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SYNO | analytical geometry | analytic geometry | coordinate geometry |

μαθ. analytic geometry {noun} | αναλυτική γεωμετρία {η} |

Usage Examples English

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- Modern
**analytic geometry**is essentially equivalent to real and complex algebraic geometry, as has been shown by Jean-Pierre Serre in his paper "GAGA", the name of which is French for "Algebraic geometry and analytic geometry". - In the early 1960s, Alexander Grothendieck introduced étale maps into algebraic geometry as algebraic analogues of local analytic isomorphisms in
**analytic geometry**. - The first and most important was the creation of
**analytic geometry**, or geometry with coordinates and equations, by René Descartes (1596–1650) and Pierre de Fermat (1601–1665). - Despite the wide use of Descartes' approach, which was called
**analytic geometry**, the definition of Euclidean space remained unchanged until the end of 19th century. - From an
**analytic geometry**point of view, the absolute value of a real number is that number's distance from zero along the real number line, and more generally the absolute value of the difference of two real numbers (their absolute difference) is the distance between them.

- Cartesian products were first developed by René Descartes in the context of
**analytic geometry**. - In
**analytic geometry**, congruence may be defined intuitively thus: two mappings of figures onto one Cartesian coordinate system are congruent if and only if, for "any" two points in the first mapping, the Euclidean distance between them is equal to the Euclidean distance between the corresponding points in the second mapping. - In
**analytic geometry**, a curve can be described as the image of a function whose argument, typically called the "parameter", lies in a real interval. - In
**analytic geometry**, an asymptote (...) of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the "x" or "y" coordinates tends to infinity. **Analytic geometry**allows the study of curves unrelated to circles and lines.

- The Cartesian coordinate system transforms a geometric problem into an analysis problem, once the figures are transformed into equations; thus the name
**analytic geometry**.

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