grinberg Joined: 10 Feb 2004 Posts: 3173 Posted: Fri Aug 27, 2004 3:41 am Post subject: The generalized Brahmagupta formula The Generalized Brahmagupta formula states: If ABCD is an arbitrary convex quadrilateral with the sidelengths a = AB, b = BC, c = CD, d = DA, then the area F of the quadrilateral ABCD is where is the semiperimeter of the quadrilateral ABCD, and and are the angles at the vertices B and D. Proof. (A buffalo proof, sorry, I haven't seen any other.) The Cosine Law for triangle ABC yields , and the Cosine Law for triangle CDA yields . Thus

38. PlanetMath: Brahmagupta's Formula Attachments proof of brahmagupta s formula (Proof) by giri This is version3 of brahmagupta s formula, born on 200110-06, modified 2001-10-31. 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 ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About 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 owner history 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 5175 times total. Classification: AMS MSC (Geometry :: General reference works ) Pending Errata and Addenda None.

39. PlanetMath: Proof Of Brahmagupta's Formula proof of brahmagupta s formula is owned by giri. This is version 3 of proofof brahmagupta s formula, born on 200211-14, modified 2002-11-14. 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 ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About 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 equation angles cosines law ... cyclic quadrilateral This is version 3 of proof of Brahmagupta's formula , born on 2002-11-14, modified 2002-11-14.

40. Brahmagupta,Legend,Brahmagupta,Brahmagupta Declared That Addition Or Subtraction brahmagupta,Legend,brahmagupta,brahmagupta declared that addition or subtractionof zero to or from any quantity, negative or positive, does not affect http://www.4to40.com/legends/index.asp?article=legends_brahmagupta

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