Analytic geometry

Summary

Analytic geometry is geometry done with coordinates: points become tuples of numbers, and figures become sets of solutions of equations. Through a Cartesian coordinate system, lines are given by linear equations, circles and conic sections by quadratic ones, and distances by the formula $\sqrt{(x_1 - y_1)^2 + \cdots + (x_n - y_n)^2}$. Geometric questions then become algebraic computations, which can be carried out systematically. It underlies much of calculus, linear algebra and algebraic geometry, and it is usually traced to Descartes and Fermat.