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What are the algebraic equations for coordinate curve and coordinate surfaces?
Wiki User
∙ 11y ago
There are infinitely many equations for each - and they are of different form, depending on the shape of the curve etc.
Wiki User
∙ 11y ago
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Uses of cartesian coordinate system?
The Cartesian coordinate system allows a geometric curve to be described in algebraic terms. This then allows the use of algebraic tools including differentiation and integration to be used to solve geometric problems such as the turning points of curves, their volumes of rotation and so on. It also enables geometric methods to be applied to solving algebraic problems.
What is the purpose of the cartesian coordinate system?
The Cartesian plane allows geometric information to be converted to a coordinate system which can then be analysed using algebraic techniques. Conversely algebraic information can be converted (by plotting) to a geometric form. Theorems that have been proved in one of these two disciplines can be used to solve problems in the other. Thus finding the volume when a curve is rotated becomes a simple matter of integration. Solving simultaneous equations is reduced to finding the point of intersection (if any) of the corresponding graphs.
Why are parametric eqautions bad?
In mathematics, parametric equations of a curve express the coordinates of the points of the curve as functions of a variable, called a parameter.[1][2] 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.A common example occurs in kinematics, where the trajectory of a point is usually represented by a parametric equation with time as the parameter.The notion of parametric equation has been generalized to surfaces, manifolds and algebraic varieties of higher dimension, with the number of parameters being equal to the dimension of the manifold or variety, and the number of equations being equal to the dimension of the space in which the manifold or variety is considered (for curves the dimension is one and one parameter is used, for surfaces dimension two and two parameters, etc.).The parameter typically is designated t because often the parametric equations represent a physical process in time. However, the parameter may represent some other physical quantity such as a geometric variable, or may merely be selected arbitrarily for convenience. Moreover, more than one set of parametric equations may specify the same curve.
The point at which a curve intersects a coordinate axis?
It is called an intercept.
What information does the graph of a function provide with respect to the algebraic equation?
The coordinates of the points on the curve represent solutions of the equation.
How did Rene Descartes use the parabola?
Descartes used the parabola to illustrate algebraic equations. He put these equations on a visible plane using the Cartesian coordinate system and they sometimes took the shape of a "u" curve, or a parabola.
Uses of cartesian coordinate system?
The Cartesian coordinate system allows a geometric curve to be described in algebraic terms. This then allows the use of algebraic tools including differentiation and integration to be used to solve geometric problems such as the turning points of curves, their volumes of rotation and so on. It also enables geometric methods to be applied to solving algebraic problems.
What is the purpose of the cartesian coordinate system?
The Cartesian plane allows geometric information to be converted to a coordinate system which can then be analysed using algebraic techniques. Conversely algebraic information can be converted (by plotting) to a geometric form. Theorems that have been proved in one of these two disciplines can be used to solve problems in the other. Thus finding the volume when a curve is rotated becomes a simple matter of integration. Solving simultaneous equations is reduced to finding the point of intersection (if any) of the corresponding graphs.
What are equations when used in co-ordinate grids?
They are simply algebaric equations. They may be linear or non-linear, continuous or not, in two or more variables. Any equation can be plotted on a coordinate grid and any point, curve, shape on a coordinate grid can be represented by an equation. However, finding the appropriate equation will not always be easy.
Why are parametric eqautions bad?
In mathematics, parametric equations of a curve express the coordinates of the points of the curve as functions of a variable, called a parameter.[1][2] 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.A common example occurs in kinematics, where the trajectory of a point is usually represented by a parametric equation with time as the parameter.The notion of parametric equation has been generalized to surfaces, manifolds and algebraic varieties of higher dimension, with the number of parameters being equal to the dimension of the manifold or variety, and the number of equations being equal to the dimension of the space in which the manifold or variety is considered (for curves the dimension is one and one parameter is used, for surfaces dimension two and two parameters, etc.).The parameter typically is designated t because often the parametric equations represent a physical process in time. However, the parameter may represent some other physical quantity such as a geometric variable, or may merely be selected arbitrarily for convenience. Moreover, more than one set of parametric equations may specify the same curve.
How many curve surfaces does a cone has?
1
The point at which a curve intersects a coordinate axis?
It is called an intercept.
How can you write the equation of the tangent line to the curve?
Well if you have found the derivative (slope of the tangent line) of the curve at that point and you know the xy coordinates for that point in the curve then you set it up in y=mx+b format where y is your y-coordinate, x is your x-coordinate and m is your derivative and solve for b
What has the author Tamal K Dey written?
Tamal K. Dey has written: 'Curve and surface reconstruction' -- subject(s): Curves on surfaces, Mathematical models, Models of Surfaces, Surfaces, Surfaces, Models of
Which tool is use for smoothing surface?
tool use for smoothing curve surfaces
What is the slope of a curve?
Slope of a Curve A number which is used to indicate the steepness of a curve at a particular point.The slope of a curve at a point is defined to be the slope of the tangent line. Thus the slope of a curve at a point is found using the derivative
What information does the graph of a function provide with respect to the algebraic equation?
The coordinates of the points on the curve represent solutions of the equation.
