
	Where results make sense

Topic: Cartesian form

	Cartesian coordinate system - Wikipedia, the free encyclopedia
		In mathematics, the Cartesian coordinate system is used to uniquely determine each point in the plane through two numbers, usually called the x-coordinate and the y-coordinate of the point.
		Cartesian coordinate systems are also used in space (where three coordinates are used) and in higher dimensions.
		Using the Cartesian coordinate system geometric shapes (such as curves) can be described by algebraic equations, namely equations satisfied by the coordinates of the points lying on the shape.
	en.wikipedia.org /wiki/Cartesian_coordinate_system (1656 words)

	Derivation of the cartesian formula for an ellipse - Wikipedia, the free encyclopedia
		This mathematics article is devoted entirely to providing mathematical proofs and support for claims and statements made in the article ellipse.
		This article is "experimental" in that it is a proposal for one way that we might be able to deal with expressing proofs.
		The derivation of the cartesian form for an ellipse is simple and instructive.
	en.wikipedia.org /wiki/Derivation_of_the_cartesian_formula_for_an_ellipse (254 words)

	[No title]
		For example, in Cartesian 3-space with coordinates \ x, y and z, the general curve expressed as a rule set is \ {x -> x[t], y -> y[t], z -> z[t]} where x[t], y[t] and z[t] are functions \ of t.
		Y is a vector valued alternating one form, basis is \ a basis for the alternating one forms, and BASIS is an orthonormal \ frame.
		This operation and \ the properties differential forms exhibit under this operation are two of the \ primary reasons differential forms are such a convenient formalism.
	www.willamette.edu /~zizza/Software/DifferentialForms.m (2111 words)

	17. First and Second Derivative differential equations.
		(b) the generalized cartesian form, represented as a(x-x.c)^2 = ax^2 -2ax(x.c) + ax.c^2, with a being an unknown constant function.
		(c) the transformed generalized cartesian form, represented as a(x-vt -x.c+vt)^2, same as for (b), = ax^2 -2ax(x.c) + ax.c^2, of course, with a being an unknown constant function.
		So, what we have seen so far is (1) differential equations in the second degree - the wave equations - must clearly be the same for all forms: the privileged form in x, the generalized cartesian form in x and the centroid, x.c, or the transformed generalized cartesian form.
	www.faqs.org /faqs/physics-faq/criticism/galilean-invariance/section-16.html (550 words)

	Waves/Vectors - Wikibooks, collection of open-content textbooks
		A vector can be represented either by its Cartesian components, which are just the projections of the vector onto the Cartesian coordinate axes, or by its direction and magnitude.
		The direction of a vector in two dimensions is generally represented by the counterclockwise angle of the vector relative to the x axis, as shown in figure 2.
		Since the laws of physics cannot depend on the choice of coordinate system being used, we insist that physical laws be expressed in terms of scalars and vectors, but not in terms of the components of vectors.
	en.wikibooks.org /wiki/Modern_Physics:Math:Vectors (1186 words)

	EcEn 360 Tutorials-Forms-Cartesian Three Forms (Site not responding. Last check: 2007-10-29)
		A Cartesian three form can be thought of as the intersection of all three possible one forms.
		The result of the three intersecting forms is a set of boxes.
		The magnitude of the form is represented by the size of the box.
	www.ee.byu.edu /em/carthree.htm (52 words)

	[No title] (Site not responding. Last check: 2007-10-29)
		If the vector is in Polar form, then the magnitude is given by the r-value.This is where a lesson on trigonometry might be needed so that the conversion between Polar and Cartesian can be performed.
		Show students the "Parallelogram Method" where the two vectors have both their tails in the same coordinate and a parallelogram is formed and the diagonal from the common endpoint is the resultant vector.
		A vector that is written in Cartesian form is already naturally resolved into an x-only vector plus a y-only vector.
	www.bu.edu /lernet/GK12/kyle/Lessons/Vector/Vectors1.html (1083 words)

	Module 2: Complex Algebra
		As in addition, the numbers must in rectangular form to be subtracted.
		Multiplication of two complex numbers in rectangular form is accomplished by multiplying, in turn, each term in one number by both terms in the other number and then combining the resulting real terms and the resulting j terms.
		Division of two complex numbers in rectangular form is accomplished by multiplying both the numerator and the denominator by the complex conjugate of the denominator and then combining terms and simplifying.
	www.usna.edu /MathDept/CDP/ComplexNum/Module_2/ComplexAlgebra.htm (344 words)

	Math::Complex - complex numbers and associated mathematical functions (Site not responding. Last check: 2007-10-29)
		The polar notation (also known as the trigonometric representation) is much more handy for performing multiplications and divisions of complex numbers, whilst the cartesian notation is better suited for additions and substractions.
		When printed, a complex number is usually shown under its cartesian form a+bi, but there are legitimate cases where the polar format [r,t] is more appropriate.
		The code is not optimized for speed, although we try to use the cartesian form for addition-like operators and the trigonometric form for all multiplication-like operators.
	tecfa.unige.ch /guides/perl/man/lib/Math/Complex.html (1626 words)

	ES 130 Lecture 16: Vector Tutorial (Site not responding. Last check: 2007-10-29)
		However, addition and subtraction of vectors in polar form is not possible.
		It is possible to add and subtract vectors in Cartesian form.
		However, multiplication of vectors in Cartesian form is not possible.
	www.vanderbilt.edu /Engineering/CIS/Sloan/web/es130/vectors/vectut2.html (173 words)

	This tutorial is to get you familiarized with complex numbers and is in no way intended to replace appendix A in our ... (Site not responding. Last check: 2007-10-29)
		A complex number is formed from two parts, a real part and an imaginary part.
		Using the previous equation for the definition of the number j, we can represent a complex number in two different forms and plot it on the complex plane where the vertical axis is the imaginary axis and the horizontal axis is the real axis.
		Remember that when plotting a complex number the correct quadrant is important, because two different complex numbers may have the same polar angle but are in different quadrants.
	www.ee.umd.edu /class/enee204-2.F99/COMPLEX.HTM (494 words)

	Cartesian oval (Site not responding. Last check: 2007-10-29)
		This bipolar equation defines the Cartesian oval as the collection of points for which the distances to F
		The curve is a quartic, in fact a bicircular quartic and a cyclic of a circle.
		For certain values the inner part of the curve has the form of an egg, the egg of Descartes.
	www.2dcurves.com /quartic/quarticct.html (175 words)

	include/su2.h File Reference
		Legacy conversion from a 4D polar struct to cartesian form.
		Convert a cartesian form 4D vector to polar form.
		Legacy conversion from a 4D cartesian vector to a polar struct.
	www.physics.uq.edu.au /people/dawson/sk/su2_8h.html (589 words)

	3.3 Cylindrical Interpolation (Site not responding. Last check: 2007-10-29)
		As a consequence, the Cartesian velocity components are solved for, whilst using interpolation of the cylindrical components of velocity to estimate face velocity values.
		Because it is the Cartesian components of velocity which are solved, not the cylindrical components, the face values of the Cartesian components need to be calculated to evaluate velocity gradients and the convection flux of the momentum components.
		Comparison of equation (3.3.14) with the Cartesian form of this equation, (3.2.2), shows that the first of the above terms is the Cartesian terms multiplied by
	www.gre.ac.uk /~ct02/research/thesis/node26.html (962 words)

	ComplexNumbers.nb
		This form of an imaginary number is the rectangular representation.
		The polar form is shown using the magnitude and angle formed from origin to endpoint.
		Representation of the angle in polar form is
	www.d.umn.edu /ece/lis/wireless/classes/ece2111/ComplexNumbers.html (301 words)

	Complex Numbers
		Division is a bit more involved in cartesian form and requires the process called rationalization of the complex number.
		The division of complex numbers which are expressed in cartesian form is facilitated by a process called rationalization.
		Since the wavefunction which defines the probability amplitude may be a complex function, the probability is defined in terms of the complex conjugate to obtain a real value.
	hyperphysics.phy-astr.gsu.edu /hbase/cmplx2.html (282 words)

	[No title]
		Change a parametric form of a curve into its corresponding Cartesian description and sketch the curve.
		Change a given point from polar form to Cartesian form and vice versa.
		Change a given equation from polar form to Cartesian form and vice versa.
	www.sci.uidaho.edu /eo175/Test_5_Outline.doc (370 words)

	Leaving Cert. Higher Level Maths - Complex Numbers - Complex Numbers In Polar Form
		When in Cartesian mode, the applet will display the complex number on the graph in Cartesian form, and display the result of converting it from Cartesian form to polar form in the small text box under the three buttons on the right hand side.
		Underneath this there is a text area which describes the steps required in the conversion, with dynamically updated values based on whatever complex number you have displayed on the graph.
		An outline-explanation of the maths required for the conversion from polar form to Cartesian form, and vice versa is available in the text-area on the bottom of the applet.
	www.netsoc.tcd.ie /~jgilbert/maths_site/applets/complex_numbers/complex_numbers_in_polar_form.html (232 words)

	Cartesian (Site not responding. Last check: 2007-10-29)
		It is the locus of a point P whose distances s and t from two fixed points S and T satisfy s + mt = a.
		The curve was also studied by Newton in his classification of cubic curves.
		1 then the Cartesian Oval C is a central conic while if m = a/c then the curve is a Limacon of Pascal (Étienne Pascal).
	www-groups.dcs.st-and.ac.uk /~history/Curves/Cartesian.html (136 words)

	October 1995/Standard C/C++ (Site not responding. Last check: 2007-10-29)
		Cartesian form represents a complex value as the pair (x, y) representing the sum x + i*y.
		Put simply, Cartesian form is far more convenient for addition and subtraction, while polar form is sometimes more convenient for multiplication and division.
		On balance, however, Cartesian form is generally more convenient.
	www.tcnj.edu /~hernande/cujv5/html/13.10/plauger/plauger.htm (1424 words)

	ENGR 2422 Problem Set 1 Questions, 2006 Winter
		Find, in symmetric Cartesian form, the equation of the line that is perpendicular to the plane
		Sketch the curve whose equation in polar form is r
		For the curve whose equation in polar form is r = 2 sec q tan q,
	www.engr.mun.ca /~ggeorge/2422/assigns/a1w06.html (359 words)

	Differentiating Parametric Equations (Site not responding. Last check: 2007-10-29)
		It is sometimes easier to write the relationship between x and y in terms of a third variable, called a parameter.
		The problem with the first method is that equations are generally given parametrically, specifically because they are hard to write in a cartesian form.
		In this case it would be difficult to write in a cartesian form.
	www.mathsyear2000.org /alevel/pure/purtutdifpar.htm (184 words)

	Notes on using ComplexRoots
		A number of methods are possible so some intervention by the teacher to clarify and encourage a consistent method is probably useful at the end of Part1 and again after the first few questions of Part2.
		The ability to convert from polar or exponential form to Cartesian form.
		Find the sixth roots of 4 in Cartesian form (hint: think about how you could use work you have already done).
	www.mathsfiles.com /excel/ComplexRootsNotes.htm (343 words)

	Complex numbers : The modulus, argument and polar form of a complex number
		When the complex number is written as a + ib where a and b are real numbers, this is known as the Cartesian form.
		This is known as the polar form of a complex number.
		In some cases calculations in polar form are much simpler so it is important to be able to work with complex numbers in both forms.
	scholar.hw.ac.uk /site/maths/topic11.asp?outline=no (465 words)

	Enhancing Data Interoperability with Ontologies, Canonical Forms, and Include Files
		The SI canonical form for length measures is the meter.
		This is read as: "The canonical form of the Length class are instances that have a 'value' property in canonical decimal form, and a 'units' property in canonical Length-Unit-of-Measure form.
		Design your application to be able to process the data in the canonical form (your application may also be coded to process data that is in the application's "preferred" form).
	www.xfront.com /interoperability/CanonicalForms.html (2833 words)

	Math Tutorial -- Vectors
		in this case, which is identical to the form given in equation (2.5).
		All that remains to be proven for equation (2.6) to hold in general is to show that it yields the same answer regardless of how the Cartesian coordinate system is oriented relative to the vectors.
		thus proving the complete equivalence of the two forms of the dot product as given by equations (2.5) and (2.6).
	www.physics.nmt.edu /~raymond/classes/ph13xbook/node21.html (703 words)

	Sketching Graphs (Site not responding. Last check: 2007-10-29)
		The square root introduces difficulties, when trying to find the properties of the curve, since it can be either positive or negative.
		When working through the list of properties, thee will be occasions when it is easier to use the parametric form.
		c) It is easier to consider the extremes of the curve by looking at the cartesian form.
	www.mathsyear2000.org /alevel/pure/purexacooskesol.htm (389 words)

	ES 130 Lecture 16: Vector Tutorial (Site not responding. Last check: 2007-10-29)
		The Cartesian form is a method of representing a vector by its perpendicular projection onto the x-axis and its perpendicular projection onto the y-axis.
		So, Polar form is a method of representing a vector by its magnitude and the angle it makes with the positive x-axis.
		Here is the method for converting a vector in Polar form to Cartesian form.
	www.vanderbilt.edu /Engineering/CIS/Sloan/web/es130/vectors/vectut1.html (170 words)

	Student Xpress Educational Supplement
		You must be able to change from one form into the other with confidence.
		To change from Polars to Cartesians simply look up the cosine and sine of the angle after changing it from radians into degrees.
		[A] When a complex number is in Polar form the first thing students do is to change it back into Cartesians because they are uncomfortable working in Polars.
	www.studentxpress.ie /educ/maths/maths1/maths1.html (242 words)

	Vector Math (Site not responding. Last check: 2007-10-29)
		However, multiplication of vectors in Cartesian form is not simple.
		It is for these reasons that one needs to be able to transform one representation into the other.
		If you don't remember how to convert from polar to Cartesian form (and vice versa), review the vector section of this module.
	www.vuse.vanderbilt.edu:8888 /es130-2/lectures/lecture10/vecmath.htm (253 words)

	Complex Numbers (Site not responding. Last check: 2007-10-29)
		This relationship is useful for expressing complex numbers in polar form, as well as many other applications.
		The standard form of a complex number is
		which is called the polar form of a complex number.
	hyperphysics.phy-astr.gsu.edu /hbase/cmplx.html (130 words)

Try your search on: Qwika (all wikis)