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  "body": "\n## Summary\n\nAnalytic geometry is geometry done with coordinates: points become tuples of numbers, and figures become sets of solutions of equations.\nThrough a [[Cartesian coordinate system|0RWKYX8339]], lines are given by linear equations, circles and [[conic sections|00HJCMC2CD]] by quadratic ones, and distances by the formula $\\sqrt{(x_1 - y_1)^2 + \\cdots + (x_n - y_n)^2}$.\nGeometric questions then become algebraic computations, which can be carried out systematically.\nIt underlies much of calculus, linear algebra and algebraic geometry, and it is usually traced to Descartes and Fermat.\n\n## Explanations\n\n### L1 human\n\nPut a grid on the plane, so that every point gets an address $(x, y)$.\nThen a line is the set of points whose addresses satisfy an equation like $y = 2x + 1$, and a circle of radius $5$ around the origin is $x^2 + y^2 = 25$.\nTo find where the line meets the circle, one solves the two equations together, with no ruler or compass needed.\nThis turns pictures into algebra, and algebra into pictures.\n",
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