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In it, geometrical shapes can be made, as well as expressions from the normal graphing calculator, with extra features. [8] In September 2023, Desmos released a beta for a 3D calculator, which added features on top of the 2D calculator, including cross products, partial derivatives and double-variable parametric equations. [9]
In the case of a single parameter, parametric equations are commonly used to express the trajectory of a moving point, in which case, the parameter is often, but not necessarily, time, and the point describes a curve, called a parametric curve. In the case of two parameters, the point describes a surface, called a parametric surface.
Equation. An animated construction gives an idea of the complexity of the curve ... The curve is given by the following parametric equations: [2]
A Lissajous figure, made by releasing sand from a container at the end of a Blackburn pendulum. A Lissajous curve / ˈ l ɪ s ə ʒ uː /, also known as Lissajous figure or Bowditch curve / ˈ b aʊ d ɪ tʃ /, is the graph of a system of parametric equations
In its simplified form, this curve is the graph of the derivative of the arctangent function. [8] The witch of Agnesi can also be described by parametric equations whose parameter θ is the angle between OM and OA, measured clockwise: [6] [7] = , = .
Parametric representation is a very general way to specify a surface, as well as implicit representation. Surfaces that occur in two of the main theorems of vector calculus , Stokes' theorem and the divergence theorem , are frequently given in a parametric form.
Such a parametric equation completely determines the curve, without the need of any interpretation of t as time, and is thus called a parametric equation of the curve (this is sometimes abbreviated by saying that one has a parametric curve). One similarly gets the parametric equation of a surface by considering functions of two parameters t and u.
In geometry, a deltoid curve, also known as a tricuspoid curve or Steiner curve, is a hypocycloid of three cusps.In other words, it is the roulette created by a point on the circumference of a circle as it rolls without slipping along the inside of a circle with three or one-and-a-half times its radius.