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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. 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: = ...

  4. 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 ...

  5. Desmos - Wikipedia

    en.wikipedia.org/wiki/Desmos

    The tool comes pre-programmed with 36 different example graphs for the purpose of teaching new users about the tool and the mathematics involved. [ 15 ] As of April 2017, Desmos also released a browser-based 2D interactive geometry tool, with supporting features including the plotting of points, lines, circles, and polygons.

  6. 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:

  7. Coordinate systems for the hyperbolic plane - Wikipedia

    en.wikipedia.org/wiki/Coordinate_systems_for_the...

    The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to the origin of a Cartesian system) is called the pole, and the ray from the pole in the reference direction is the polar axis.

  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. Golden spiral - Wikipedia

    en.wikipedia.org/wiki/Golden_spiral

    The polar equation for a golden spiral is the same as for other logarithmic spirals, but with a special value of the growth factor b: [10] = or = ⁡ (/), with e being the base of natural logarithms, a being the initial radius of the spiral, and b such that when θ is a right angle (a quarter turn in either direction): =.