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HISTORY OF MATHEMATICS

The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From BC the Mesopotamian states of SumerAkkad and Assyriafollowed closely by Ancient Egypt and the Levantine state of Ebla began using arithmeticalgebra and geometry for purposes of taxation, commerce, trade cbde also in the patterns in naturethe field of astronomy and to record time and formulate calendars.

The earliest mathematical texts available are from Mesopotamia and Egypt � Plimpton Babylonian c. History of mathematics class 10 cbse only of these texts mention the so-called Pythagorean triplesso, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry. Chinese mathematics made early contributions, including a place value system and the first use of negative numbers.

Many Greek and Arabic texts on mathematics were translated into Latin from the 12th century onward, leading to further development of mathematics in Medieval Europe. From ancient times through the Middle Agesperiods of mathematical discovery were often followed by centuries of stagnation. Beginning in Renaissance Italy in the 15th century, new mathematical clqss, interacting with new scientific discoveries, were made at an increasing pace that continues through the present day.

This includes the groundbreaking work of both Isaac Newton and Gottfried Wilhelm Leibniz in the development of infinitesimal calculus during the course of the 17th century. At the end of the 19th century the International Congress of Mathematicians was founded and continues to spearhead advances in the field. The origins of mathematical thought lie in the concepts of numberpatterns history of mathematics class 10 cbse only naturemagnitudeand form.

Such concepts would have been part of everyday life in hunter-gatherer societies. The idea of the "number" concept evolving gradually over time is supported by the existence of languages which preserve the mathemarics between "one", "two", and "many", but not of numbers larger than two.

Prehistoric artifacts discovered in Africa, dated 20, years old or more suggest early mathematjcs to quantify time. Common interpretations are that the Ishango bone shows either a tally of the earliest known demonstration of sequences of prime numbers [12] or a six-month lunar calendar.

He also writes that "no attempt has been made to explain why a tally of something should exhibit multiples of two, prime numbers between 10 and 20, and some numbers that are almost multiples of Predynastic Egyptians of the 5th millennium BC pictorially represented geometric designs. It has been claimed that megalithic monuments in England and Scotlanddating from the 3rd millennium BC, incorporate geometric ideas such as circlesellipsesand Pythagorean triples in their design.

Babylonian mathematics refers to any mathematics of the peoples of Mesopotamia modern Iraq from the days of the history of mathematics class 10 cbse only Sumerians through the Hellenistic period almost to the dawn of Christianity. Later under the Arab EmpireMesopotamia, especially Baghdadonce again became an important center of study for History of mathematics class 10 cbse only mathematics.

In contrast to the sparsity of sources in Egyptian mathematicsknowledge of Babylonian mathematics is derived from more than clay tablets unearthed since history of mathematics class 10 cbse only s. Some of these appear to be graded homework. The earliest evidence of written mathematics dates back to the ancient Sumerianswho built the earliest civilization in Mesopotamia.

They developed a complex system of metrology from BC. From around BC onward, the Sumerians wrote cbsse tables on clay tablets and dealt with geometrical exercises and division problems.

The earliest traces of the Babylonian numerals onlt date back to this period. Babylonian mathematics were written using a sexagesimal base numeral. It is likely the sexagesimal system was chosen because 60 can be evenly divided by 2, 3, 4, 5, 6, 10, 12, 15, 20 and Other topics covered by Babylonian mathematics include fractions, algebra, quadratic and cubic equations, and the calculation of regular numbersand their reciprocal pairs.

Egyptian mathematics refers to mathematics written in the Egyptian language. From the Hellenistic periodGreek replaced Egyptian as the written language of Egyptian scholars. Mathematical study in Egypt later continued under the Arab Empire as part of Islamic mathematicswhen Arabic became the written language of Egyptian scholars.

The most extensive Egyptian mathematical text is the Rhind papyrus sometimes also called the Ahmes Papyrus after its authordated to c. In addition to giving area history of mathematics class 10 cbse only and methods for multiplication, division and working with unit fractions, it also contains evidence of other mathematical knowledge, [28] including composite and prime numbers ; arithmeticgeometric and harmonic means ; and simplistic understandings of both the Sieve of Eratosthenes and perfect number theory namely, that mathwmatics the number 6.

Another significant Egyptian mathematical text is the Moscow papyrusalso from the Middle Kingdom period, dated to c. One problem is considered to be of particular importance because it gives a method for finding the volume of nistory frustum truncated pyramid. Finally, the Berlin Papyrus c. Greek mathematics of the period following Alexander the Great is sometimes called Hellenistic mathematics. Greek mathematics was much more history of mathematics class 10 cbse only than the mathematics that had been developed by earlier cultures.

All surviving records of pre-Greek mathematics show the use of inductive reasoningthat is, repeated observations used to establish rules of thumb. Greek mathematicians, by contrast, used deductive reasoning.

The Greeks used logic to derive conclusions from history of mathematics class 10 cbse only and axioms, and used mathematical rigor hostory prove. Greek mathematics is thought to have begun with Thales of Miletus c.

Although the extent of the influence is disputed, they were probably inspired by Egyptian and Babylonian mathematics. According to legend, Pythagoras traveled to Egypt to learn clasx, geometry, and astronomy from Egyptian priests.

Thales used geometry to solve problems such as calculating the height of pyramids clsss the distance of ships from the shore. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. As a result, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed.

The Pythagoreans are credited with the first proof of the Pythagorean theorem[39] though the statement of the theorem has a long history, and with the proof of the existence of irrational numbers.

History of mathematics class 10 cbse only �c. Though he made no specific technical mathematical discoveries, Aristotle �c. In the 3rd century BC, the premier center of mathematical education and research was the Musaeum of Alexandria.

Although most of the contents of the Elements were already known, Euclid arranged them into a single, coherent logical framework. Euclid also wrote extensively on other subjects, such as conic sections histroy, opticsspherical geometryand mechanics, but only half of his writings survive. Archimedes c. Apollonius of Perga c. Around the same time, Eratosthenes of Cyrene c.

AD 90�a landmark astronomical treatise whose trigonometric tables would be used by astronomers for the next thousand years. Following a period cbsee stagnation after Ptolemy, the period between and AD is sometimes referred to as the "Silver Age" of Greek mathematics. His main work was the Arithmeticaa collection of algebraic problems dealing with exact solutions to determinate and indeterminate equations.

He is known for his hexagon theorem and centroid theoremas well as the Pappus configuration and Pappus graph. His Collection is a major source of knowledge history of mathematics class 10 cbse only Greek mathematics as most of it has survived. The first woman mathematician recorded by history was Hypatia of Alexandria AD � She succeeded her father Theon of Alexandria as Librarian at the Great Library [ citation needed ] and wrote many works on applied mathematics.

Because of a political dispute, the Christian community in Alexandria had her stripped publicly and executed. The closure of the neo-Platonic Academy of Athens by the emperor Justinian in Oc is traditionally held as marking history of mathematics class 10 cbse only end of the era of Greek mathematics, although the Greek tradition continued unbroken in the Byzantine empire with mathematicians such as Anthemius of Tralles and Isidore of Miletusthe architects of the Hagia Sophia.

Although ethnic Greek mathematicians continued under the rule of the late History of mathematics class 10 cbse only Republic and subsequent Roman Empirethere were no noteworthy native Latin mathematicians in comparison.

Using calculation, Romans were adept at both instigating and detecting financial fraudas well mathemattics managing taxes for the treasury. The creation of the Roman calendar also necessitated basic mathematics. The first calendar allegedly dates back to 8th century BC during the Roman Kingdom and included days plus a leap year every other year.

At roughly the same time, the Han Chinese and the Romans both invented the wheeled odometer device for measuring distances traveled, the Roman model first described by the Roman civil engineer and architect Vitruvius c.

With each revolution, a pin-and-axle device engaged a tooth cogwheel that turned a second gear responsible for dropping pebbles into a box, each pebble representing one mile traversed. An analysis of early Chinese mathematics has demonstrated its unique development compared to other parts of the world, leading scholars to assume an entirely independent development.

Of particular note is the use in Chinese mathematics of a decimal positional notation system, the so-called "rod numerals" in which distinct ciphers were used for numbers between 1 and 10, and additional ciphers for powers of ten.

This was the most advanced number system in the world at the time, apparently in use several centuries before the common era and well before the development of the Indian numeral.

The date of the invention of the suan pan is not certain, but the earliest written mention dates from ADin Xu Yue 's Supplementary Notes on the Art of Figures. The oc existent work on geometry in China comes from the philosophical Mohist canon c. The Mo Jing described various aspects of many fields associated with physical science, history of mathematics class 10 cbse only provided a small number of geometrical theorems as. This decree was not universally obeyed, but as a consequence of this order little is known about ancient Chinese mathematics knly this date.

After the book hiatory of BC, the Han dynasty BC� AD produced works of mathematics which presumably expanded on works that are now lost. The most important of these is The Nine Chapters on the Mathematical Artthe full title of which appeared by ADbut existed in part under other titles.

It consists of word problems involving agriculture, business, clwss of geometry on,y figure height spans and dimension ratios for Chinese pagoda towers, engineering, surveyingand includes material on right triangles. The high-water mark of Chinese mathematics occurred in the 13th century during the latter half of the Song dynasty �with the development of Chinese algebra.

The most important text from that period is the Precious Mirror of the Four Elements by Zhu Shijie �dealing with the solution of simultaneous higher order algebraic equations using a method similar to Horner's method. Even after European mathematics began to flourish during the RenaissanceEuropean and Chinese mathematics were separate traditions, with significant Chinese mathematical output in decline from the 13th century onwards.

Jesuit missionaries such as Matteo Ricci carried mathematical ideas back and forth between the two cultures from the 16th to 18th centuries, though at this point far more mathematical ideas were entering China than leaving.

Japanese mathematicsKorean histodyand Vietnamese mathematics are traditionally viewed as stemming from Chinese mathematics and belonging to the Confucian -based East Asian cultural sphere. The earliest civilization on the Indian subcontinent is the Indus Valley Civilization mature phase: to BC that flourished in the Indus river basin. Their cities were laid out with geometric regularity, but no known mathematical documents survive from this civilization.

The oldest extant mathematical records from India are the Sulba Sutras dated variously between the 8th century BC mathematic the 2nd century AD[] appendices to religious texts which give hstory rules for constructing altars of various shapes, such as squares, rectangles, parallelograms, and. As in China, there is a lack of continuity in Indian mathematics; significant advances are separated by long periods of inactivity. The next significant mathematical documents from India after the Sulba Sutras are the Siddhantasastronomical treatises from the 4th and 5th centuries AD Gupta period showing strong Hellenistic influence.

Around AD, Aryabhata wrote the Aryabhatiyaa slim volume, written in verse, intended to supplement the rules of calculation used in astronomy and mathematical mensuration, though with no feeling for logic or deductive methodology.

Several centuries later, the Muslim mathematician Abu Rayhan Biruni described the Aryabhatiya as a "mix of common pebbles and costly crystals". In the 7th century, Brahmagupta identified the Brahmagupta theoremBrahmagupta's identity and Brahmagupta's formulaand for the first time, in Brahma-sphuta-siddhantahe lucidly explained the use of zero as both a placeholder and decimal digitand explained the History of mathematics class 10 cbse only numeral.

Islamic scholars carried knowledge of this number system to Europe by the 12th century, and it has now displaced all older number systems throughout the world.

Various symbol sets are used to represent numbers in the Hindu�Arabic numeral system, all of which evolved from the Brahmi numerals. Each of the roughly dozen major scripts of India has its own numeral glyphs.

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In , moderation took the effect of giving up to 11 extra marks: [18]. The total mark obtained by a student through moderation cannot exceed 95; if so, it is capped at 95 unless the student's actual mark is 96 or more. This is the reason a mark of 95 is relatively common for such subjects, and why it is much tougher to get 96 than to get a Moderation was also applied in the infamous CBSE Class 12 mathematics papers of and , wherein the paper created a huge furor as students and teachers complained that the paper was too tough.

Moderation can also take the form of giving grace marks to enable students who have scored near the pass mark to pass. This is the reason marks between 25 and 33 are unheard of in subjects like Mathematics, and also explains why the difference between D1 and D2 cutoff is sometimes very small. This is to ensure the exams finish earlier. For many core subjects, the number of internal choices wherein students pick one to answer out of two has increased.

The English Core paper of Class 12 has been modified in a bid to make it less 'speedier'. The Central Board of Secondary Education CBSE will conduct two separate examinations for mathematics in class 10 board examination starting from session. The current Mathematics exam is now Mathematics Standard, and an easier version of Mathematics has been introduced called Mathematics Basic. Students taking the latter version may not study Mathematics to any further level.

The option of choosing mathematics will be mentioned in the registration form for class 10 CBSE board examination. Candidates will be required to select their choice of the test while filling the registration form for CBSE Class 10 board examination Minister of Human Resource Development HRD amid the coronavirus outbreak had ordered rescheduling of pending examinations.

The exams rescheduled were to be conducted between 1 and 15 July. For some students of Delhi, who were able to give 3 or less exams were scored as per their performance in internal exams. On 7 April , Rakesh Kumar an economics teacher and two other employees of a private school in Una, Himachal Pradesh were arrested for leaking the Class 12 economics paper. According to the official website of CBSE, there are 28 government as well as private affiliated schools in different countries outside India.

The reason for their establishment is largely serving the Indian community abroad, or at least, children or relatives of Indian diplomats. For countries where the population of Indian nationals even surpasses the country's native population or in countries where they form a substantial share of the population, like Saudi Arabia , the United Arab Emirates , Oman , Qatar , Bahrain , etc.

But, however, in countries where Indians do not reside, the Indian diplomatic missions have set up schools in countries like Russia and Iran which mainly serves children of diplomats.

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Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed. February Learn how and when to remove this template message. India portal Education portal. Polynomials Class 10 has total of four exercises consists of 13 Questions.

Problems related to finding polynomials, Properties zeros and coefficient, long division of polynomials, finding a quadratic polynomial, finding zeros of polynomials are scoring topics. Pair of Linear Equations Class 10 has total of seven exercises consists of 55 Problems.

The problems will be based on concepts like linear equations in two variables, algebraic methods for solving linear equations, elimination method, cross-multiplication method Time and Work, Age, Boat Stream and equations reducible to a pair of linear equations these answers will give you ease in solving problems related to linear equations.

Quadratic Equations Class 10 has total of four exercises consists of 24 Problems. The Questions are related to find roots of quadratic equations and convert world problem into quadratic equations are easily scoring topics in board exams. Arithmetic Progressions Class 10 has total of four exercises consists of 49 Problems. Triangles Class 10 has total of six exercises consists of 64 Problems. The Questions are based on properties of triangles and 9 important theorems which are important in scoring good marks in CBSE Class 10 Exams.

Coordinate Geometry Class 10 has total of four exercises consists of 33 Problems. The Questions related to finding the distance between two points using their coordinates, Area of Triangle, Line divided in Ratio Section Formula are important models in class 10 boards.

Introduction to Trigonometry Class 10 has total of four exercises consists of 27 Problems. The questions based on trigonometric ratios of specific angles, trigonometric identities and trigonometric ratios of complementary angles are the main topics you will learn in this chapter.

Download all chapters of the book in PDF. This book has all the concepts elaborately explained that presents even the complex topics in the easiest way before you. Now, at this time when the schools are unable to conduct the classes in the new academic session on the account of the COVID pandemic, students can themselves start their studies at home with the help of NCERT books available online. Chapter-wise links are provided below from where students can download the PDF of any chapter as per their requirement.

Chapter 1: Real Numbers. Chapter 2: Polynomials. Chapter 4: Quadratic Equations. Chapter 5: Arithmetic Progression. Chapter 6: Triangles. Chapter 7: Coordinate Geometry. Chapter 8: Introduction to Trigonometry. Chapter 9: Some Applications of Trigonometry.

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