Geometry and Pythagoreans
<p>In <a href="https://en.wikipedia.org/wiki/Ancient_Greece" title="Ancient Greece">ancient Greece</a> the <a href="https://en.wikipedia.org/wiki/Pythagoreans" class="mw-redirect" title="Pythagoreans">Pythagoreans</a> considered the role of numbers in geometry. However, the discovery of incommensurable lengths, which contradicted their philosophical views, made them abandon abstract numbers in favor of concrete geometric quantities, such as length and area of figures. </p>
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Numbers were reintroduced into geometry in the form of <a href="https://en.wikipedia.org/wiki/Coordinate" class="mw-redirect" title="Coordinate">coordinates</a> by <a href="https://en.wikipedia.org/wiki/Descartes" class="mw-redirect" title="Descartes">Descartes</a>, who realized that the study of geometric shapes can be facilitated by their algebraic representation, and for whom the <a href="https://en.wikipedia.org/wiki/Cartesian_plane" class="mw-redirect" title="Cartesian plane">Cartesian plane</a> is named. <a href="https://en.wikipedia.org/wiki/Analytic_geometry" title="Analytic geometry">Analytic geometry</a> applies methods of algebra to geometric questions, typically by relating geometric <a href="https://en.wikipedia.org/wiki/Curve" title="Curve">curves</a> to algebraic <a href="https://en.wikipedia.org/wiki/Equation" title="Equation">equations</a>. These ideas played a key role in the development of <a href="https://en.wikipedia.org/wiki/Calculus" title="Calculus">calculus</a> in the 17th century and led to the discovery of many new properties of plane curves. Modern <a href="https://en.wikipedia.org/wiki/Algebraic_geometry" title="Algebraic geometry">algebraic geometry</a> considers similar questions on a vastly more abstract level.</p>