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  2. Polar coordinate system - Wikipedia

    en.wikipedia.org/wiki/Polar_coordinate_system

    The equation defining a plane curve expressed in polar coordinates is known as a polar equation. In many cases, such an equation can simply be specified by defining r as a function of φ. The resulting curve then consists of points of the form (r(φ), φ) and can be regarded as the graph of the polar function r.

  3. Desmos - Wikipedia

    en.wikipedia.org/wiki/Desmos

    In addition to graphing both equations and inequalities, it also features lists, plots, regressions, interactive variables, graph restriction, simultaneous graphing, piecewise function graphing, recursive function graphing, polar function graphing, two types of graphing grids – among other computational features commonly found in a ...

  4. Tschirnhausen cubic - Wikipedia

    en.wikipedia.org/wiki/Tschirnhausen_cubic

    The parameter t can be eliminated easily giving the Cartesian equation 27 a y 2 = ( a − x ) ( 8 a + x ) 2 {\displaystyle 27ay^{2}=(a-x)(8a+x)^{2}} . If the curve is translated horizontally by 8 a and the signs of the variables are changed, the equations of the resulting right-opening curve are

  5. Rose (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Rose_(mathematics)

    Graphs of roses are composed of petals.A petal is the shape formed by the graph of a half-cycle of the sinusoid that specifies the rose. (A cycle is a portion of a sinusoid that is one period T = ⁠ 2π / k ⁠ long and consists of a positive half-cycle, the continuous set of points where r ≥ 0 and is ⁠ T / 2 ⁠ = ⁠ π / k ⁠ long, and a negative half-cycle is the other half where r ...

  6. Archimedean spiral - Wikipedia

    en.wikipedia.org/wiki/Archimedean_spiral

    Archimedean spiral represented on a polar graph. The Archimedean spiral has the property that any ray from the origin intersects successive turnings of the spiral in points with a constant separation distance (equal to 2πb if θ is measured in radians), hence the name "arithmetic spiral".

  7. Butterfly curve (transcendental) - Wikipedia

    en.wikipedia.org/wiki/Butterfly_curve...

    The curve is given by the following parametric equations: [2] = ... or by the following polar equation: = ...

  8. Pole and polar - Wikipedia

    en.wikipedia.org/wiki/Pole_and_polar

    Conversely, the polar line (or polar) of a point Q in a circle C is the line L such that its closest point P to the center of the circle is the inversion of Q in C. If a point A lies on the polar line q of another point Q, then Q lies on the polar line a of A. More generally, the polars of all the points on the line q must pass through its pole Q.

  9. Fermat's spiral - Wikipedia

    en.wikipedia.org/wiki/Fermat's_spiral

    The Fermat spiral with polar equation = can be converted to the Cartesian coordinates (x, y) by using the standard conversion formulas x = r cos φ and y = r sin φ.Using the polar equation for the spiral to eliminate r from these conversions produces parametric equations for one branch of the curve: