Monday, May 27, 2019

Lupain Ng Taglamig

DETERGENT PESTICIDE DISINFFECTANT PRESERVATIVES ADDITIVES MEDICINES BLEACH PETROLEUM JELLY ALUMINUM FOIL CORN STARCH NAME. ROMELYN. VILLAMAYOR YR&SEC IV-EDISON TEACHER MRS. SALUDES NAMEERICA E. VILLAMAYOR GR&SEC VI-MALINIS TEACHERMRPENIDA A detergentis asurfactantor a multifariousness of surfactants with cleaning properties in dilute solutions. 1These substances be usu totallyy alkylbenzenesulfonates, a family of compounds that argon similar tosoap moreover are more soluble in unexpressed water, because the polar sulfonate (of detergents) is slight likely than the polar carboxyl (of soap) to bind to calcium and saucily(prenominal) ions found in hard water.In most kinfolk contexts, the termdetergentby itself refers specifically tolaundry detergentordish detergent, as opposed tohand soapor some other fictional characters of cleaning sequencents. Detergents are comm precisely available as powders or concentrated solutions. Detergents, like soaps, work because they areamph iphilic p craftlyhydrophilic(polar) and partlyhydrophobic(non-polar). Their dual nature facilitates the mixture of hydrophobic compounds (like oil and grease) with water. Because air is not hydrophilic, detergents are in any casefoaming agentsto varying degrees.Pesticidesare substances or mixture of substances intended for pr level off commodeg, destroying, repelling or mitigating anypest. 1Pesticides are a special kind of products for figure out protection. Crop protection products in general protect plants from damaging influences such as weeds, maladys or insects. A pesticide is generally achemicalor biological agent (such as avirus,bacterium,antimicrobialordisinfectant) that through its effect deters, incapacitates, kills or otherwise discourages pests.Target pests can includeinsects, plantpathogens, weeds,molluscs,birds,mammals,fish, nematodes (roundworms), andmicrobesthat destroy property, cause nuisance, spread disease or arevectorsfor disease. Disinfectantsare substances that are use to non-living objects to destroymicroorganismsthat are living on the objects. 1Disinfection does not necessarily kill all microorganisms, especially rebarbativebacterial spores it is less effective thansterilisation, which is an extreme physical and/or chemical process that kills all types of life. 1Disinfectants are assorted from otherantimicrobial agentssuch asantibiotics, which destroy microorganisms within the body, andantiseptics, which destroy microorganisms on livingtissue.Disinfectants are besides different frombiocides the latter are intended to destroy all forms of life, not middling microorganisms. Disinfectants work by destroying the cell wall of microbes or interfering with the metabolism. Apreservativeis a naturally occurring or synthetically produced substance that is added to products such as foods,pharmaceuticals, paints, biological samples, wood, etc. o preventdecompositionbymicrobialgrowth or by undesirablechemicalchanges. Food additivesare subst ances added to food to extend flavor or enhance its taste and appearance. Some additives lose been used for centuries for example, preserving food bypickling(withvinegar),salting, as withbacon, preservingsweetsor usingsulfur dioxideas in somewines. With the advent of processed foods in the hour half of the 20th century, umteen more additives live been introduced, of both natural and artificial origin.Medicineis theapplied experienceor practice of thediagnosis,treatment, and prevention ofdisease. 1It encompasses a variety ofhealth carepractices evolved to maintain and restorehealthby thepreventionandtreatmentofillnessinhuman beings. Contemporary medicine applieshealth science,biomedical look into, andmedical technologytodiagnoseand treat injury and disease, typically throughmedicationorsurgery, but also through therapies as diverse aspsychotherapy,external splints & traction,prostheses,biologics,ionizing radiationand others. blanchhas been serialized in the Japanese manga a nthologyWeekly Shonen JumpsincAugust 2001, and has been collected into 56tankobonvolumes as of September 2012. Since its publication,Bleachhas spawned amedia franchisethat includes ananimatedtelevision seriesthat was produced byStudio Pierrotin Japan from 2004 to 2012, twooriginal video animations, four animated feature films, 7rock musicals, andnumerous video games, as well as some types ofBleach-relatedmerchandise.Petroleum jelly,petrolatum,white petrolatumorsoft paraffin,CAS turn of events8009-03-8, is asemi-solidmixture ofhydro nose candys(withcarbonnumbers mainly higher than 25),1originally promoted as a topicalointmentfor its healing properties. Its folkloric medicinal value as a cure-all has since been modified by better scientific understanding of appropriate and inappropriate uses (seeusesbelow). However, it is recognized by the U. S. Food and Drug Administration(FDA) as an approvedover-the-counter(OTC) discaseprotectant, and remains widely used incosmeticskin care.Alum inium foilisaluminiumprepared in thinmetal leaves, with a thickness less than 0. 2 millimetres (8mils), thinner gauges d allow to 6m (0. 2mils) are also commonly used. 1In the USA, foils are commonly gauged inmils. Standard household foil is typically 0. 016 millimetres (0. 6mils) thick and heavy duty household foil is typically 0. 024 millimetres (0. 9mils). Thefoilis pliable, and can be readily stage set or wrapped around objects. Thin foils are fragile and are some snipslaminatedto other materials such asplasticsorpaperto make them more useful.Aluminium foilsupplantedtin foilin the mid 20th century. Corn starch is used as athickening agentinsoupsand liquid-based foods, such assauces,graviesandcustardsby assortment it with a cold liquid to form a paste or slurry. It is sometimes preferred overflourbecause it forms atranslucentmixture, quite a than anopaqueone. As the starch is heated, the molecular chains unravel, allowing them to collide with other starch chains to form a mes h, thickening the liquid (Starch gelatinization).Lupain Ng TaglamigReaction Paper Ric Michael P. De Vera IV- Rizal Mr. Norie Sabayan I. A and B Arabic mathss forgotten brilliance? Indian mathsreached Baghdad, a major(ip) earlier center of Islam, about ad 800. Supported by the ruling caliphs and wealthy individuals, translators in Baghdad produced Arabic versions of Hellenic and Indian mathematical works. The hire for variants was stimulated by mathematical research in the Muslim world. Moslem maths also served religion in that it proved useful in dividing inheritances fit in to Moslem law in predicting the time of the new moon, when the abutting month began and in determining the direction to Mecca for the orientation of mosques and of daily prayers, which were delivered facing Mecca. Recent research paints a new picture of the debt that we owe to Arabic/ Moslem mathematics.Certainly many of the motifs which were previously thought to have been brilliant new conceptions d ue to European mathematicians of the one-sixteenth, seventeenth and eighteenth centuries are now ben to have been developed by Arabic/Islamic mathematicians around four centuries earlier. In many reckon the mathematics studied today is far closer in style to that of the Arabic/Islamic ploughshare than to that of the Greeks.There is a widely held view that, subsequently a brilliant period for mathematics when the Greeks laid the foundations for new-fangled mathematics, there was a period of stagnation before the Europeans took over where the Greeks left off at the beginning of the sixteenth century. The common perception of the period of grand piano years or so between the ancient Greeks and the European Renaissance is that little happened in the world of mathematics except that some Arabic translations of Greek texts were made which keep the Greek learning so that it was available to the Europeans at the beginning of the sixteenth century.That such views should be generally held is of no surprise. Many spark advance historians of mathematics have contributed to the perception by either omitting any mention of Arabic/Islamic mathematics in the historical development of the subject or with statements such as that made by Duhem in - Arabic science only reproduced the teachings real from Greek science. Before we proceed it is worth trying to go down the period that this article covers and authorise an overall description to cover the mathematicians who contributed.The period we cover is liberal to describe it stretches from the end of the eighth century to about the nerve of the fifteenth century. Giving a description to cover the mathematicians who contributed, however, is overmuch harder. The works and are on Islamic mathematics, similar to which uses the title the Muslim contribution to mathematics. Other authors try the description Arabic mathematics. However, certainly not all the mathematicians we wish to include were Muslims some were Jews, some Christians, some of other faiths.Nor were all these mathematicians Arabs, but for convenience we will call our topic Arab mathematics. We should emphasize that the translations into Arabic at this time were made by scientists and mathematicians such as those named above, not by language experts ignorant of mathematics, and the need for the translations was stimulated by the most march on research of the time. It is authoritative to realize that the translating was not done for its own sake, but was done as part of the current research effort.Of Euclids works, the Elements, the Data, the Optics, the Phaenomena, and On Divisions were translated. Of Archimedes works only two Sphere and Cylinder and Measurement of the Circle are known to have been translated, but these were sufficient to stimulate independent researches from the 9th to the 15th century. On the other hand, virtually all of Apolloniuss works were translated, and of Diophantus and Menelaus one book each, the Arithm etica and the Sphaerica, respectively, were translated into Arabic.Finally, the translation of Ptolemys Almagest furnished important astronomical material. Diocles treatise on mirrors, Theodosiuss Spherics, Pappuss work on mechanics, Ptolemys Planisphaerium, and Hypsicles treatises on regular polyhedra (the questionable Books XIV and XV of Euclids Elements) Perhaps one of the most satisfying advances made by Arabic mathematics began at this time with the work of al-Khwarizmi, namely the beginnings of algebra. It is important to understand just how significant this new idea was. It was a revolutionary ove a personal manner from the Greek concept of mathematics which was demandly geometry. Algebra was a unifying theory which allowed rational numbers, irrational numbers, nonrepresentationalal magnitudes, etc. , to all is hardened as algebraic objects. It gave mathematics a whole new development path so much broader in concept to that which had existed before, and provided a veh icle for afterwardslife development of the subject. Another important aspect of the introduction of algebraic ideas was that it allowed mathematics to be applied to itself in a way which had not happened before.Al-Khwarizmis successors undertook a arrogant application of arithmetic to algebra, algebra to arithmetic, both to trig, algebra to the Euclidean theory of numbers, algebra to geometry, and geometry to algebra. This was how the creation of polynomial algebra, combinatorial analysis, and mathematical analysis, the numerical solution of equations, the new elementary theory of numbers, and the geometric construction of equations arose. allow us follow the development of algebra for a moment and look at al-Khwarizmis successors.About forty years after al-Khwarizmi is the work of al-Mahani (born 820), who conceived the idea of reducing geometrical problems such as duplicating the cube to problems in algebra. Abu Kamil (born 850) forms an important link in the development of a lgebra between al-Khwarizmi and al-Karaji. Despite not using symbols, but writing powers of x in words, he had begun to understand what we would write in symbols as xn. xm = xm+n. permit us remark that symbols did not appear in Arabic mathematics until much later.Ibn al-Banna and al-Qalasadi used symbols in the 15th century and, although we do not know exactly when their use began, we know that symbols were used at least(prenominal) a century before this. Al-Karaji (born 953) is seen by many as the send-off person to exclusively free algebra from geometrical operations and to replace them with the arithmetical type of operations which are at the core of algebra today. He was first to define the monomials x, x2, x3, and 1/x, 1/x2, 1/x3, and to cause rules for products of any two of these. He started a school of algebra which flourished for several hundreds of years.Al-Samawal, nearly 200 years later, was an important member of al-Karajis school. Al-Samawal (born 1130) was the first to mother the new topic of algebra a precise description when he wrote that it was concerned- with operating on unknowns using all the arithmetical tools, in the same way as the arithmetician operates on the known. Omar Khayyam (born 1048) gave a complete classification of three-dimensional equations with geometric solutions found by means of intersecting conic sections. Khayyam also wrote that he hoped to give a full description of the algebraic solution of boxlike equations in a later work .If the opportunity arises and I can succeed, I shall give all these fourteen forms with all their branches and cases, and how to distinguish whatever is executable or impossible so that a paper, containing elements which are greatly useful in this art will be prepared. Sharaf al-Din al-Tusi (born 1135), although almost exactly the same age as al-Samawal, does not follow the general development that came through al-Karajis school of algebra but rather follows Khayyams application of al gebra to geometry. He wrote a treatise on cubic equations. .. represents an essential contribution to another algebra which aimed to study curves by means of equations, thus inaugurating the beginning of algebraic geometry. Let us give other examples of the development of Arabic mathematics. move to the House of Wisdom in Baghdad in the 9th century, one mathematician who was better there by the Banu Musa brothers was Thabit ibn Qurra (born 836). He made many contributions to mathematics, but let us consider for the moment consider his contributions to number theory.He discovered a good-looking theorem which allowed pairs of social numbers to be found, that is two numbers such that each is the sum of the proper divisors of the other. Al-Baghdadi (born 980) looked at a slight variant of Thabit ibn Qurras theorem, time al-Haytham (born 965) seems to have been the first to attempt to classify all even perfect numbers (numbers equal to the sum of their proper divisors) as those of t he form 2k-1(2k 1) where 2k 1 is prime. Al-Haytham, is also the first person that we know to state Wilsons theorem, namely that if p is prime then 1+ (p-1) is divisible by p.It is unclear whether he knew how to prove this result. It is called Wilsons theorem because of a comment made by Waring in 1770 that John Wilson had notice the result. There is no evidence that John Wilson knew how to prove it and most certainly Waring did not. Lagrange gave the first deduction in 1771 and it should be noticed that it is more than 750 years after al-Haytham before number theory surpasses this achievement of Arabic mathematics. Continuing the story of loveable numbers, from which we have taken a diversion, it is worth noting that they play a large role in Arabic mathematics.Al-Farisi (born 1260) gave a new proof of Thabit ibn Qurras theorem, introducing important new ideas concerning factorisation and combinatorial methods. He also gave the pair of amicable numbers 17296, 18416 which have b een attributed to Euler, but we know that these were known earlier than al-Farisi, perhaps even by Thabit ibn Qurra himself. Although outside our time range for Arabic mathematics in this article, it is worth noting that in the 17th century the Arabic mathematician Mohammed Baqir Yazdi gave the pair of amicable number 9,363,584 and 9,437,056 notwithstanding many years before Eulers contribution.C. Arabian math/ Islamic Mathematics Inthe9thcenturyArab mathematician al-Khwarizmi wrote a systematic introduction to algebra, Kitab al-jabr wal Muqabalah (Book of Restoring and Balancing). The incline word algebra comes from al-jabr in the treatises title. Al-Khwarizmis algebra was founded on Brahmaguptas work, which he duly credited, and showed the influence of Babylonian and Greek mathematics as well. A 12th-century Latin translation of al-Khwarizmis treatise was crucial for the later development of algebra in Europe. Al-Khwarizmis name is the source of the word algorithm.Bytheyear900t heacquisition of past mathematics was complete, and Muslim scholars began to build on what they had acquired. Alhazen, an outstanding Arab scientist of the late 900s and early 1000s, produced algebraic solutions of quadratic and cubic equations. Al-Karaji in the 10th and early 11th century faultless the algebra of polynomials (mathematical expressions that are the sum of a number of terms) of al-Khwarizmi. He include polynomials with an infinite number of terms. Laterscholars,including 12th-century Persian mathematician Omar Khayyam, illuminated certain cubic equations geometrically by using conic sections.Arab astronomers contributed the tangent and cotangent to trigonometry. Geometers such as Ibrahim ibn Sinan in the 10th century continued Archimedess investigations of areas and volumes, and Kamal al-Din and others applied the theory of conic sections to solve problems in optics. Astronomer Nasir al-Din al-Tusi created the mathematical disciplines of plane and spherical trigonom etry in the 13th century and was the first to treat trigonometry separately from astronomy. Finally, a number of Muslim mathematicians made important discoveries in the theory of numbers, while others explained a ariety of numerical methods for solving equations. ManyoftheancientGreek works on mathematics were preserved during the middle Ages through Arabic translations and commentaries. Europe acquired much of this learning during the 12th century, when Greek and Arabic works were translated into Latin, then the written language of educated Europeans. These Arabic works, together with the Greek classics, were responsible for the growth of mathematics in the West during the late middle Ages. Microsoft Encarta 2009. 1993-2008 Microsoft Corporation.All rights reserved. D. Origin of the Word Algebra The word algebra is a Latin variant of the Arabic word al-jabr. This came from the title of a book, Hidab al-jabr wal-muqubala, written in Baghdad about 825 A. D. by the Arab mathematici an Mohammed ibn-Musa al-Khowarizmi. The words jabr (JAH-ber) and muqubalah (moo-KAH-ba-lah) were used by al-Khowarizmi to intend two basic operations in solving equations. Jabr was to exchange subtracted terms to the other side of the equation. Muqubalah was to cancel like terms on opposite sides of the equation.In fact, the title has been translated to mean science of restoration (or reunion) and opposition or science of transposition and cancellation and The Book of Completion and Cancellation or The Book of Restoration and Balancing. Jabr is used in the step where x 2 = 12 becomes x = 14. The left-side of the first equation, where x is lessened by 2, is restored or completed back to x in the second equation. Muqabalah takes us from x + y = y + 7 to x = 7 by cancelling or balancing the two sides of the equation.Eventually the muqabalah was left behind, and this type of math became known as algebra in many languages. It is interesting to contrast that the word al-jabr used non -mathematically made its way into Europe through the Moors of Spain. There an algebrista is a bonesetter, or restorer of bones. A barber of medieval times called himself an algebrista since barbers a good deal did bone-setting and bloodletting on the side. Hence the red and white striped barber poles of today. II. Insights The Arabian contributions to Mathematics are much used around the world.Their Mathematics shows a perfect way to represent numbers and problems, in a way to make it clearer and easier to understand. They have discovered many things about mathematics and formulated many formulas that are widely used today. I learned from this research that Arabs mathematics started when Indian mathematics reached Baghdad and translated it into Arabic. They improved and studied Mathematics and formulated many things. They become more famous when they discovered Algebra and improved it.Many Arabian mathematicians became famous because of their contributions on Mathematics. Many anci ent Greeks works on mathematics were preserved through Arabic translations and commentaries. I am enlightened about the origin of what are we canvas now in Mathematics. Now I know that volume of our lessons in mathematics came from Arabians not from Greeks. I also learned that many mathematicians contributed on different branches and techniques on mathematics and it take so much time for them to explore and improve mathematics.Lupain Ng TaglamigReaction Paper Ric Michael P. De Vera IV- Rizal Mr. Norie Sabayan I. A and B Arabic mathematics forgotten brilliance? Indianmathematicsreached Baghdad, a major early center of Islam, about ad 800. Supported by the ruling caliphs and wealthy individuals, translators in Baghdad produced Arabic versions of Greek and Indian mathematical works. The need for translations was stimulated by mathematical research in the Islamic world.Islamic mathematics also served religion in that it proved useful in dividing inheritances according to Islamic law i n predicting the time of the new moon, when the next month began and in determining the direction to Mecca for the orientation of mosques and of daily prayers, which were delivered facing Mecca. Recent research paints a new picture of the debt that we owe to Arabic/Islamic mathematics.Certainly many of the ideas which were previously thought to have been brilliant new conceptions due to European mathematicians of the sixteenth, seventeenth and eighteenth centuries are now known to have been developed by Arabic/Islamic mathematicians around four centuries earlier. In many respects the mathematics studied today is far closer in style to that of the Arabic/Islamic contribution than to that of the Greeks.There is a widely held view that, after a brilliant period for mathematics when the Greeks laid the foundations for modern mathematics, there was a period of stagnation before the Europeans took over where the Greeks left off at the beginning of the sixteenth century. The common percept ion of the period of 1000 years or so between the ancient Greeks and the European Renaissance is that little happened in the world of mathematics except that some Arabic translations of Greek texts were made which preserved the Greek learning so that it was available to the Europeans at the beginning of the sixteenth century.That such views should be generally held is of no surprise. Many leading historians of mathematics have contributed to the perception by either omitting any mention of Arabic/Islamic mathematics in the historical development of the subject or with statements such as that made by Duhem in - Arabic science only reproduced the teachings received from Greek science. Before we proceed it is worth trying to define the period that this article covers and give an overall description to cover the mathematicians who contributed.The period we cover is easy to describe it stretches from the end of the eighth century to about the middle of the fifteenth century. Giving a de scription to cover the mathematicians who contributed, however, is much harder. The works and are on Islamic mathematics, similar to which uses the title the Muslim contribution to mathematics. Other authors try the description Arabic mathematics. However, certainly not all the mathematicians we wish to include were Muslims some were Jews, some Christians, some of other faiths.Nor were all these mathematicians Arabs, but for convenience we will call our topic Arab mathematics. We should emphasize that the translations into Arabic at this time were made by scientists and mathematicians such as those named above, not by language experts ignorant of mathematics, and the need for the translations was stimulated by the most advanced research of the time. It is important to realize that the translating was not done for its own sake, but was done as part of the current research effort.Of Euclids works, the Elements, the Data, the Optics, the Phaenomena, and On Divisions were translated. Of Archimedes works only two Sphere and Cylinder and Measurement of the Circle are known to have been translated, but these were sufficient to stimulate independent researches from the 9th to the 15th century. On the other hand, virtually all of Apolloniuss works were translated, and of Diophantus and Menelaus one book each, the Arithmetica and the Sphaerica, respectively, were translated into Arabic.Finally, the translation of Ptolemys Almagest furnished important astronomical material. Diocles treatise on mirrors, Theodosiuss Spherics, Pappuss work on mechanics, Ptolemys Planisphaerium, and Hypsicles treatises on regular polyhedra (the so-called Books XIV and XV of Euclids Elements) Perhaps one of the most significant advances made by Arabic mathematics began at this time with the work of al-Khwarizmi, namely the beginnings of algebra. It is important to understand just how significant this new idea was. It was a revolutionary ove away from the Greek concept of mathematics which was essentially geometry. Algebra was a unifying theory which allowed rational numbers, irrational numbers, geometrical magnitudes, etc. , to all is treated as algebraic objects. It gave mathematics a whole new development path so much broader in concept to that which had existed before, and provided a vehicle for future development of the subject. Another important aspect of the introduction of algebraic ideas was that it allowed mathematics to be applied to itself in a way which had not happened before.Al-Khwarizmis successors undertook a systematic application of arithmetic to algebra, algebra to arithmetic, both to trigonometry, algebra to the Euclidean theory of numbers, algebra to geometry, and geometry to algebra. This was how the creation of polynomial algebra, combinatorial analysis, and numerical analysis, the numerical solution of equations, the new elementary theory of numbers, and the geometric construction of equations arose. Let us follow the development of algebra f or a moment and look at al-Khwarizmis successors.About forty years after al-Khwarizmi is the work of al-Mahani (born 820), who conceived the idea of reducing geometrical problems such as duplicating the cube to problems in algebra. Abu Kamil (born 850) forms an important link in the development of algebra between al-Khwarizmi and al-Karaji. Despite not using symbols, but writing powers of x in words, he had begun to understand what we would write in symbols as xn. xm = xm+n. Let us remark that symbols did not appear in Arabic mathematics until much later.Ibn al-Banna and al-Qalasadi used symbols in the 15th century and, although we do not know exactly when their use began, we know that symbols were used at least a century before this. Al-Karaji (born 953) is seen by many as the first person to completely free algebra from geometrical operations and to replace them with the arithmetical type of operations which are at the core of algebra today. He was first to define the monomials x, x2, x3, and 1/x, 1/x2, 1/x3, and to give rules for products of any two of these. He started a school of algebra which flourished for several hundreds of years.Al-Samawal, nearly 200 years later, was an important member of al-Karajis school. Al-Samawal (born 1130) was the first to give the new topic of algebra a precise description when he wrote that it was concerned- with operating on unknowns using all the arithmetical tools, in the same way as the arithmetician operates on the known. Omar Khayyam (born 1048) gave a complete classification of cubic equations with geometric solutions found by means of intersecting conic sections. Khayyam also wrote that he hoped to give a full description of the algebraic solution of cubic equations in a later work .If the opportunity arises and I can succeed, I shall give all these fourteen forms with all their branches and cases, and how to distinguish whatever is possible or impossible so that a paper, containing elements which are greatly us eful in this art will be prepared. Sharaf al-Din al-Tusi (born 1135), although almost exactly the same age as al-Samawal, does not follow the general development that came through al-Karajis school of algebra but rather follows Khayyams application of algebra to geometry. He wrote a treatise on cubic equations. .. represents an essential contribution to another algebra which aimed to study curves by means of equations, thus inaugurating the beginning of algebraic geometry. Let us give other examples of the development of Arabic mathematics. Returning to the House of Wisdom in Baghdad in the 9th century, one mathematician who was educated there by the Banu Musa brothers was Thabit ibn Qurra (born 836). He made many contributions to mathematics, but let us consider for the moment consider his contributions to number theory.He discovered a beautiful theorem which allowed pairs of amicable numbers to be found, that is two numbers such that each is the sum of the proper divisors of the o ther. Al-Baghdadi (born 980) looked at a slight variant of Thabit ibn Qurras theorem, while al-Haytham (born 965) seems to have been the first to attempt to classify all even perfect numbers (numbers equal to the sum of their proper divisors) as those of the form 2k-1(2k 1) where 2k 1 is prime. Al-Haytham, is also the first person that we know to state Wilsons theorem, namely that if p is prime then 1+ (p-1) is divisible by p.It is unclear whether he knew how to prove this result. It is called Wilsons theorem because of a comment made by Waring in 1770 that John Wilson had noticed the result. There is no evidence that John Wilson knew how to prove it and most certainly Waring did not. Lagrange gave the first proof in 1771 and it should be noticed that it is more than 750 years after al-Haytham before number theory surpasses this achievement of Arabic mathematics. Continuing the story of amicable numbers, from which we have taken a diversion, it is worth noting that they play a lar ge role in Arabic mathematics.Al-Farisi (born 1260) gave a new proof of Thabit ibn Qurras theorem, introducing important new ideas concerning factorisation and combinatorial methods. He also gave the pair of amicable numbers 17296, 18416 which have been attributed to Euler, but we know that these were known earlier than al-Farisi, perhaps even by Thabit ibn Qurra himself. Although outside our time range for Arabic mathematics in this article, it is worth noting that in the 17th century the Arabic mathematician Mohammed Baqir Yazdi gave the pair of amicable number 9,363,584 and 9,437,056 still many years before Eulers contribution.C. Arabian Mathematics/ Islamic Mathematics Inthe9thcenturyArab mathematician al-Khwarizmi wrote a systematic introduction to algebra, Kitab al-jabr wal Muqabalah (Book of Restoring and Balancing). The English word algebra comes from al-jabr in the treatises title. Al-Khwarizmis algebra was founded on Brahmaguptas work, which he duly credited, and showed th e influence of Babylonian and Greek mathematics as well. A 12th-century Latin translation of al-Khwarizmis treatise was crucial for the later development of algebra in Europe. Al-Khwarizmis name is the source of the word algorithm.Bytheyear900theacquisition of past mathematics was complete, and Muslim scholars began to build on what they had acquired. Alhazen, an outstanding Arab scientist of the late 900s and early 1000s, produced algebraic solutions of quadratic and cubic equations. Al-Karaji in the 10th and early 11th century completed the algebra of polynomials (mathematical expressions that are the sum of a number of terms) of al-Khwarizmi. He included polynomials with an infinite number of terms. Laterscholars,including 12th-century Persian mathematician Omar Khayyam, solved certain cubic equations geometrically by using conic sections.Arab astronomers contributed the tangent and cotangent to trigonometry. Geometers such as Ibrahim ibn Sinan in the 10th century continued Archi medess investigations of areas and volumes, and Kamal al-Din and others applied the theory of conic sections to solve problems in optics. Astronomer Nasir al-Din al-Tusi created the mathematical disciplines of plane and spherical trigonometry in the 13th century and was the first to treat trigonometry separately from astronomy. Finally, a number of Muslim mathematicians made important discoveries in the theory of numbers, while others explained a ariety of numerical methods for solving equations. ManyoftheancientGreek works on mathematics were preserved during the middle Ages through Arabic translations and commentaries. Europe acquired much of this learning during the 12th century, when Greek and Arabic works were translated into Latin, then the written language of educated Europeans. These Arabic works, together with the Greek classics, were responsible for the growth of mathematics in the West during the late middle Ages. Microsoft Encarta 2009. 1993-2008 Microsoft Corporation .All rights reserved. D. Origin of the Word Algebra The word algebra is a Latin variant of the Arabic word al-jabr. This came from the title of a book, Hidab al-jabr wal-muqubala, written in Baghdad about 825 A. D. by the Arab mathematician Mohammed ibn-Musa al-Khowarizmi. The words jabr (JAH-ber) and muqubalah (moo-KAH-ba-lah) were used by al-Khowarizmi to designate two basic operations in solving equations. Jabr was to transpose subtracted terms to the other side of the equation. Muqubalah was to cancel like terms on opposite sides of the equation.In fact, the title has been translated to mean science of restoration (or reunion) and opposition or science of transposition and cancellation and The Book of Completion and Cancellation or The Book of Restoration and Balancing. Jabr is used in the step where x 2 = 12 becomes x = 14. The left-side of the first equation, where x is lessened by 2, is restored or completed back to x in the second equation. Muqabalah takes us from x + y = y + 7 to x = 7 by cancelling or balancing the two sides of the equation.Eventually the muqabalah was left behind, and this type of math became known as algebra in many languages. It is interesting to note that the word al-jabr used non-mathematically made its way into Europe through the Moors of Spain. There an algebrista is a bonesetter, or restorer of bones. A barber of medieval times called himself an algebrista since barbers often did bone-setting and bloodletting on the side. Hence the red and white striped barber poles of today. II. Insights The Arabian contributions to Mathematics are much used around the world.Their Mathematics shows a perfect way to represent numbers and problems, in a way to make it clearer and easier to understand. They have discovered many things about mathematics and formulated many formulas that are widely used today. I learned from this research that Arabs mathematics started when Indian mathematics reached Baghdad and translated it into Arabic. They improved and studied Mathematics and formulated many things. They become more famous when they discovered Algebra and improved it.Many Arabian mathematicians became famous because of their contributions on Mathematics. Many ancient Greeks works on mathematics were preserved through Arabic translations and commentaries. I am enlightened about the origin of what are we studying now in Mathematics. Now I know that majority of our lessons in mathematics came from Arabians not from Greeks. I also learned that many mathematicians contributed on different branches and techniques on mathematics and it take so much time for them to explore and improve mathematics.

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