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Topic: Parallelogram law

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Inner product space

Normed vector space

Parallelogram

Equilateral parallelogram

Pythagorean triangle

Discrete topology

Pythagorean theorem

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	Parallelogram - Wikipedia, the free encyclopedia
		Every parallelogram is a polygon, and more specifically a quadrilateral.
		The three-dimensional counterpart of a parallelogram is a parallelepiped.
		The area of a parallelogram can be seen as twice the area of a triangle created by one of its diagonals.
	en.wikipedia.org /wiki/Parallelogram (271 words)

	Parallelogram - The Old Joel on Software Forum - Parallelogram Offices ? Ever (Site not responding. Last check: 2007-11-05)
		Robert Owen (1771-1858) was a pioneer of the early In a line across the center of the parallelogram.
		The Varignon parallelogram of a given quadrilateral is the parallelogram formed by the midpoints of the four sides of the quadrilateral.
		The area of Varignon's parallelogram is half that of the quadrilateral.
	siteslinks.com /q/parallelogram.htm (414 words)

	PlanetMath: alternate proof of parallelogram law
		Proof of this is simple, given the cosine law:
		"alternate proof of parallelogram law" is owned by drini.
		This is version 2 of alternate proof of parallelogram law, born on 2002-06-04, modified 2002-06-04.
	planetmath.org /encyclopedia/AlternateProofOfParallelogramLaw.html (110 words)

	Thébault's Problem I
		On the sides of parallelogram ABCD erect squares -- all either on the outside or the inside of the parallelogram.
		Consider the case of the squares erected on the outside of the parallelogram.
		The tesselation of the plane into parallelograms and squares that serves to proof the Law of Cosines and provides an additional demonstration of Thebault's theorem.
	www.cut-the-knot.org /Curriculum/Geometry/Thebault1.shtml (284 words)

	D4 Addition Method II - Vector and Complex Numbers: Parallelogram Method
		When two arrows or vectors (representing motions if you wish) have a tail at the same place, they may be added together by moving the tail of one to the head of the other with the aid of a parallelogram, and then using the head to tail method for addition.
		From the parallelogram rule or law for addition, the calculation of the sum of vectors AB + AC and the calculation of AC + AB is identical.
		The applet illustrates the parallelogram law for the addition of vectors with tails at the origin.
	whyslopes.com /etc/ComplexNumbers/apCmplx06.html (484 words)

	David Spurrett: Cartwright on Laws and Composition
		This is supposed to follow for the most part from Newton’s second law, the law that changes of motion (accelerations) occur in the direction of the impressed force, and the first law, that motions persist with unchanging direction and speed unless forces are applied.
		The distinction works by making the force laws into laws of causal influence, which are to be read factually as saying that certain forces are exerted in certain conditions, but where what actually happens in a given situation depends on the laws of causal action, which determine how the various causal influences will work together.
		The law, in short, of each of the concurrent causes remains the same, however their collocations may vary; but the law of their joint effect varies with every difference in the collocations (Mill 1973: 469).
	philsci-archive.pitt.edu /archive/00000128/00/Cartwright.html (7672 words)

	Practical Auto Crash Reconstruction in LOSRIC, Part II
		In fact, originally, his second law was expressed in terms of momentum rather than acceleration.
		The law of conservation of momentum states that in any group of objects that act upon each other, the total momentum before the action is equal to the total momentum after the action.
		The parallelogram law states that two vectors may be replaced by a single vector called a resultant R, obtained by drawing the diagonal of the parallelogram which has sides equal to the given vectors (see Figure 4).
	www.chiroweb.com /hg/17/14/01.html (2071 words)

	LAB 6 - Equipollence (Site not responding. Last check: 2007-11-05)
		The parallelogram law of force addition allowed us to add the concurrent force vectors in both the collinear and coplanar concurrent force problems to a sum equal to a null vector.
		In a coplanar and non-concurrent force system, the forces cannot be summed vectorially using the parallelogram law of force addition because they do not have a common point of concurrency.
		If we move a force from one line of action to another line of action that is common with the other forces in the system, then the parallelogram law of force addition could be used.
	tardis.union.edu /~krouglin/esc021.fall01/Lab-7/Lab-7.htm (836 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		That is, if two vectors are drawn and one represents 1000 pounds (vector "A") and the other represents 500 pounds (vector "B") then the vector "A" should be twice as long as vector "B".
		If we have two force vectors acting on a body and we wish to replace these two vectors with a single vector that has the same effect on the body, we can use the parallelogram law for the addition of force vectors.
		The resultant force (or the force that can replace the two vectors and still have the same effect of the body as the original two) is the diagonal of the parallelogram (vector "R").
	www.pre-engineering.com /resources/parallel.htm (210 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		a rule for finding the resultant of two vectors by constructing a parallelogram, each pair of parallel sides of which represents the magnitude to scale, and the direction and sense of the given vectors; its diagonal then represents the direction and magnitude of the resultant.
		A parallelogram of forces is a diagram in which the combined effect of two forces acting on the same body is determined using this rule.
		For example, if the two forces are represented by the vectors OA and OB in the figure below, then their resultant, to the same scale, is OR, where R completes the parallelogram.
	www.mathresources.com /products/mathresource/demo/parallelogram.htm (157 words)

	Area Entrance - Vector and Complex Numbers:
		In one or two, he described physic as the addition and multiplication of arrows in the plane, with addition given using the parallelogram law and multiplication being given with polar coordinate rule, add the angles, multiply the lengths.
		The distributive law in its left and right forms, assisted by associative laws for addition and multiplication of points in the plane (see the previous lesson) implies a second way to compute products using the rectangular coordinates, or real and imaginary parts, of the factors.
		Drawing parallelograms, tessellating the plane with them, implies or suggests that multiplication of vectors by whole numbers and then fractions distributes over the sum of two different vectors.
	whyslopes.com /etc/ComplexNumbers (2743 words)

	Linear Algebra (1.4) ~ 3DSoftware.com
		One of those properties is the Parallelogram Law.
		The resulting vector is always the diagonal where the two halves of the parallelogram meet.
		The area of a parallelogram is the magnitude (vector length) of the cross product of two adjacent sides of a parallelogram.
	www.3dsoftware.com /Math/Programming/LinAlg01/04 (507 words)

	Vector Addition and Subtraction: Vectors: Plus 2 Physics (Site not responding. Last check: 2007-11-05)
		If two vectors P and Q can be represented in magnitude and direction by two adjacent sides of a parallelogram drawn outwards from a point, then their vector sum R is the diagonal of the same parallelogram drawn outwards from the same point.
		The opposide side of the parallelogram being of the same magnitude and having the same direction, must also be the same vector Q. this vector Q can be resolved into components Qcos
		It should be noted that the vector sum R is identical to that calculated from the parallelogram.
	www.plus2physics.com /vectors/study_material.asp?chapter=2 (304 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		Wave equation and fundamental solutions Wave equation: Maxwell’s wave equation in linear isotropic media, one-dimensional case, counter-propagating waves, refractive-index and the speed of light, temporal Fourier transform and the complex representation for a monochromatic field, Helmholtz equation, dispersion relation for plane-waves, linearly and circularly polarized fields, complex basis vectors, phase and group velocities.
		Scalar and vector potentials: Vector and scalar potentials and their relation to the physical fields, wave equations for the potentials, nonuniqueness of potentials and gauge transformations, Lorentz gauge and Coulomb (or radiation) gauge and associated wave equations for the potentials, seperation into transverse and longitudinal fields in the Coulomb gauge.
		Stokes parameters and the Poincare sphere: Stokes parameters and their relation to the coherency matrix, representation of states of polarization of light on the Poincare sphere, Mueller matrices, action of optical elements as motion on the Poincare sphere.
	www.optics.arizona.edu /wright/images/EMwavesDetail.doc (1056 words)

	COURSE DESCRIPTION Revised: 1-May 97
		Students can apply the parallelogram law to determine the resultant of two forces.
		Students can resolve a force into two components using the parallelogram law.
		Students can determine the force required to place a system of wedges in equilibrium by applying the laws of dry friction and the angle of friction.
	www.engr.iupui.edu /~zecher/MET111.htm (325 words)

	Atlas: Parallelogram law and comparability axioms in orthomodular lattices by B. N. Waphare (Site not responding. Last check: 2007-11-05)
		Atlas: Parallelogram law and comparability axioms in orthomodular lattices by B. Waphare
		In the similar way using parallelogram law we have obtained the sublatticeness of finite projections in a *-ring.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caiv-07.
	atlas-conferences.com /c/a/i/v/07.htm (190 words)

	Learn more about Pythagorean theorem in the online encyclopedia. (Site not responding. Last check: 2007-11-05)
		This can be proven using the law of cosines which is a generalization of the Pythagorean theorem applying to all (Euclidean) triangles, not just right-angled ones.
		Another generalization of the Pythagorean theorem was already given by Euclid in his Elements:
		pythagorean triple, orthogonality, linear algebra, synthetic geometry, Fermat's last theorem, parallelogram law
	www.onlineencyclopedia.org /p/py/pythagorean_theorem.html (926 words)

	Vector algebra. (from vector analysis) -- Encyclopædia Britannica
		Figure 1: Parallelogram law for addition of vectors
		A prototype of a vector is a directed line segment AB (see Figure 1) that can be thought to represent the displacement of a particle from its initial position A to a new position B.
		In their modern form, vectors appeared late in the 19th century when Josiah Willard Gibbs and Oliver Heaviside (of the United States and Britain, respectively) independently developed vector analysis to express the new laws of...
	www.britannica.com /eb/article-7612 (758 words)

	EM 274 - Objectives/Vector Algebra (Review) (Site not responding. Last check: 2007-11-05)
		Be able to construct and understand diagrams that describe the operations of addition and subtraction of vectors.
		Be able to use the laws of trigonometry to evaluate the sides of the triangles used in the addition and subtraction of vectors.
		Be able to calculate the Cartesian (rectangular) components of two- and three-dimensional vectors given two points on the line of action of the vector.
	www.iastate.edu /~statics/objectives/ch021.html (172 words)

	ScienceDaily: Parallelogram law (Site not responding. Last check: 2007-11-05)
		3 Normed vector spaces satisfying the parallelogram law
		In real inner product spaces, the statement of the parallelogram law reduces to the algebraic identity
		Most real and complex normed vector spaces do not have inner products, but all normed vector spaces have norms (hence the name), and thus one can evaluate the expressions on both sides of "=" in the identity above.
	www.sciencedaily.com /encyclopedia/parallelogram_law (948 words)

	ENGR 208, STATICS AND STRENGTH OF MATERIALS
		The first law is a statement of the condition when forces are in state of balance or equilibrium.
		Quantities that can be represented by directed line segments and which combine according to the parallelogram law of addition (or triangle rule of addition) are called vectors, or geometric vectors to be precise.
		Example 1: law of cosines and law of sines.
	www.calstatela.edu /faculty/sfelsze/e208.htm (4549 words)

	[No title]
		The magnitude of is given by uv sinq, which corresponds to the area of the parallelogram bounded by and.
		They are a consequence of, and equivalent to, the parallelogram law for addition of vectors.
		Any function of the components of vectors which remains unchanged upon changing the coordinate system is called an invariant of the vectors from which the components are obtained.
	neon.mems.cmu.edu /rollett/27750.old.Spg03/Rot.matrices.21Jan03.ppt (1450 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		In order to get the resultant (sum) of two vectors, they can be combined using the parallelogram law.
		If a parallelogram is constructed with the two vectors to be added as sides, the diagonal represents the resultant.
		Also solve by the law of cosines (cosine law) and/or law of sines (sine law) Repeat part (a) for the case when the 600 lb force is directed in the opposite sense from that shown.
	www.rpi.edu /dept/core-eng/WWW/IEA/locker/lecture/vectors.doc (3043 words)

	Scalars and Vectors
		Vector: A quantity like heat flux or force which has both a magnitude and a direction (denoted by a bold faced character, an underlined character, or a character with a arrow on it)
		Vector Addition: Vector Addition follows the parallelogram law described be the figure
		Resolution of a Vector: A vector can be resolved along different directions using the parallelogram rule.
	em-ntserver.unl.edu /Negahban/em223/note2/note2.htm (92 words)

	EM 274 - Objectives/Concurrent Force Systems - 1 (Site not responding. Last check: 2007-11-05)
		Be able to describe how the Principle of Transmissibility allows us to move forces around on bodies.
		Be able to calculate the magnitude and direction of the resultant of a pair of concurrent forces using the parallelogram law of addition, the law of sines, and the law of cosines.
		Be able to calculate the components of a given force using the parallelogram law of addition, the law of sines, and the law of cosines.
	www.iastate.edu /~statics/objectives/ch022.html (157 words)

	Syllabus of XI Standard (Site not responding. Last check: 2007-11-05)
		Verification of parallelogram law, triangle law and lami’s theorem
		Biot-savart law ; Magnetic induction at a point due to a current carrying conductor
		Methods of generating induced emf – by changing magnetic induction, by changing the area enclosed by the coil, by changing the orientation of the coil
	education.vsnl.com /gks_details/Syllabus_of_Physics_for_Higher_Secondary (788 words)

	[No title]
		Review the theory for each section, including the proofs for the theorems listed, and homework problems.
		Ch.1 Vector spaces - Vectors (intuitive): magnitude & direction, addition (Parallelogram Law) and scaling - Vector spaces: def.
		; properties: functions multilinear in columns/rows; - Invertible iff det not 0; det(At)=det(A); multiplicative; - Orientation, left/right handed basis, parallelogram & area, parallelepiped & volume; - Change of determinants under elementary operations - Cramer’s rule (solving linear systems using determinants) - Determinant and n-dimensional volume (of n-dim.
	www.ilstu.edu /~lmiones/337rvu04.doc (524 words)

	ADDITION OF VECTORS-PARALLELOGRAM LAW-PARALLELOGRAM LAW OF VECTOR ADDITION
		Acccording to the parallelogram law of vector addition:
		then the diagonal of parallelogram will be equal to the resultant of these two vectors."
		MAGNITUDE OF Magintude or resultant vector can be determined by using either sine law or cosine law.
	www.citycollegiate.com /vectorXIb.htm (73 words)

	[No title]
		Introduction to Vector Algebra, Vector Operations, Parallelogram law, Free vector, Bound Vector; representation of Forces and Moments in terms of i,j,k; Cross product and Dot product and their applications.
		Concept of Friction; Laws of Coulomb friction, Angle of Repose.
		Stress and strains under axial loading stress-strain diagram of ductile materials, Working stress, Factor of safety, Proportional limit, Elastic Limit, Ultimate stress, Yielding, Modulus of elasticity, Definitions of malleability, ductility, toughness and resilience.
	www.wbut.net /syllabus/new/Syllabus_of_ME_subjects.DOC (1462 words)

	Class Preparation Guide (Site not responding. Last check: 2007-11-05)
		Give yourself extra time to read it and prepare for the Quiz.
		* Parallelogram Law for the Addition of Farces
		* Know the various methods for adding vectors: the parallelogram law, the triangle rule/polygon rule, summing rectangular components
	users.rowan.edu /~everett/courses/st/cprpst99.htm (664 words)

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