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For example, the equations = = form a parametric representation of the unit circle, where t is the parameter: A point (x, y) is on the unit circle if and only if there is a value of t such that these two equations generate that point.
For example, the position of a point that moves on a curve in three-dimensional space is determined by the time needed to reach the point when starting from a fixed origin. If x , y , z are the coordinates of the point, the movement is thus described by a parametric equation [ 1 ]
A parametric equation for a curve expresses the coordinates of the points of the curve as functions of a variable, called a parameter. [8] [9] For example, = = are parametric equations for the unit circle, where t is the parameter. Together, these equations are called a parametric representation of the curve.
The third essential description of a curve is the parametric one, where the x- and y-coordinates of curve points are represented by two functions x(t), y(t) both of whose functional forms are explicitly stated, and which are dependent on a common parameter . Examples of implicit curves include:
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.
A letter written by Albert Einstein in which he writes out his famous E = mc2 equation has sold at auction for more than $1.2 million, about three times more than it was expected to get, Boston ...
Plane section of an ellipsoid (see example) Given: Ellipsoid x 2 / a 2 + y 2 / b 2 + z 2 / c 2 = 1 and the plane with equation n x x + n y y + n z z = d, which have an ellipse in common. Wanted: Three vectors f 0 (center) and f 1, f 2 (conjugate vectors), such that the ellipse can be represented by the parametric equation
While the modalities have a lot in common (they both draw influence from yoga and dance and even share some of their movements, for example), depending on your goals, you might actually want to do ...