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Topic: Parametric equation

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	Parametric equation - Wikipedia, the free encyclopedia
		Parametrized surfaces, of great use in such vector calculus applications as Stokes' theorem, are functions of two parameters, most commonly (s, t) or (u,v).
		Considering the equation as representing a circle in the plane, it is evident that this represents a cylinder.
		Converting a set of parametric equations to a single equation involves solving one of the equations (usually the simplest of the two) for the parameter.
	en.wikipedia.org /wiki/Parametric_equation (536 words)

	Parametric Equations (Site not responding. Last check: 2007-11-02)
		The curve defined parametrically by the equations was identical to the graph of the function.
		One nice interpretation of parametric equations is to think of the parameter as time (measured in seconds, say) and the functions f and g as functions that describe the x and y position of an object moving in a plane.
		In order to obtain parametric equations that describe the motion of a projectile it is useful to set up a rectangular coordinate system with the positive x-axis along the (horizontal) ground and in the direction we will send the projectile and the y-axis perpendicular to the ground.
	colalg.math.csusb.edu /~devel/precalcdemo/param/src/param.html (1618 words)

	Equations of the Straight Line
		The coefficients A and B in the general equation are the components of vector
		Note that the line defined by a general equation would not change if the equation were to be multiplied by a non-zero coefficient.
		The normalized equation is conveniently used in determining the distance from a point to a line.
	www.cut-the-knot.org /Curriculum/Calculus/StraightLine.shtml (569 words)

	Math Basics - Line Equation
		Let's determine the equation of a straight line L that passes through point P and is parallel to the direction vector
		Equation (0.11) is the symmetric form or point-direction number form of equation of line L, where
		Substituting equations (0.4), (0.5), (0.12) in (0.13) and equating corresponding components, we obtain the following set of equations.
	cs.fit.edu /~wds/classes/cse5255/thesis/lineEqn/lineEqn.html (312 words)

	McGraw-Hill AccessScience: Parametric equation
		type of mathematical equation used, typically, to represent curves in a plane or in space of three dimensions.
		In elementary analytic geometry a curve in the xy plane is often studied, in the first instance, as the locus of an equation y = F(x) or G(x,y) = 0.
		The parametric form x = f(t), y = g(t) is often the most convenient; moreover, it is often the naturally occurring form of representation of the curve.
	www.accessscience.com /Encyclopedia/4/48/Est_488000_frameset.html?doi (197 words)

	[No title]
		You can find the vector equation of any straight line through 3D space, but suppose a mathematical model you were working on required the vector equation of a general curve through 3D space - such as a roller coaster, or trajectory of a satellite.
		A parametric curve is defined by a function.
		The function can be given any real number, known as the parameter t (from a chosen segment of the real number line [a, b]) and returns a vector, the point on the line corresponding to t.
	members.tripod.com /~Paul_Kirby/quantum/param.html (362 words)

	Parametric Equations - HMC Calculus Tutorial
		It is often possible to re-write the parametric equations without the parameter.
		Every equation y = f(x) may be re-written in parametric form by letting x = t, y = f(t).
		A curve in the xy-plane may be described by a pair of parametric equations
	www.math.hmc.edu /calculus/tutorials/parametric_eq (311 words)

	Calculus III (Math 2415) - 3-Dimensional Space - Equations of Lines
		There are several other forms of the equation of a line. To get the first alternate form let’s start with the vector form and do a slight rewrite.
		This set of equations is called the parametric form of the equation of a line. Notice as well that this is really nothing more than an extension of the parametric equations we've seen previously. The only difference is that we are now working in three dimensions instead of two dimensions.
		Once we have this equation the other two forms follow. Here are the parametric equations of the line.
	tutorial.math.lamar.edu /AllBrowsers/2415/EqnsOfLines.asp (1056 words)

	Math Is Fun Forum / parametric equations as a cartesian equation help
		my lecturer has told me that i need to be able to express parametric equations as a cartesian equation and then Simplify it into the form y = a x² + b x + c in my exam later this month.
		Express the parametric equations x = t + 1 and y = -3 t² + 3 t as a Cartesian equation in just x and y.
		This is the parametric equation of y given.
	www.mathsisfun.com /forum/viewtopic.php?pid=30808 (538 words)

	Parametric-Equation Representative of Biconcave Erythrocytes -- from Mathematica Information Center
		The representation of the shape of a biconcave erythrocyte by a set of three parametric equations was achieved by using the expressions that transform the curvilinear coordinates from the disc-cyclide coordinate system [denoted J2R; Moon and Spencer (1998), Field Theory Handbook, Springer-Verlag, Berlin] to Cartesian coordinates.
		The equations are products of elliptic functions, so the challenge was to relate the three major 'shape-defining' measurements of the human erythrocyte in Cartesian coordinates to three parameters in the new curvilinear coordinates, to give a realistic representation of the shape of the membrane-surface.
		The relationships between the coefficients of the Cartesian degree-4 surface that describes the discocyte and the coordinate transformation equations were derived with the aid of Mathematica; and this 'package'.
	library.wolfram.com /infocenter/Articles/1415 (222 words)

	Comparametric equation - Wikipedia, the free encyclopedia
		A comparametric equation is an equation that describes a parametric relationship between a function and a dilated version of the same function, where the equation does not involve the parameter.
		Comparametric equations arise naturally in signal processing when we have multiple measurements of the same phenomenon, in which each of the measurements was acquired using a different sensitivity.
		They are used in radar, microphone arrays, and have been used in processing crime scene video in homicide trials in which the only evidence against the accused was video recordings of the murder.
	en.wikipedia.org /wiki/Comparametric_equation (250 words)

	Parametric Equations (Site not responding. Last check: 2007-11-02)
		Even though the lines intersect, the equations themselves do not tell us whether there will be a mid air collision.
		To be able to mathematically model this scenario, we use parametric equation.
		If a curve is given by parametric equations, we often are interested in finding an equation for the curve in standard form:
	ltcconline.net /greenl/courses/107/PolarParam/PARAMEQ.HTM (201 words)

	About Lines and Distance to a Line
		The 2D explicit equation is the one most people are first taught in school, but it is not the most flexible one to use in computational software.
		The implicit equation is a bit more useful, and the conversion of an explicit to an implicit equation is easy to do.
		-dimensional space, the parametric equation for the line is valid and is the most versatile one to use.
	softsurfer.com /Archive/algorithm_0102/algorithm_0102.htm (1957 words)

	Parametric Equations (Site not responding. Last check: 2007-11-02)
		Objectives: In this tutorial, we define parametric equations in the plane.
		We illustrate how to draw the graph of parametric equations.
		Derivation of the equations of the cycloid [Using Flash]
	archives.math.utk.edu /visual.calculus/0/parametric.6 (75 words)

	Midterm #1 Solutions
		Find a parametric equation for the line which is the intersection of the planes
		Now, to have the equation for a line, we also need an initial point, which means that we need to find a point on the line
		Method 2: This is another method, but it seemed to be one which was prone to errors and misinterpretation, for which reason I suggest the previous method.
	math.ucsd.edu /~dmcallas/other/20C_Gross_MT1 (435 words)

	parametric - OneLook Dictionary Search
		Tip: Click on the first link on a line below to go directly to a page where "parametric" is defined.
		Parametric : AMEX Dictionary of Financial Risk Management [home, info]
		Phrases that include parametric: parametric equations, parametric quantity, parametric polymorphism, non parametric methods, optical parametric oscillator, more...
	www.onelook.com /?w=parametric (150 words)

	[No title]
		Find the equation of the plane that a) passes through the point P(2, - 3, 4) and is normal to the vector N =
		Write a parametric equation for each of the following a) x + 2y = 4 (b) x2 - y = 2x (2.
		The graph of a linear equation (first-degree equation) of the form Ax + By + Cz = D (not all three A, B, C equal to zero) is a plane in space.
	www.angelo.edu /faculty/jmontema/1321-notes4.doc (2354 words)

	About Planes and Distance to a Plane
		Also in any dimension, similar to the parametric line equation, one can replace either or both of the two specified points
		The pair of parameters (s,t) is referred to as the parametric coordinate of
		Then, the associated implicit equation ax+by+cz+d=0 is said to be normalized.
	geometryalgorithms.com /Archive/algorithm_0104/algorithm_0104.htm (1649 words)

	Simple Graph(Parametric Function) (Site not responding. Last check: 2007-11-02)
		The applet draws the graph of parametric functions.
		Using the applet, graph the functions in the table.
		The following is the list of functions defined in this applet.
	www.ies.co.jp /math/java/calc/sg_para/sg_para.html (28 words)

	Parametric Curves (Site not responding. Last check: 2007-11-02)
		This applet draws a parametric curve [x(t),y(t)], for t in a specified range (unfortunately this range is not shown in the applet, you have to look at the html source) of values.
		It does this by plotting a sequence of points on the curve and connecting them with lines.
		If you click this button, a crosshair will move along the curve.
	www.scottsarra.org /applets/calculus/Parametric.html (75 words)

	Partial Derivative of a Parametric Equation
		I'm getting confused over a few points on the derivative of a parametric equation.
		We then parametrize this world line by the parameter t.
		x does have an explicit time dependance, you've given it one when you equated x to f(t).
	www.physicsforums.com /showthread.php?p=972565 (506 words)

	Hexapedia - Parametric equation (via CobWeb/3.1 planetlab-5.cs.princeton.edu) (Site not responding. Last check: 2007-11-02)
		In mathematics, a parametric equation explicitly relates two or more variables in terms of one or more independent parameters.
		Parametrized surfaces, of great use in such vector calculus applications as Stokes' theorem, are functions of two parameters, most commonly
		The fact that this represents a cylinder is evident when one considers the equation as representing a circle in the plane, which is then allowed to take on arbitrary values of z.
	www.hexafind.com.cob-web.org:8888 /encyclopedia/parametric_equation (310 words)

	Parametric Equation Problem - MathsNet Forums
		An ellipse has parametric equations: x= 3- 4cost, y = -1 + sint.
		b) Hence find an expression for the equation of the tangent to the ellipse at the point were t = theta
		can you write down the equation from there?
	www.mathsnet.net /forums/index.php?showtopic=2540 (251 words)

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