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Bhaskara II
Bhāskara[1] (also known as Bhāskarāchārya ("Bhāskara, the teacher"), and as Bhāskara II to avoid confusion with Bhāskara I) (1114–1185), was an Indian mathematician and astronomer. He was born in Bijapur in Karnataka.[2] Bhāskara and his works represent a significant contribution to mathematical and astronomical knowledge in the 12th century. He has been called the greatest mathematician of medieval India.[3] His main work Siddhānta Shiromani, ( Sanskrit
Sanskrit
for "Crown of Treatises")[4] is divided into four parts called Lilāvatī, Bījagaṇita, Grahagaṇita and Golādhyāya,[5] which are also sometimes considered four independent works.[6] These four sections deal with arithmetic, algebra, mathematics of the planets, and spheres respectively
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Bhāskara I
Bhāskara (c. 600 – c. 680) (commonly called Bhaskara I to avoid confusion with the 12th century mathematician Bhāskara II) was a 7th-century mathematician, who was the first to write numbers in the Hindu decimal system with a circle for the zero, and who gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhata's work.[1] This commentary, Āryabhaṭīyabhāṣya, written in 629 CE, is among the oldest known prose works in Sanskrit
Sanskrit
on mathematics and astronomy
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Leonhard Euler
Leonhard Euler
Leonhard Euler
(/ˈɔɪlər/ OY-lər;[2] Swiss Standard German: [ˈɔɪlər] ( listen); German Standard German: [ˈɔʏlɐ] ( listen); 15 April 1707 – 18 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function.[3] He is also known for his work in mechanics, fluid dynamics, optics, astronomy, and music theory.[4] Euler was one of the most eminent mathematicians of the 18th century and is held to be one of the greatest in history
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Pythagorean Theorem
In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry
Euclidean geometry
among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the "Pythagorean equation":[1] a 2 + b 2 = c 2 , displaystyle a^ 2 +b^ 2 =c^ 2 , where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides. Although it is often argued that knowledge of the theorem predates him,[2][3] the theorem is named after the ancient Greek mathematician Pythagoras
Pythagoras
(c
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Area
Area
Area
is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane
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Quadratic Equation
In algebra, a quadratic equation (from the Latin
Latin
quadratus for "square") is any equation having the form a x 2 + b x + c = 0 displaystyle ax^ 2 +bx+c=0 where x represents an unknown, and a, b, and c represent known numbers such that a is not equal to 0. If a = 0, then the equation is linear, not quadratic. The numbers a, b, and c are the coefficients of the equation, and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.[1] Because the quadratic equation involves only one unknown, it is called "univariate"
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Quartic Equation
In algebra, a quartic function is a function of the form f ( x ) = a x 4 + b x 3 + c x 2 + d x + e , displaystyle f(x)=ax^ 4 +bx^ 3 +cx^ 2 +dx+e, where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial. Sometimes the term biquadratic is used instead of quartic, but, usually, biquadratic function refers to a quadratic function of a square (or, equivalently, to the function defined by a quartic polynomial without terms of odd degree), having the form f ( x ) = a x 4 + c x 2 + e . displaystyle f(x)=ax^ 4 +cx^ 2 +e
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Indeterminate Equation
An indeterminate equation, in mathematics, is an equation for which there is more than one solution; for example, 2x = y is a simple indeterminate equation, as are ax + by = c and x2 = 1. Indeterminate equations cannot be solved uniquely
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Renaissance
The Renaissance
Renaissance
(UK: /rɪˈneɪsəns/, US: /rɛnəˈsɑːns/)[1] is a period in European history, covering the span between the 14th and 17th centuries. It is an extension of the Middle Ages, and is bridged by the Age of Enlightenment
Age of Enlightenment
to modern history. It grew in fragments, with the very first traces found seemingly in Italy, coming to cover much of Europe, for some scholars marking the beginning of the modern age. The intellectual basis of the Renaissance
Renaissance
was its own invented version of humanism, derived from the concept of Roman Humanitas and the rediscovery of classical Greek philosophy, such as that of Protagoras, who said that "Man is the measure of all things." This new thinking became manifest in art, architecture, politics, science and literature
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Diophantine Equation
In mathematics, a Diophantine equation
Diophantine equation
is a polynomial equation, usually in two or more unknowns, such that only the integer solutions are sought or studied (an integer solution is a solution such that all the unknowns take integer values). A linear Diophantine equation equates the sum of two or more monomials, each of degree 1 in one of the variables, to a constant. An exponential Diophantine equation
Diophantine equation
is one in which exponents on terms can be unknowns. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations
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France
France
France
(French: [fʁɑ̃s]), officially the French Republic (French: République française [ʁepyblik fʁɑ̃sɛz]), is a country whose territory consists of metropolitan France
France
in western Europe, as well as several overseas regions and territories.[XIII] The metropolitan area of France
France
extends from the Mediterranean Sea
Mediterranean Sea
to the English Channel
English Channel
and the North Sea, and from the Rhine
Rhine
to the Atlantic Ocean. The overseas territories include French Guiana
French Guiana
in South America and several islands in the Atlantic, Pacific and Indian oceans
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Pierre De Fermat
Pierre de Fermat
Pierre de Fermat
(French: [pjɛːʁ də fɛʁma]; (Between 31 October and 6 December 1607[1] – 12 January 1665) was a French lawyer[3] at the Parlement
Parlement
of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of differential calculus, then unknown, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics
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Negative Number
In mathematics, a negative number is a real number that is less than zero. Negative numbers represent opposites. If positive represents a movement to the right, negative represents a movement to the left. If positive represents above sea level, then negative represents below sea level. If positive represents a deposit, negative represents a withdrawal. They are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset, a decrease in some quantity may be thought of as a negative increase. If a quantity may have either of two opposite senses, then one may choose to distinguish between those senses—perhaps arbitrarily—as positive and negative. In the medical context of fighting a tumor, an expansion could be thought of as a negative shrinkage. Negative numbers are used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit
Fahrenheit
scales for temperature
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India
India, officially the Republic
Republic
of India
India
(IAST: Bhārat Gaṇarājya),[e] is a country in South Asia. It is the seventh-largest country by area, the second-most populous country (with over 1.2 billion people), and the most populous democracy in the world. It is bounded by the Indian Ocean
Indian Ocean
on the south, the Arabian Sea on the southwest, and the Bay of Bengal
Bay of Bengal
on the southeast. It shares land borders with Pakistan
Pakistan
to the west;[f] China, Nepal, and Bhutan
Bhutan
to the northeast; and Myanmar
Myanmar
and Bangladesh
Bangladesh
to the east. In the Indian Ocean, India
India
is in the vicinity of Sri Lanka
Sri Lanka
and the Maldives
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Mathematical Analysis
Mathematical analysis
Mathematical analysis
is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.[1][2] These theories are usually studied in the context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis
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Infinitesimal
In mathematics, infinitesimals are things so small that there is no way to measure them. The insight with exploiting infinitesimals was that entities could still retain certain specific properties, such as angle or slope, even though these entities were quantitatively small.[1] The word infinitesimal comes from a 17th-century Modern Latin coinage infinitesimus, which originally referred to the "infinite-th" item in a sequence. Infinitesimals are a basic ingredient in the procedures of infinitesimal calculus as developed by Leibniz, including the law of continuity and the transcendental law of homogeneity. In common speech, an infinitesimal object is an object that is smaller than any feasible measurement, but not zero in size—or, so small that it cannot be distinguished from zero by any available means. Hence, when used as an adjective, "infinitesimal" means "extremely small"
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