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Topic: Irreducible fraction

Related Topics

continued fraction

fractional calculus

vulgar fraction

partial fraction

Fractional reserve banking

fractional distillation

ejection fractions

Egyptian fractions

Fractional Fourier transform

irreducible fraction

fractional electrodynamics

Integration by partial fractions

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	Fraction article - Fraction unit mathematics vulgar fraction rational number integer divided - What-Means.com (Site not responding. Last check: 2007-10-08)
		A vulgar fraction is a rational number written as one integer (the numerator) divided by a non-zero integer (the denominator).
		Irreducible fraction: a vulgar fraction "in lowest terms", where the numerator is an integer, the denominator is a positive integer, and the highest common factor of the numerator and the denominator is 1.
		Unit fraction: A vulgar fraction with a numerator of 1.
	www.what-means.com /encyclopedia/Fractions (334 words)

	Partial fraction - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-08)
		In algebra, the partial fraction decomposition of a rational function expresses the function as a sum of fractions, in each term of which, the denominator is an irreducible (i.e., prime, not factorable) polynomial and the numerator is a polynomial of smaller degree than the denominator.
		See partial fractions in integration for an account of their use in finding antiderivatives.
		Just which polynomials are irreducible depends on which field of scalars one adopts.
	www.sterlingheights.us /project/wikipedia/index.php/Partial_fraction_decomposition (1117 words)

	Irreducible fraction -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		Irreducible fraction -- Facts, Info, and Encyclopedia article
		For example the fraction 2/4 is equal to 1/2 and therefore not irreducible, but the fractions 1/4, 5/6 and -101/100 are irreducible.
		It can be shown that a fraction a/b is irreducible if, and only if, a and b are (Click link for more info and facts about coprime) coprime.
	www.absoluteastronomy.com /encyclopedia/i/ir/irreducible_fraction.htm (69 words)

	One half - Wikipedia, the free encyclopedia
		One half is the irreducible fraction resulting from dividing one by two (½), or any number by its double; multiplication by one half is equivalent to division by two.
		It is the fraction occurring most often in mathematical equations, recipes, measurements, etc.
		One of the few fractions which is commonly expressed in natural languages by suppletion rather than regular derivation; compare English one half with regular formations like one sixth from six.
	en.wikipedia.org /wiki/%c2%bd (258 words)

	Stern-Brocot Tree
		On the next stage of the construction, we form four new fractions: 1/3 from 0/1 and 1/2, 2/3 from 1/2 and 1/1, 3/2 from 1/1 and 2/1, and, finally, the mediant of 2/1 and 1/0 which is 3/1.
		To see this, every fraction at the n-th level is the mediant of a fraction at the (n-1)-st level and one at a higher level.
		The nd sum of a fraction at the (n-1)-st level is at least n+1 and the nd sum of a fraction at a higher level is at least 1.
	www.cut-the-knot.org /blue/Stern.shtml (718 words)

	5.4 - Partial Fractions
		If the partial fractions we're decomposing the rational expression into must be proper, then an irreducible quadratic factor could have a linear term and/or a constant term in the numerator.
		The implications of this for partial fraction decomposition are that when you have a repeated factor (a factor with a multiplicity other than one), you need to include a factor in the expansion for each power possible.
		A proper fraction is a fraction where the numerator is less than the denominator.
	www.richland.edu /james/lecture/m116/systems/partial.html (1322 words)

	4.0 SST Gas Release Mechanisms (Site not responding. Last check: 2007-10-08)
		Displacement occurred at a void fraction of 0.14 in the deep supernatant case (2a) and at 0.20 in the shallow supernatant case (2b).
		The fraction connected varies with the void fraction between a threshold at which connection begins and an upper limit where the entire volume is connected.
		The fraction of the total gas available and interconnected that is actually discharged to the next level is expressed by a factor, F that is allowed to vary between two values depending on the extent of connectedness.
	www.pnl.gov /tws/reports/dir24878/11391-4.html (16799 words)

	Element Operations
		Given a rational function f in K, the field of fractions of R, return the numerator P of f=P/Q as an element of the polynomial ring R. Denominator(f) : FldFunRatElt -> RngElt
		Given a rational function f in K, the field of fractions of R, return the denominator Q of f=P/Q as an element of the polynomial ring R. Degree(f) : FldFunRatElt -> RngIntElt
		Finally, we compute the partial fraction decomposition of a fraction in a function field whose coefficient ring is a multivariate function field.
	www.math.lsu.edu /magma/text700.htm (544 words)

	Generalized continued fraction (Site not responding. Last check: 2007-10-08)
		In mathematics, a generalized continued fraction is a generalization of the concept of continued fraction in which the numerators are allowed to differ from unity.
		Another meaning for generalized continued fraction would be a generalisation to higher dimensions.
		For example, there is a close relationship between the continued fraction for the irrational real number, and the way lattice points in two dimensions lie to either side of the line y x.
	read-and-go.hopto.org /Fractions/Generalized-continued-fraction.html (389 words)

	Distributions of Rationals on the Unit Interval (or, How to (mis)-Count Rationals)
		In fact, any fraction with a denominator that is a multiple of 2,3,4,5, or 6 will have this problem; fractions that have a multiple of 7 in the denominator don't seem to have this problem, perhaps because they are not on a bin boundary.
		This one shows irreducible fractions with denominators less than 16000, which, as we've mentioned, represents a sample size almost 16 times larger than the first sets of graphs.
		That is, the fractions given by the rows and columns are all visible from the origin.
	linas.org /math/chap-rat/chap-rat.html (3468 words)

	Problem L - 2001 Regionals Warmup Contest
		A fraction m / n is basic if 0 <= m < n and it is irreducible if gcd(m, n) = 1.
		Given a positive integer n, in this problem you are required to find out the number of irreducible basic fractions with denominator n.
		For example, the set of all basic fractions with denominator 12, before reduction to lowest terms, is
	acm.uva.es /p/v101/10179.html (177 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		To determine the denominators of the partial fraction decomposition, factor the denominator of the rational function
		The degree of the numerator in the integrand must be less than the degree of the denominator before using partial fraction decomposition; if not, divide the denominator into the numerator using long division
		For each power of a linear (quadratic) factor in the denominator, you need to include another term in the partial fraction decomposition.
	www.rhodes.edu /mathcs/faculty/shelton/classes/math122/m122jan30.asp (285 words)

	Third - Wikipedia, the free encyclopedia
		Third is also the third album by the band Soft Machine.
		In mathematics, Third is also the ordinal number corresponding to three, as well as the irreducible fraction
		This is a disambiguation page, a list of pages that otherwise might share the same title.
	en.wikipedia.org /wiki/Third (150 words)

	Element Operations
		Given a rational function f in K, the field of fractions of R, return the numerator P of f=P/Q as an element of the polynomial ring R. Denominator(f) : FldFunElt -> RngElt
		Given a rational function f in K, the field of fractions of R, return the denominator Q of f=P/Q as an element of the polynomial ring R. Degree(f) : FldFunElt -> RngIntElt
		We compute the squarefree and complete (irreducible) partial fraction decompositions of a fraction in Q(t).
	www.math.wisc.edu /help/magma/text460.html (544 words)

	Irrational number In mathematics
		The discovery of irrational numbers is usually attributed to Pythagoras, more specifically to the Pythagorean Hippasus of Metapontum, who produced a (most likely geometrical) proof of the irrationality of the square root of 2.
		The seventeenth century saw decimal fractions with the modern notation quite generally used by mathematicians.
		Then √2 can be written as an irreducible fraction (the fraction is shortened as much as possible) a / b such that a and b are co-prime integers and (a / b)2 = 2.
	www.metu.edu.tr /~e128327/Irras.htm (1677 words)

	Partial Fraction Decomposition (Site not responding. Last check: 2007-10-08)
		Partial fractions: (take a fraction and write this fraction as a sum of two or more similar fractions.)
		is an improper fraction, divide the denominator into the numerator to obtain:
		Since this project is managed by one student, I must rely on my peers for assistance.
	www.mathematicshelpcentral.com /lecture_notes/precalculus_algebra_folder/partial_fraction_decomposition.htm (196 words)

	Cognitive Decline: The Irreducible Legacy of Open Borders
		They form what I call a nation's 'smart fraction.' When their supply is exhausted, economic growth shuts down.
		A value for the smart constant was determined, in Smart Fraction Theory II: Why Asians Lag, to be 5.58/15 or 0.372 SD, corresponding to a threshold IQ (in conventional units) of 105.58.
		is the smart fraction in a native European population with a mean IQ of 100 and a standard deviation of 15 IQ points, i.e.
	www.lagriffedulion.f2s.com /imm.htm (2918 words)

	wikien.info: Main_Page (Site not responding. Last check: 2007-10-08)
		The sixteenth century saw the final acceptance of negative numbers, integral and fractional.
		Continued fractions, closely related to irrational numbers (and due to Cataldi, 1613), received attention at the hands of Euler, and at the opening of the nineteenth century were brought into prominence through the writings of Joseph Louis Lagrange.
		can be written as an irreducible fraction (the fraction is shortened as much as possible) a / b such that a and b are coprime integers and (a / b)
	www.alanaditescili.net /index.php?title=Irrational_number (1672 words)

	Proof that sqrt(2) is irrational (Site not responding. Last check: 2007-10-08)
		A proof that the square root of 2 is not a fraction
		Firstly, assume sqrt(2) is rational, i.e can be represented as the irreducible fraction m/n where m and n are integers.
		So if m is even and n is even, then m/n is not an irreducible fraction.
	home.egge.net /~savory/maths8.htm (142 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Entrainment or frequency locking phenomena can be observed in many systems, either by local coupled oscillators or by externally applied periodic forcing, examples include nonlinear optics, chemical reactions or biological rhythms.
		A system is frequency locked when its oscillation frequency is adjusted to an irreducible fraction of the forcing frequency.
		Although the frequency locking phenomena have been extensively studied for single oscillator type systems, the fundamental description of resonance phenomena for spatially extended systems is missing.
	www.math.technion.ac.il /~techm/20040309143020040309yoc (286 words)

	6.5.2 The Method Of Partial Fractions
		Since their denominators are already identical, it remains that their numerators must be identical.
		Observe that the numerator of the first partial fraction is a constant, while that of the second is a linear function.
		Corresponding to a linear denominator we use a constant numerator, and corresponding to a quadratic denominator we
	www.geocities.com /pkving4math2tor6/6_the_intgrl/6_05_02_the_meth_of_partl_fract.htm (477 words)

	2blowhards.com: History of Math
		It's true that the Sumerian scribes could solve quadratics--but they were a very small fraction of the population.
		The key sentence: " The most profound engine of civilization is the inability of a larger and larger fraction of the population to do the basic things needed to survive.
		I wasn't trying to say that the average Babylonian was in advance of the average American, just that the mathematical elite of a 4,000 year old civilization was still ahead of the average man-on-the-street today.
	www.2blowhards.com /archives/001250.html (7764 words)

	AFMA Home page
		The endogenous faecal loss of P actually corresponds to an irreducible fraction that may represent the actual net maintenance requirement and also an excretory component that permits the organism to eliminate the P absorbed in excess of its requirement.
		This explains the quasi-linear relationship between the endogenous faecal loss and the level of P intake (Grace, 1981; Braithwaite, 1985; Ternouth, 1989; Scott et al, 1987; Scott et al, 1995).
		These are strongly related to P recycling in the saliva, and, in particular, the non-reabsorbed fraction.
	www.afma.co.za /AFMA_Template/1,2491,768_425,00.html (1403 words)

	A Matrix Euclidean Algorithm induced by State Space Realization - Allen, Rosenthal (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		In systems theory, irreducible matrix fraction descriptions of transfer function matrices can be found.
		In linear algebra, the greatest common divisor can be seen as a basis for a free module generated by the columns of...
		3 A matrix euclidean algorithm and matrix continued fraction e..
	citeseer.ist.psu.edu /allen99matrix.html (489 words)

	Graphical patterns in quadratic residues (Site not responding. Last check: 2007-10-08)
		The fraction 2a/b m in the approximation of Δ turn to be a/b' m with b' = b/2.
		Then, only b/2 parabolas are drawn in the plot when we experiment with the parameters a=1, b=6 or a=3, b=8.
		(i) The QRs for x near a fraction a/b of the modulus spreads as integer points of a set of b (or b/2 if b is even) parabolas.
	www.iec.csic.es /~ismael/QRs.htm (1263 words)

	www.cpp-home.com : View topic - Alvaro: new problems (Site not responding. Last check: 2007-10-08)
		Let's write it as the irreducible fraction p/q.
		We divide both sides by 2 and get 2k^2=q^2, which tells us that q^2 is even, and therefore q is even.
		But p and q cannot possibly be both even, or the fraction p/q wouldn't be irreducible.
	www.cpp-home.com /forum/viewtopic.php?p=61806 (776 words)

	Irrationality proofs
		Irrational numbers are numbers which cannot be expressed as a fraction of two integers (see Classification of numbers).
		Theorem 1 If an irreducible fraction p/q is a root of P, then p divides a
		The proof was rather complex and based on a continued fraction for the tanx function.
	numbers.computation.free.fr /Constants/Miscellaneous/irrationality.html (814 words)

	The CTK Exchange Forums
		Case1: If both n and d are odd, all the fractions will be odd.
		Case2/3: If one (n or d) is even and the other is odd, they will stay that way no matter what.
		Now, to get an irreducible fraction of the form (2i+1)/(2j+1) we have to start with (2i+1)2^r/((2j+1)2^r), for which we should pick two numbers divisible by 2^r but not by 2^(r+1).
	www.cut-the-knot.com /htdocs/dcforum/DCForumID6/443.shtml (1996 words)

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