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  2. Cartesian coordinate system - Wikipedia

    en.wikipedia.org/wiki/Cartesian_coordinate_system

    The equation of a circle is (x − a) 2 + (y − b) 2 = r 2 where a and b are the coordinates of the center (a, b) and r is the radius. Cartesian coordinates are named for René Descartes, whose invention of them in the 17th century revolutionized mathematics by allowing the expression of problems of geometry in terms of algebra and calculus.

  3. Analytic geometry - Wikipedia

    en.wikipedia.org/wiki/Analytic_geometry

    In three dimensions, a single equation usually gives a surface, and a curve must be specified as the intersection of two surfaces (see below), or as a system of parametric equations. [18] The equation x 2 + y 2 = r 2 is the equation for any circle centered at the origin (0, 0) with a radius of r.

  4. Archimedean spiral - Wikipedia

    en.wikipedia.org/wiki/Archimedean_spiral

    From the above equation, it can thus be stated: position of the particle from point of start is proportional to angle θ as time elapses. Archimedes described such a spiral in his book On Spirals . Conon of Samos was a friend of his and Pappus states that this spiral was discovered by Conon.

  5. Circle - Wikipedia

    en.wikipedia.org/wiki/Circle

    In an x–y Cartesian coordinate system, the circle with centre coordinates (a, b) and radius r is the set of all points (x, y) such that + =. This equation , known as the equation of the circle , follows from the Pythagorean theorem applied to any point on the circle: as shown in the adjacent diagram, the radius is the hypotenuse of a right ...

  6. Curvilinear coordinates - Wikipedia

    en.wikipedia.org/wiki/Curvilinear_coordinates

    Equations with boundary conditions that follow coordinate surfaces for a particular curvilinear coordinate system may be easier to solve in that system. While one might describe the motion of a particle in a rectangular box using Cartesian coordinates, it is easier to describe the motion in a sphere with spherical coordinates.

  7. Logarithmic spiral - Wikipedia

    en.wikipedia.org/wiki/Logarithmic_spiral

    In Cartesian coordinates [ edit ] The logarithmic spiral with the polar equation r = a e k φ {\displaystyle r=ae^{k\varphi }} can be represented in Cartesian coordinates ( x = r cos ⁡ φ , y = r sin ⁡ φ ) {\displaystyle (x=r\cos \varphi ,\,y=r\sin \varphi )} by x = a e k φ cos ⁡ φ , y = a e k φ sin ⁡ φ . {\displaystyle x=ae^{k ...

  8. Euclidean plane - Wikipedia

    en.wikipedia.org/wiki/Euclidean_plane

    Plane equation in normal form. In Euclidean geometry, a plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional space. A prototypical example is one of a room's walls, infinitely extended and assumed infinitesimal thin.

  9. Kampyle of Eudoxus - Wikipedia

    en.wikipedia.org/wiki/Kampyle_of_Eudoxus

    Download as PDF; Printable version ... [γραμμή], meaning simply "curved [line], curve") is a curve with a Cartesian equation of = ... the Kampyle has the equation