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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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Real Number
In mathematics, a real number is a value that represents a quantity along a line. The adjective real in this context was introduced in the 17th century by René Descartes, who distinguished between real and imaginary roots of polynomials. The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as √2 (1.41421356..., the square root of 2, an irrational algebraic number). Included within the irrationals are the transcendental numbers, such as π (3.14159265...). Real numbers can be thought of as points on an infinitely long line called the number line or real line, where the points corresponding to integers are equally spaced. Any real number can be determined by a possibly infinite decimal representation, such as that of 8.632, where each consecutive digit is measured in units one tenth the size of the previous one
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Solid Geometry
In mathematics, solid geometry is the traditional name[citation needed] for the geometry of three-dimensional Euclidean space. Stereometry deals with the measurements of volumes of various solid figures (three-dimensional figures) including pyramids, prisms and other polyhedrons; cylinders; cones; truncated cones; and balls bounded by spheres.[1]Contents1 History 2 Topics 3 Techniques 4 Applications 5 See also 6 Notes 7 ReferencesHistory[edit] The Pythagoreans dealt with the regular solids, but the pyramid, prism, cone and cylinder were not studied until the Platonists. Eudoxus established their measurement, proving the pyramid and cone to have one-third the volume of a prism and cylinder on the same base and of the same height
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Metre
The metre (British spelling and BIPM spelling[1]) or meter (American spelling) (from the French unit mètre, from the Greek noun μέτρον, "measure") is the base unit of length in some metric systems, including the International System of Units
International System of Units
(SI). The SI unit symbol is m.[2] The metre is defined as the length of the path travelled by light in a vacuum in 1/299 792 458 second.[1] The metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole. In 1799, it was redefined in terms of a prototype metre bar (the actual bar used was changed in 1889). In 1960, the metre was redefined in terms of a certain number of wavelengths of a certain emission line of krypton-86. In 1983, the current definition was adopted. The imperial inch is defined as 0.0254 metres (2.54 centimetres or 25.4 millimetres). One metre is about ​3 3⁄8 inches longer than a yard, i.e
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Formula
In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula
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Polygon Triangulation
In computational geometry, polygon triangulation is the decomposition of a polygonal area (simple polygon) P into a set of triangles,[1] i.e., finding a set of triangles with pairwise non-intersecting interiors whose union is P. Triangulations may be viewed as special cases of planar straight-line graphs
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History Of Calculus
Calculus, known in its early history as infinitesimal calculus, is a mathematical discipline focused on limits, functions, derivatives, integrals, and infinite series. Isaac Newton
Isaac Newton
and Gottfried Leibniz independently discovered calculus in the mid-17th century
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Plane Curve
In mathematics, a plane curve is a curve in a plane that may be either a Euclidean plane, an affine plane or a projective plane. The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves.Contents1 Symbolic representation 2 Smooth plane curve 3 Algebraic plane curve 4 Examples 5 See also 6 References 7 External linksSymbolic representation[edit] A plane curve can often be represented in Cartesian coordinates
Cartesian coordinates
by an implicit equation of the form f ( x , y ) = 0 displaystyle f(x,y)=0 for some specific function f
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Greek Mathematics
Greek mathematics
Greek mathematics
refers to mathematics texts and advances written in Greek, developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean from Italy to North Africa but were united by culture and language. Greek mathematics of the period following Alexander the Great
Alexander the Great
is sometimes called Hellenistic mathematics
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Paint
Paint
Paint
is any liquid, liquefiable, or mastic composition that, after application to a substrate in a thin layer, converts to a solid film. It is most commonly used to protect, color, or provide texture to objects. Paint
Paint
can be made or purchased in many colors—and in many different types, such as watercolor, synthetic, etc
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Surface (topology)
In topology and differential geometry, a surface is a two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space
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Unit Square
In mathematics, a unit square is a square whose sides have length 1. Often, "the" unit square refers specifically to the square in the Cartesian plane with corners at the four points (0, 0), (1, 0), (0, 1), and (1, 1).Contents1 Cartesian coordinates 2 Complex coordinates 3 Rational distance problem 4 See also 5 References 6 External linksCartesian coordinates[edit] In a Cartesian coordinate system
Cartesian coordinate system
with coordinates (x, y) the unit square is defined as the square consisting of the points where both x and y lie in a closed unit interval from 0 to 1. That is, the unit square is the Cartesian product
Cartesian product
I × I, where I denotes the closed unit interval. Complex coordinates[edit] The unit square can also be thought of as a subset of the complex plane, the topological space formed by the complex numbers
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Analysis
Analysis
Analysis
is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle
Aristotle
(384–322 B.C.), though analysis as a formal concept is a relatively recent development.[1] The word comes from the Ancient Greek
Ancient Greek
ἀνάλυσις (analysis, "a breaking up", from ana- "up, throughout" and lysis "a loosening").[2] As a formal concept, the method has variously been ascribed to Alhazen,[3] René Descartes
René Descartes
(Discourse on the Method), and Galileo Galilei
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Plane (geometry)
In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space
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Planar Lamina
In mathematics, a planar lamina is a closed set in a plane of mass m displaystyle m and surface density ρ   ( x , y ) displaystyle rho (x,y) such that: m = ∫ ∫ ρ   ( x , y ) d x d y displaystyle m=int int _ rho (x,y),dx,dy , over the closed set.The center of mass of the lamina is at the point ( M y m , M x m ) displaystyle left( frac M_ y m , frac M_ x m right) where M y displaystyle M_ y <
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Axiom
An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Greek axíōma (ἀξίωμα) 'that which is thought worthy or fit' or 'that which commends itself as evident.'[1][2] The term has subtle differences in definition when used in the context of different fields of study
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