Irrational - Factbites

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Topic: Irrational

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	Number - Wikipedia, the free encyclopedia
		The first existence proofs 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.
		This number is denoted by i, a symbol assigned by Leonhard Euler.
		The arithmetical operations of numbers, such as addition, subtraction, multiplication and division, are generalized in the branch of mathematics called abstract algebra, the study of abstract number systems such as groups, rings and fields.
	en.wikipedia.org /wiki/Number (3655 words)

	RHYTHM - LoveToKnow Article on RHYTHM
		Rhythm in Verse.Professor Jakob Minor has adduced a figure, valuable in helping us to realize what poetic rhythm is, when he remarks that to strike a bell twelve times, at exactly equal intervals, is to produce what may be called, indeed, a rhythmic effect, but not to awaken anything resembling the sensation of poetical rhythm.
		In speaking of rhythm, it is customary to think of the formal rules which govern the fixed cadence of feetin poetry, but there is also a rhythm in prose, which imitates the measured movements of the body in stately speech.
		According to Renan, the rhythm of the ancient poetry of the Hebrews is solely founded on this prose movement, which differs, in fact, from that of modern European poetry merely in its undefined and indeterminate character.
	2.1911encyclopedia.org /R/RH/RHYTHM.htm (3273 words)

	PlanetMath: irrational
		An irrational number is a real number which cannot be represented as a ratio of two integers.
		This is version 6 of irrational, born on 2001-11-04, modified 2005-04-10.
		The sum, difference, product, and quotient (when defined) of two numbers, one rational and another irrational, is irrational.
	planetmath.org /encyclopedia/IrrationalNumber.html (132 words)

	irrational number
		There are two types of irrational number: algebraic numbers, such as the square root of 2, which are the roots of algebraic equations, and the transcendental numbers, such as pi and e, which aren't.
		The vast majority of real numbers are irrational, so that if you were to pick a single point on the real number line at random the chances are overwhelmingly high that it would be irrational.
		The decimal expansion of an irrational numbers doesn't come to an end or repeat itself (in equal length blocks), though it may have a pattern such as 0.101001000100001...
	www.daviddarling.info /encyclopedia/I/irrational_number.html (344 words)

	TypeLogic FAQ
		In Jung's typology, sensing is an irrational function.
		In Jung's typology, intuition is an irrational function.
		P actually means that the extraverted function is a Perceiving (data-collecting, or irrational) function, but since the dominant function is introverted (by definition for Introverts), the I _ _ P types' first functions are Judging (deciding or rational) functions.
	www.typelogic.com /faq.html (344 words)

	Irrational numbers - Hutchinson encyclopedia article about Irrational numbers
		Irrational numbers include some square roots (for example, √2, √3, and √5 are irrational); numbers such as π (for circles), which is approximately equal to the decimal 3.14159; and e (the base of natural logarithms, approximately 2.71828).
		If an irrational number is expressed as a decimal it would go on for ever without repeating.
		An irrational number multiplied by itself gives a rational number.
	encyclopedia.farlex.com /Irrational+numbers (134 words)

	PlanetMath: e is not a quadratic irrational
		This is version 8 of e is not a quadratic irrational, born on 2003-11-21, modified 2005-03-18.
		"e is not a quadratic irrational" is owned by mathcam.
		(Number theory :: Diophantine approximation, transcendental number theory :: Irrationality; linear independence over a field)
	planetmath.org /encyclopedia/EIsIrrational.html (109 words)

	High-Tech Dictionary Definition
		A real number which is not a ratio of two integers; for example, pi and the square root of two.An irrational number can be expressed as an infinite decimal in which not set of consecutive digits repeats itself infinitely.
	www.computeruser.com /resources/dictionary/definition.html?lookup=2541 (39 words)

	What's a number?
		Thus Cantor studied such decimal expansions and observed that periodic expansions correspond to rational numbers whereas the non-periodic ones correspond (by his definition) to the irrational numbers.
		The theory of irrational numbers belongs to Calculus.
		The rest of the complex numbers could also be defined by adding this new number i to the set of reals and postulating that usual arithmetic operations (addition, subtraction, multiplication) apply to the expanded set and all the laws known to hold for these operations hold for the new set as well.
	www.cut-the-knot.org /do_you_know/numbers.shtml (3529 words)

	Definitions
		A number that cannot be expressed as the ratio of two integers.
	www.math.com /school/glossary/defs/irrational_number.html (12 words)

	Definition of Irrational Exuberance
		The term "irrational exuberance" derives from some words that Alan Greenspan, chairman of the Federal Reserve Board in Washington, used in a black-tie dinner speech entitled "The Challenge of Central Banking in a Democratic Society" before the American Enterprise Institute at the Washington Hilton Hotel December 5, 1996.
		Probably, "irrational exuberance" are Greenspan's own words, and not a speech writer's, and probably Alan Greenspan had written a draft of his 1996 speech even before I testified.
		The term "irrational exuberance" is often used to describe a heightened state of speculative fervor.
	www.irrationalexuberance.com /Def-ie.htm (430 words)

	Skyclad - Irrational Anthems
		The band is in top form on "Irrational Anthems." The songs rock, Walkyier's lyrics are superb and the songs "The Wrong Song", "Penny Dreadful", "The Sinful Ensemble" and "Quantity Time" are by themselves worth the price of this disk.
		After the first spin of "Irrational Anthems" though, I had a huge grin on my face and felt relief that one of my favourite bands still rocked.
		"The Sinful Ensemble" is another highlight on "Irrational Anthems" with the lyrics talking about the great "villains" of our history enjoying an evening out in a pub ("Vlad impales glace cherries on a stick just for a lark, when Pol Pot turns the lights out they'll play murder in the dark").
	hypnos-reviews.tripod.com /hypnosreviews/id146.html (430 words)

	Irrational Fear and Phobia - Symptoms, Causes and Coping Techniques for social phobia and more
		An irrational fear of public speaking is very common, and it falls into a general class know as social phobias.
		It is not unusual for people of either gender to be "closet phobics" keeping their irrational fears to themselves and pretending to others that they are better than they actually feel.
		Irrational Fears and Phobias - An Introduction to Symptoms
	www.thehealthcenter.info /emotions/irrationalfear (430 words)

	FUNCTION - LoveToKnow Article on FUNCTION
		Functions of Several Variables.A function of several variables differs from a function of one variable in that the argument of the function consists of a set of variables, or is a variable point in.
		The notion of functionality or functional relation of two magnitudes was thus of geometrical origin; but a function soon came to be regarded as an analytical expression, not necessarily an algebraic expression, containing the variable or variables.
		Such functions were introduced into analysis somewhat unsystematically as the need for them arose, and the later developments of analysis led to the introduction of other classes of functions.
	www.1911encyclopedia.org /F/FU/FUNCTION.htm (430 words)

	CD Baby: IRRATIONAL FEAR: Closer to Daylight
		Irrational Fear's unique sound blends elements of Alternative rock, acoustic folk, and the abandon of Punk, to create a sound that is fresh, slightly off center and never generic.
		Irrational Fear is touring regionally in support of their new CD Closer to Daylight.
		Irrational Fear is an active member of LMIA (Louisville Music Industry Alliance) which advocates the Louisville original music scene.
	www.cdbaby.com /irrationalfear (595 words)

	Duple - Open Encyclopedia
		An irrational rhythm, it may also be used as a polyrhythm when played against the regular duration.
		In relation to duple time triple meter rhythms would be triplets.
		Duple is also a duration 3/2 the regular note value duration in compound and or triple meter.
	www.open-encyclopedia.com /Duple (53 words)

	Composite number for pi satisfies Euler's equation.
		is a transcendental number, i.e., an irrational number that is not, and cannot be, the root of an algebraic equation having rational coefficients.
		Transcendental number — An irrational number that cannot be expressed as the root of an algebraic equation having rational coefficients.
		is an irrational number that cannot be expressed as the root of an algebraic equation having rational coefficients, it is called a transcendental number.
	members.ispwest.com /r-logan/fullbook.html (4935 words)

	Square root of 2 is irrational
		It's edifying to recall an estimate of approximation of irrational numbers with rational ones.
		Since the rational numbers form a dense set (i.e., in every interval no matter how small there are always rational numbers) and, since the sum of lengths of all covering intervals is found to be infinite, it would seem that, having so generously covered all rational numbers, we have automatically covered all numbers.
		Consider all rational numbers in the interval from 0 to 1, excluding 0.
	www.cut-the-knot.org /proofs/sq_root.shtml (1034 words)

	Math Forum: Ask Dr. Math FAQ: Integers, Rational Numbers, Irrational Numbers
		The square root of 2 is an irrational number because it can't be written as a ratio of two integers.
		A real number is a number that is somewhere on a number line, so any number on a number line that isn't a rational number is irrational.
		Pi is an irrational number because it cannot be expressed as a ratio (fraction) of two integers: it has no exact decimal equivalent, although 3.1415926 is good enough for many applications.
	mathforum.org /dr.math/faq/faq.integers.html (736 words)

	irrational number - a Whatis.com definition
		An irrational number is a real number that cannot be reduced to any ratio between an integer p and a natural number q.
		Irrational numbers are primarily of interest to theoreticians.
		The union of the set of irrational numbers and the set of rational numbers forms the set of real numbers.
	whatis.techtarget.com /gDefinition/0,294236,sid44_gci283983,00.html (335 words)

	Irrational Anthems mp3 download Skyclad mp3 music download songs
		Irrational Anthems mp3 download Skyclad mp3 music download songs
	albums.vmuz.com /file194440.html (335 words)

	Poster Project, I am a Mathematician: Analysis
		It could be a fraction (which we term a rational number), an integer, or even what is called an irrational number.
		The slope of an arbitrary function at any given point, if it exists, is the slope of a tangent line to the function at that point.
		Is a given function continuous (that is: can you draw its graph without lifting your pencil?) The function we have been looking at is, but that need not be the general case.
	www.math.sunysb.edu /posterproject/www/materials/i-am-math/analysis.html (335 words)

	Aristotle -- General Introduction [Internet Encyclopedia of Philosophy]
		The human soul has an irrational element which is shared with the animals, and a rational element which is distinctly human.
		They are determined ultimately by the judgment of "the good person." Our chief end is the perfect development of our true nature; it thus must be particularly found in the realization of our highest faculty, that is, reason.
		Pleasures accordingly differ in kind, varying along with the different value of the functions of which they are the expression.
	www.iep.utm.edu /a/aristotl.htm (335 words)

	alogon - index page - Free MP3 downloads, CDs, Bio Info, Tour Dates, Lyrics and More!"
		Irrational numbers forced their existence upon the Classical consciousness, but they were demonized, and the Greeks would have no truck with them.
		The terms logos and alogos, loosely translated to mean rational and irrational, give some indication of the significance that the concept of "number as unit" held in the Classical worldview.
		That the Pythagoreans should understand irrational numbers and understand that this knowledge must be suppressed, reflects the incredible dilemma raging in the minds of advanced Classical Greek thinkers.
	www.iuma.com /IUMA/Bands/alogon/index-1.html (274 words)

	poetics.mb.txt
		Such is the irrational element in the introduction of Aegeus by Euripides and the badness of Menelaus in the Orestes.
		The irrational, on which the wonderful depends for its chief effects, has wider scope in Epic poetry, because there the person acting is not seen.
		Thus in the music of the flute and of the lyre, 'harmony' and rhythm alone are employed; also in other arts, such as that of the shepherd's pipe, which are essentially similar to these.
	classics.mit.edu /Aristotle/poetics.mb.txt (13064 words)

	Ring of Living Rhythm Zoëin Jewels
		The irrational and undivided circle is like a blank interval, a poised sound.
		Rhythm is indeed the timing which divides and is divided by, the silent interval.
		The interval is the center of an endless spiral, upon which the harmonies of life resound.
	www.zoeinjewels.com /z_rings/z7.htm (193 words)

	Math Forum - Ask Dr. Math
		The reason it can't have just one irrational root is that an irrational multiplied by a rational is still irrational, so the constant at the end of the quadratic would be irrational.
		Date: 4/10/96 at 14:23:37 From: kelli rostkowski Subject: Algebra: quadratic equations Would you explain to me why a quadratic equation cannot have one irrational or one imaginary root.
		If h is irrational and g isn't, then -h - g is irrational, and hg must also be irrational*.
	mathforum.org /dr.math/problems/rostkowski4.10.96.html (280 words)

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In the News (Fri 18 Dec 09)