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Topic: Square root of minus one

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Imaginary number

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	Square root of minus 1 in The AnswerBank: Science
		basically they couldn't think what the square root of a negative number would be, so they decided that they'd use their imagination.
		as I should have posted earlier, (and fo3nix has since said), the square root of -1 is literally impossible but for at least one branch of theoretical mathematics it has proven helpful to create an answer to it so that other problems can be approached.
		Remember, this only affects theoretical maths and isn't supposed to claim that calculating the square root of any minus number is literally possible.
	www.theanswerbank.co.uk /Science/Question176793.html (354 words)

	Linear Algebra Part Three
		A minus sign is to be prefixed to any term, whose factors are an odd permutation of the principal diagonal.
		Depending on the parity of the taxicab-metric distance from the left-upper corner of the original matrix to the given element, a minus sign is to be prefixed for an odd parity.
		Even worse, the square of the distance may be negative, in which case the metric is not positive.
	www.rism.com /LinAlg/LAthree.htm (4886 words)

	Aisle Say (Boston): THE SQUARE ROOT OF MINUS ONE
		In higher mathematics, the square root of minus one, an imaginary number, is symbolized as lowercase i.
		In Peter Morris's prize-winning undergraduate play, The Square Root of Minus One, this numerical shorthand -- never directly referenced in the text -- is one of the many bits of adolescent cleverness embedded in this rather shallow excellently crafted script.
		And confusion over imaginary numbers is a weak metaphor for the perceived inability of the children of privilege to get a life.
	www.aislesay.com /MA-SQUARE.html (725 words)

	Imaginary Numbers
		By the same token, it could be laid down as a rule that taking the square root of a negative number will not be allowed in algebra: This is actually the practice of my calculator, which flashes "ERROR" when I try that operation.
		Asimov protested that "the square root of minus one is just as real as any other number." Pace the departed and beloved Asimov, this is not quite right, but he certainly is correct that it does not turn mathematicians into mystics.
		A number that is the actual result of an operation of squaring will always be positive, which means that the square root of that number can be either positive or negative.
	www.friesian.com /imagine.htm (4918 words)

	Strand Bookstore: Imaginary Tale; by Paul Nahin (Site not responding. Last check: 2007-11-03)
		In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i, re-creating the baffling mathematical problems that conjured it up and the colorful characters who tried to solve them.
		In the first century, the mathematician-engineer Heron of Alexandria encountered i in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense.
		In "An Imaginary Tale", Paul J. Nahin tells the 2,000-year-old history of one of mathematics most elusive numbers, the square root of minus one, re-creating the baffling mathematical problems that conjured it up and the colorful characters who tried to solve them.
	www.strandbooks.com /profile?isbn=0691027951 (356 words)

	Science a GoGo Forums: Leonhard Euler Worlds Greatest Mathematician, invented.... (Site not responding. Last check: 2007-11-03)
		For those who understand such things, his formula shows that when:- One is added to the transcendental number "e" (2.71828...) raised to the power of Pi (3.14159...) and then multiplied by the square-root of minus one, the result is zero, precisely.
		One is added to the transcendental number "e" (2.71828...) raised to the power of Pi (3.14159...) and then multiplied by the square-root of minus one, the result is zero, precisely.
		One is added to the transcendental number "e" (2.71828...) raised to the power of Pi (3.14159...) multiplied by the square-root of minus one, the result is zero, precisely.
	scienceagogo.com /cgi-bin/ultimatebb.cgi?ubb=get_topic;f=1;t=000225;p=0 (283 words)

	THE DEGREE 33 AND BERNOULLI (Site not responding. Last check: 2007-11-03)
		That is, we should power one third the square root of minus one, which is impossible to do either with a calculating machine or with any of the methods habitually used by the known arithmetic calculus.
		If those calculus could be solved we could know the size of the vector’s module in any of the turning angles, that is how to vary the associated intensity of the unitary vector as it turns.
		With it, the disposition of the system consists in a real axis X and an imaginary axis Y, which is the real X, but multiplied by the square root of -1.
	www.thesymbol.net /Philosophy/degree-33.htm (1087 words)

	GLOSSARY - j 1/j = -j (Site not responding. Last check: 2007-11-03)
		The mathematical Imaginary constant "j" is equal to the square root of minus one.
		In the Complex Plane "j" corresponds to the vertical axis, which can also be called the Y axis, quadrature axis or Imaginary axis.
		The concept of the square root of minus one is a mathematical trick which allows the mathematics of signal processing (and many other disciplines) to be considerably simplified.
	www.magma.ca /~masonjl/Glossary/glos6jai.htm (111 words)

	The Nature of Complex Numbers
		They seem to be predicated upon the existence of a logical contradiction; i.e., the square root of minus one.
		To hypothesize the existence of a square root of minus one and call it imaginary does not asuage the skepticism of the student.
		Thus the square root of -1 is not fictitious or imaginary in the ordinary sense but is simply (0,1).
	www2.sjsu.edu /faculty/watkins/complex.htm (530 words)

	Jack Parsons & the Curious Origins of the American Space Program, Part 22, by The Magician
		We get that the log—we're referring to the natural log, of course—the log of minus one is pi = 3.141592 etc. multiplied by i, the square root of minus one.
		Then they pretended that imaginary numbers, ones involving the square root of minus one, didn't exist, or were absurd, or were meaningless.
		Now, that is exactly how it is today when it comes to the spiritual world, the aliens, the things that go bump in the night, the hyper-dimensional entities that intersect our space-time, cases of coincidence, telepathy, teleportation.
	www.aci.net /Kalliste/Jpar22.htm (1257 words)

	An Imaginary Tale: The Story of i [the square root of minus one] by Princeton University Press
		The author does a great job explaining what the square root of -1 is used and how it is used.
		At the very beginning of his book on i, the square root of minus one, Paul Nahin warns his readers: "An Imaginary Tale has a very strong historical component to it, but that does not mean it is a mathematical lightweight.
		Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma.
	www.negative-procreative.biz /stuff-0691027951.html (1554 words)

	Sokal
		Postulating that a signifier, S, divided by what is signified, s, equals a statement, s, Lacan said that if the signifier is -1, the statement becomes the square root of minus one.
		"That is why it is equivalent to the square root of minus one of the signification produced above, of the enjoyment that it restores by the coefficient of its statement to the function of the lack of signifier.
		There was also no attempt to explain what the male sex organ had to do with the square root of minus one.
	www.ma.utexas.edu /users/blanki/LoveSokal.html (688 words)

	Square Root of Negative One, MP3 Album Music Download at eMusic (Site not responding. Last check: 2007-11-03)
		Now even the snobbiest hardcore, hardstep Anglocentric junglists have no excuse but to give the American drum scene its due: just about everything on We's second album gives the best of the U.K. crew a run for their money.
		Granted, Square Root of Minus One starts out weak, with the shapeless, beatless and tuneless drone of "Birimbau," but things pick up immediately with the frenetic breakbeats and kid vocal samples of "Diablos" and they basically never let up.
		Thrill to the slow and smoky "Caya's Kids," with its dubwise effects, to the cool ethnic percussion and backward bass on "You Gone?," and to the eerie electric piano and reggae-fied beat of "Hielo." Marvel almost as much to most everything else, too.
	www.emusic.com /album/10585/10585983.html (318 words)

	sci.crypt: Re: New formula unlocks base 10 encryption????
		Calculating the extra squarings and testing would be O ^2.
		to the ratio of two integers, such as the square root of 2)...
		enough to judge for themselves whether 3 is a square root...
	www.derkeiler.com /Newsgroups/sci.crypt/2004-01/0740.html (610 words)

	Complex Variables (Site not responding. Last check: 2007-11-03)
		The square root of minus one is not an ordinary or real number.
		But the square root of minus one has such useful properties that its use is unavoidable and has given rise to the branch of mathematics known as complex variables.
		This unusual number has come to be known as i, the imaginary unit, the basis of complex numbers.
	www.dekker.com /sdek/abstract~db=enc~content=a713548076 (227 words)

	Circlemath Homepage
		It is the result of years of study of the Hegelian Philosophy, medicine and physics by Dr. Stephen Taylor.
		of minus one’ can make sense, and how the mind is capable of conceiving objects (a mathematical theory of how nerve cells operate is included).
		Going deeper it examines religion and science in general and looks at the division between matter (the study of physics) and mind.
	homepages.slingshot.co.nz /~robeetay (201 words)

	Amazon.co.uk: An Imaginary Tale: The Story of "I" (the Square Root of Minus One): Books (Site not responding. Last check: 2007-11-03)
		Today, complex numbers have such widespread practical use - from electrical engineering to aeronautics - that few people would expect the story behind their derivation to be filled with adventure and enigma.
		By the time of Descartes, a theoretical use for these elusive square roots - now called "imaginary numbers" - was suspected, but efforts to solve them led to intense, bitter debates.
		The book goes well beyond providing a narrative on the history of "square root of -1".
	www.amazon.co.uk /exec/obidos/ASIN/0691027951 (1080 words)

	Understanding Without Proof
		The hard part is the first: the number e raised to a power with the product of the square root of minus one and pi.
		The square root of minus one is not a regular number like 2 or 3.15159; you cannot place it somewhere on the ancient `number line'; you cannot crawl to it.
		We end up at the location of minus one on the ancient `number line'.
	www.rattlesnake.com /notions/math-metaphor.html (1289 words)

	Theatre Mirror Reviews - "The Square Root of Minus One" (Site not responding. Last check: 2007-11-03)
		In "The Square Root of Minus One" playwright Peter Morris deals, graphically, with nudity, homosexuality, discipline, sado-masochism, masturbation and submission (amid the students) and fatuous, self-serving hypocrisy (among the faculty) of a posh boys boarding-school where only one out of four students (and none of the faculty) even thinks of rules of civil behavior.
		The one --- the point-of-view character --- is a bewildered natural mathematician fascinated by the depravities of everyone around him who searches for the moral equivalent of a useful imaginary number, such as the title, to make sense of it all.
		"The Square Root of Minus One" (15 September - 7 October)
	www.theatermirror.com /sromomtls.htm (338 words)

	Table of Contents for Nahin, P.J.: An Imaginary Tale: The Story of i [the square root of minus one].
		Table of Contents for Nahin, P.J.: An Imaginary Tale: The Story of i [the square root of minus one].
		The Story of i [the square root of minus one]
		([the square root of] -1)[superscript [square root of] -1] to 135 Decimal Places, and How It Was Computed
	www.pupress.princeton.edu /TOCs/c6388.html (71 words)

	Amazon.ca: An Imaginary Tale: The Story of "I" [The Square Root of Minus One]: Books (Site not responding. Last check: 2007-11-03)
		In high school and college mathematics courses it is generally stated that, since the square root of -1 cannot be expressed as any real number, it must be a so-called imaginary number, usually designated as i.
		In this fascinating book Nahin traces the history of the centuries-long struggles which the concept of negative numbers and, eventually, of their square roots caused both mathematicians and philosophers until an obscure Norwegian surveyor discovered the true meaning of i in 1797.
		Clearly this book is not for everyone; but it should be quite interesting to anyone who, like I, never full accepted the concept of an imaginary number.
	www.amazon.ca /exec/obidos/ASIN/0691027951 (1033 words)

	Exchange with a Correspondent on God, Soul, Etc., and Logical Positivism
		The square root of minus one is a mere construction in math.
		> >>The square root of minus one is a mere construction in >>math.
		I can easily think of something for "mermaid" to refer to but there is no way to think of anything for "God" to mean because you cannot have learned the word "creator" except from cases of usage when it meant "creator within the universe".
	www.friesian.com /psitivst.htm (16043 words)

	Amazon.com: An Imaginary Tale: The Story of i [the square root of minus one]: Books: Paul J. Nahin (Site not responding. Last check: 2007-11-03)
		For the most part, however, this is a book that illustrates the equations (or at least their modern counter parts) that led mathematicians to develop the concept of the square root of a negative number, eventually leading to the branch of mathematics we call today complex analysis.
		It was a real let down when I finally finished, and realized how tough it was going to be finding another book to which I would look with such yearning at the end of the day for a relaxing evening of intellectual entertainment.
		The book begins with the story of cubics, and how their solutions involved the square root of negative numbers.
	www.amazon.com /exec/obidos/tg/detail/-/0691027951?v=glance (2926 words)

	Amazon.de: An Imaginary Tale. The Story of the Square Root of Minus One: English Books (Site not responding. Last check: 2007-11-03)
		In "An Imaginary Tale", Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i.
		The material in this book will enable me to flesh out and personalize some ideas which are found in a variety of courses which I teach.
		When someone asks me why anyone ever thought of having a square root of negative one, or what kinds of problems it's good for, this book will enable me to give some interesting answers.
	www.amazon.de /exec/obidos/ASIN/0691027951 (1346 words)

	2005th Meeting, Friday, January 08, 1993 8:30 PM (Site not responding. Last check: 2007-11-03)
		The Square Root of Minus One and Other Mathematical Oddities
		Notable examples include zero, pi, negative numbers, square roots and logarithms.
		Grant will review the first principles (e.g., 2+3=5), present a brief history of the concepts and show how they led to the discovery of the square root of minus one.
	www.philsoc.org /1992Fall/2005abstract.html (161 words)

	Find in a Library: An imaginary tale : the story of [the square root of minus one]
		Find in a Library: An imaginary tale : the story of [the square root of minus one]
		An imaginary tale : the story of [the square root of minus one]
		WorldCat is provided by OCLC Online Computer Library Center, Inc. on behalf of its member libraries.
	worldcatlibraries.org /wcpa/ow/c2d598a580bcd30aa19afeb4da09e526.html (73 words)

	An Imaginary Tale: The Story of i [the square root of minus one] - doctorsbookstore.com Info and Reviews (Site not responding. Last check: 2007-11-03)
		An Imaginary Tale: The Story of i [the square root of minus one] - doctorsbookstore.com Info and Reviews
		Book / An Imaginary Tale: The Story of i [the square root of minus one]
		An Imaginary Tale: The Story of i [the square root of minus one]
	www.doctorsbookstore.com /shop/asinsearch_0691027951.html (533 words)

	Amazon.com: Square Root of Negative One: Music: We (Site not responding. Last check: 2007-11-03)
		Amazon.com: Square Root of Negative One: Music: We Your
		By matching detailed compositions with various physical environments, the idea is that these gatherings will give the music a functional feel.
		Think of Square Root of Minus One as a portable gallery.
	www.amazon.com /exec/obidos/tg/detail/-/B00000I9UP?v=glance (973 words)

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