An alternate approach using coordinate geometry was developed recently.
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They are easily calculated from coordinate geometry once the coordinates of each vertex is known.
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In 1936, Du Val took up an assistant lectureship in the Turkish and even wrote a book on coordinate geometry in that language.
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A proof that this characterization of the hyperbola is equivalent to the conic-section characterization can be done without coordinate geometry by means of Dandelin spheres.
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So maybe I did something wrong with my vector arithmetic or coordinate geometry ?-- talk ) 21 : 36, 15 September 2014 ( UTC)
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The French mathematicians Franciscus Vieta and later Ren?Descartes and Pierre de Fermat revolutionized the conventional way of thinking about construction problems through the introduction of coordinate geometry.
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His books, " The Elements of Coordinate Geometry " and " Plane Trigonometry, " are also popular in India among students preparing for competitive exams.
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:The green area can be straightforwardly attacked with coordinate geometry : put the lower-left corner of the square at the origin and scale it to have sides of length 1.
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The company developed engineering software for coordinate geometry, subdivision design, earthwork, highway & traffic design, and hydrology and watershed analysis widely used throughout the U . S . and by the State of New York.
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Periodic boundary conditions in 1, 2 and 3 dimensions have been implemented through the Lorentz field ( \ Gamma-point ), and an internal coordinate geometry optimizer allows full ( atom + cell ) relaxation using analytic derivatives.
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