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Topic: Addition theorem

	Addition theorem -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-09)
		The scope of the idea of an addition theorem was fully explored in the (additional info and facts about nineteenth century) nineteenth century, prompted by the discovery of the addition theorem for (additional info and facts about elliptic function) elliptic functions.
		An algebraic addition theorem is one in which G can be taken to be a vector of (A mathematical expression that is the sum of a number of terms) polynomials, in some set of variables.
		The connected, (additional info and facts about projective variety) projective variety examples are indeed exhausted by abelian functions, as is shown by a number of results characterising an (additional info and facts about abelian variety) abelian variety by rather weak conditions on its group law.
	www.absoluteastronomy.com /encyclopedia/a/ad/addition_theorem.htm (301 words)

	Lake Zurich Middle School South - Gifted Education - Geometry
		Theorem 19: All radii of a circle are congruent.
		Theorem 51: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
		Theorem 52: A segment joining the midpoints of two sides of a triangle is parallel to the third side, and its length is one-half the length of the third side.
	www.freewebs.com /lzmssgeometry/theorems (1030 words)

	Addition theorem - Wikipedia, the free encyclopedia
		Slightly more generally, as is the case with the trigonometric functions sin and cos, several functions may be involved; this is more apparent than real, in that case, since there cos is an algebraic function of sin (in other words, we usually take there functions both as defined on the unit circle).
		The scope of the idea of an addition theorem was fully explored in the nineteenth century, prompted by the discovery of the addition theorem for elliptic functions.
		An algebraic addition theorem is one in which G can be taken to be a vector of polynomials, in some set of variables.
	en.wikipedia.org /wiki/Addition_theorem (333 words)

	Mordell–Weil theorem - Wikipedia, the free encyclopedia
		In mathematics, the Mordell–Weil theorem states that for an abelian variety A over a number field K, the group A(K) of K-rational points of A is a finitely-generated abelian group.
		The case with A an elliptic curve E and K the rational number field Q is Mordell's theorem, answering a question apparently posed by Poincaré around 1908; it was proved by Louis Mordell in 1922.
		The tangent-chord process (one form of addition theorem on a cubic curve) had been known as far back as the seventeenth century.
	en.wikipedia.org /wiki/Mordell-Weil_theorem (423 words)

	Vector Addition
		The Pythagorean theorem is a useful method for determining the result of adding two (and only two) vectors which make a right angle to each other.
		The Pythagorean theorem is a mathematical equation which relates the length of the sides of a right triangle to the length of the hypotenuse of a right triangle.
		Additional examples of vector addition using the head-to-tail method are given on a separate WWW page at this same site.
	www.glenbrook.k12.il.us /gbssci/phys/Class/vectors/u3l1b.html (1638 words)

	Koopmans' theorem (Site not responding. Last check: 2007-10-09)
		Koopmans' theorem is an approximation in molecular orbital theory, such as density functional theory, or Hartree-Fock theory, in which the first ionization energy of a molecule is equal to the energy of the highest occupied molecular orbital (the HOMO), and the electron affinity is the negative of the energy of the lowest unoccupied, i.e.
		In Hartree-Fock theory, Koopmans' theorem specifically states that the ionization energies of a molecule are equal to the eigenvalues of the Fock operator associated to the occupied molecular orbitals, and the electron affinity is the negative of the eigenvalues of the Fock operator associated to the lowest unoccupied, i.e.
		Koopmans' Theorem, like Hartree-Fock theory, operates under the assumption that the electronic wavefunction of a multi-electron atom can be described as the Slater determinant of a set of one-electron wavefunctions, (which are the eigenfunctions of the corresponding Fock operators).
	www.punweb.com /article/Koopmans'_theorem (281 words)

	ADDITION OF VELOCITIES IN SPECIAL RELATIVITY
		The Galilean theorem of addition of velocities is proved hereunder as a mathematical and geometrical theorem.
		Thus for their formulation, the "mathematics" and "geometry" of Relativity require a postulate additional to the axioms, postulates and propositions from which the rest of mathematics and geometry (as we know them to be) are formulated.
		Since the Special Relativistic "theorem" of addition of velocities contradicts the Galilean theorem, it is demonstrated that the postulate on which Special Relativistic "mathematics" and "geometry" are based — namely the postulate of the constancy of the speed of light — cannot be a part of mathematics and/or geometry as we know them.
	www.wbabin.net /physics/srmath.htm (620 words)

	Chapter 13. Theorem of the Addition of Velocities. The Experiment of Fizeau. Einstein, Albert. 1920. Relativity: The ...
		In Section VI we derived the theorem of the addition of velocities in one direction in the form which also results from the hypotheses of classical mechanics.
		which corresponds to the theorem of addition for velocities in one direction according to the theory of relativity.
		The question now arises as to which of these two theorems is the better in accord with experience.
	www.bartleby.com /173/13.html (847 words)

	Pier Paolo Pasolini's Theorem
		In addition, Theorem expresses that realism may quell traditional family roles and affords the realisation of the meaninglessness of traditional family values.
		In addition, anti-Catholic positions may be found in Pasolini’s writings such as the poem “To A Pope” (1958), in which he scathingly denounces Pope Pius XII at his death and created a literary scandal.
		Returning to the metaphor of the visitor as Christ, the narrative of Theorem can be considered as sharing similarities with the death and resurrection of Jesus and subsequent parting of his disciples to “spread the good news”.
	www.geocities.com /briandy_au/theorem.html (1864 words)

	Theorem 8.3 (Site not responding. Last check: 2007-10-09)
		By Theorem 5.1, the Well Ordering Principle, there is a smallest element c in this set which will then be the smallest nonzero natural number that can be written as a sum or difference of multiples of a and b.
		Now since c is a sum or difference of multiples of a and b, so is qc by the Distributive Properties of Addition, Theorem 6.10, and Subtraction, Theorem 7.5.
		By Theorem 6.8, Theorem 6.10 and Theorem 7.5, the Associative and Distributive Properties of Multiplication, d will divide any natural number which is a sum or difference or multiples of a and b including c.
	www.sonoma.edu /users/w/wilsonst/papers/finite/8/t8-3.html (409 words)

	Addition and Multiplication (Site not responding. Last check: 2007-10-09)
		Theorem 6.3: (The Commutative Property for Addition of Natural Numbers) Let a and b be natural numbers.
		Theorem 6.4: (The Associative Property for Addition of Natural Numbers) Let a, b, and c be natural numbers.
		Theorem 6.8: (The Associative Property for Multiplication of Natural Numbers): Let a, b, and c be natural numbers.
	www.sonoma.edu /users/w/wilsonst/papers/finite/6 (267 words)

	[No title]
		In addition, some theorem provers are fully programmable: users have access to a general purpose programming language to encode arbitrary patterns of reasoning.
		In addition, I would also like to further develop my model of probabilistic programs by verifying more random algorithms: a self-stabilizing algorithm and randomized quicksort are two promising candidates.
		It is often the case that mathematical theories have to be formalized in the theorem prover to define the specification of a system.
	www.cl.cam.ac.uk /users/jeh1004/cv/research.html (948 words)

	Einstein's Theory of Relativity - Scientific Theory or Illusion?
		The cause of the error lies in the fact that Einstein's equations for the addition of speeds and the subtraction of speeds were derived for conditions which differ greatly from the conditions under which the experiment was performed.
		It is clear that in the new environment equation derived for the addition of speeds in a vacuum is not valid.
		On the contrary, it shows that the theorem on addition of speeds is wrong, that it is based on a wrong assumption and it is applied in a wrong way.
	users.net.yu /~mrp/chapter20.html (1439 words)

	Damjan Bojadziev: Mind Versus Gödel
		The theorems do not imply that there can be no formal, computational model of the mind, but on the contrary, suggest the existence of such models within a conception of mind as subject to similar limitations as formal systems.
		This theorem, and related results by Gödel and Church, are frequently used in arguments about the existence of formal models of the mind; interestingly enough, they have been used to argue both for and against that possibility.
		Gödel's theorems uncover a fundamental limitation of formalization, but they say that this limitation could be overcome only at the price of consistency; we might thus say that the limitation is so fundamental as to be no limitation at all.
	nl.ijs.si /~damjan/g-m-c.html (3858 words)

	SPHERICAL HARMONICS - Online Information article about SPHERICAL HARMONICS
		Spherical and other harmonic functions are of additional importance in view of the fact that they are largely employed in the treatment of the partial differential equations of physics, other than Laplace's equation; as examples of this, we may refer to the equation al =k0'u, which is fundamental in the theory of See also:
		Euler's theorem for homogeneous functions, this becomes n' y J' (YnZn,dS = 0, whence the theorem (22), which is due to Laplace, is proved.
		The following case of this theorem should he remarked: If f(x, y, z) is homogeneous and of degree n ffYn(x, y, z)f,,(x, y, z)dS47rR2n+2(2n2+1I)!Yn (ar ay' az) f (x,y,E) if f,,(x, y, z) is a spherical harmonic, we Obtain from this a theorem, due to Maxwell (Electricity, vol.
	encyclopedia.jrank.org /SOU_STE/SPHERICAL_HARMONICS.html (6657 words)

	Theorem Solutions - Leading Suppliers of CAD/CAM/CAE Data Translators, Converters and Viewers
		Theorem Solutions is recognised as one of the world leaders in CAD/CAM product data exchange, offering application programs for Direct Database conversion and for International Standards-based conversion methods (STEP).
		The Theorem CADverter family is the widest range of direct CAD translators available from any single source.
		Theorem also provides on-line CAD Data Translation Services to enable customers with a small volume of translation requirements to receive the benefits of CADverter technology whilst managing overall project costs.
	www.theorem.co.uk (268 words)

	Frege's Logic, Theorem, and Foundations for Arithmetic
		In addition, we hope to prepare students of Frege to read his original work (in translation) and to prepare the reader to understand a number of excellent articles in the secondary literature on Frege's work.
		Again, these are essentially the same as the rules for the first-order predicate calculus, except for the addition of new rules for the second-order quantifiers that correspond to the generalization and instantiation rules (i.e., introduction and elimination rules) for the first-order quantifiers.
		Theorem 5 now follows from the Lemma on Successors and the fact that successors of natural numbers are natural numbers.
	plato.stanford.edu /entries/frege-logic (15095 words)

	The "Mathematics" of Relativity
		The Galilean theorem of addition of velocities is proved hereunder as a mathematical theorem.
		Since the so-called Relativistic "theorem" of addition of velocities contradicts the Galilean theorem, it is demonstrated logically that the postulate on which Relativistic "mathematics" and "geometry" are based -- namely the postulate of the constancy of the speed of light -- cannot be a part of mathematics and/or geometry as we know them.
		This logically and mathematically proves the Galilean theorem of addition of velocities.
	homepage.mac.com /ardeshir/RelativityMath.html (571 words)

	Theorem Solutions Announces Availability CADverter Revision 8.0 (Site not responding. Last check: 2007-10-09)
		Theorem Solutions has announced the immediate availability of CADverter Revision 8, the latest release of its family of advanced CAD data translators.
		Like previous Theorem releases, Revision 8 CADverters will be available in both uni- and bi-directional forms; enabling customers to tailor installations to their specific requirements.
		All new Theorem sales from the 1st August 2004 will be shipped as Revision 8 products, and existing Theorem customers will receive upgrades to Revision 8 under current maintenance contracts.
	www.theorem.co.uk /pr/pr18.htm (386 words)

	Mathematical Tidbits
		The index of a radical must be larger than the exponent on each prime factor in the radicand for a radical to be in simplified radical form.
		This means that the grouping of terms (addition) or factors (multiplication) is irrelevant to the answer.
		Subtraction and division are defined in terms of addition and multiplication and the same identities hold.
	www.richland.edu /james/misc/prop.html (969 words)

	Trigonometric identity
		These can be proven by expanding their right-hand-sides using the addition theorems.
		Having established these two limits, one can use the limit definition of the derivative and the addition theorems to show that sin′ = cos and cos′ = −sin.
		If the sine and cosine functions are defined by their Taylor series, then the derivatives can be found by differentiating the power series term-by-term.
	www.brainyencyclopedia.com /encyclopedia/t/tr/trigonometric_identity.html (1185 words)

	[No title]
		The argument is Enderton's Now, by the Recursion Theorem, for all $n \in \mathbb{N}$, there exists exactly one function $p_n:\mathbb{N} \rightarrow \mathbb{N}$ such that $p_n(0) = n$ and $p_n(s(m)) = s(p_n(m))$ for all $m \in \mathbb{N}$.
		By the Recursion Theorem we can let $f$ be the unique function such that $f(0) = n$ and $f(s(l)) = s(f(l))$ for all $l \in \mathbb{N}$.
		By the Recursion Theorem, there is a unique function $f:\mathbb{N} \rightarrow \mathbb{N}$ such that $f(0) = n$ and $f(s(l)) = s(f(l))$ for all $l \in \mathbb{N}$.
	www.math.umn.edu /~jodeit/course/LBonADDed (2349 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.
		Answer: Points in the plane with the rectangular coordinate method of addition and the polar coordinate way for multiplication provide a geometric viewpoint and understanding of complex numbers with their real and imaginary parts of complex numbers are identified.
		This method for vector or arrow addition is suggested by the navigational use of arrows or vectors to represent or summarize a sequence of movements.
	whyslopes.com /etc/ComplexNumbers (2835 words)

	Hyperbolic Trigonometric Functions
		The addition theorems for the hyperbolic secant, cosecant, versed sine, and haversed sine are not interesting.
		Theorem: A hyperbola is the locus of points, the difference of the distances to each of the focal-points is a constant 2a.
		Carl Friedrich Gauss (1727-1855) derived the Gauss theorem and from it the flux-divergence theorem.
	www.rism.com /Trig/hyperbol.htm (9675 words)

	3rd Year Project Proposals: Theorem Proving (Site not responding. Last check: 2007-10-09)
		Automated theorem proving is a topic of relevance to program development, verification of hardware and software, artificial intelligence, and mathematical packages, among other areas.
		Powerful theorem provers have been developed for a variety of logical systems.
		In addition, some theorem-proving capability has been built in to languages like constraint logic programming languages.
	www.cs.bris.ac.uk /~john/Projects/theorem.html (90 words)

	The Theorem of Barbier
		At the end of the August's column we arrived at Barbier's theorem as a surprising consequence of Count Buffon's experiment.
		The algebraic concept fundamental to the proof is Minkowski's addition of convex sets.
		Several important properties of Minkowski's addition could be discerned with the help of the following applet that shows the sum of two ("Left" and "Right") polygons.
	www.maa.org /editorial/knot/Barbier.html (1101 words)

	[No title]
		One interesting aspect of Theorem 2.4 is that we have been able to state it in terms of visual objects: Euler and Conway items, and in terms of visual magic squares: Euler and Conway squares.
		Again, note that Theorem 2.5 is just a restatement of Theorem 2.4 in terms of numerical representations of Euler and Conway squares, and so this exercise is really just a continuation of Exercise 2.4 (b) and (c) with a more detailed hint on what numerical representations to use.
		In addition, items 0 and 5 are bicomplementary, and so are items 0 and 10, items 15 and 5, and items 15 and 10.
	www.mi.sanu.ac.yu /vismath/pais/pais2/pais2.html (4453 words)

	Chapter 6. The Theorem of the Addition of Velocities Employed in Classical Mechanics. Einstein, Albert. 1920. ... (Site not responding. Last check: 2007-10-09)
		The Theorem of the Addition of Velocities Employed in Classical Mechanics.
		The only possible answer seems to result from the following consideration: If the man were to stand still for a second, he would advance relative to the embankment through a distance v equal numerically to the velocity of the carriage.
		As a consequence of his walking, however, he traverses an additional distance w relative to the carriage, and hence also relative to the embankment, in this second, the distance w being numerically equal to the velocity with which he is walking.
	www.bonus.com /contour/bartlettqu/http@@/www.bartleby.com/173/6.html (282 words)

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