
	Where results make sense

Topic: Imagining Numbers

Related Topics

Ross Noble Goes Global

Rules of Engagement (movie)

Absolute Monarchy in Sweden

Aland Islands

Emperor Otto II

1996 Republican National Convention

Structural pattern

	Amazon.com: Reviews for Imagining Numbers: (particularly the square root of minus fifteen): Books: Barry Mazur (Site not responding. Last check: 2007-11-02)
		Now imaginary numbers, and roots in general for that matter, are not the most straightforward things in math, yet many of us encounter them in high school, along with trig functions, polar coordinates, and other things we didn't understand.
		Barry Mazur's Imagining Numbers is a noble effort to get the reader [especially those of a more poetical bent] to think about [and perhaps experience] abstract mathematical thinking that falls short of its goal, but because Professor Mazur muses in such an entertaining and literate fashion, the book is worth a read.
		In Imagining Numbers (particularly the square root of minus fifteen) (Farrar, Straus, and Giroux), Harvard mathematician Barry Mazur has given a poetic and absorbing illustration of what it is to imagine mathematically.
	www.amazon.com /Imagining-Numbers-particularly-square-fifteen/dp/customer-reviews/0374174695 (3120 words)

	Read This: Imagining Numbers (Site not responding. Last check: 2007-11-02)
		The example Mazur is referring to is the acceptance into the collective mathematical imagination of the square root of negative numbers.
		Insofar as Imagining Numbers has something to offer mathematicians, it is the approach he adopts, and the literary devices he employs, to try to convey something of the act of mathematical imagination to readers who have never knowingly experienced it.
		Publication Data: Imagining Numbers (particularly the square root of minus fifteen), by Barry Mazur.
	www.maa.org /reviews/imagining.html (948 words)

	[No title] (Site not responding. Last check: 2007-11-02)
		The complex numbers fill out the "complex plane." The point up one unit from 0 is written i.
		Maybe complex numbers seem obscure because you are used to imagining numbers by giving them units: 5 cars, or -3 miles.
		It takes a number to the number pointing in the opposite direction with the same distance from the origin.
	www-math.mit.edu /18.03/spr04/lectures/lec05.txt (735 words)

	Hilldale Lectures in the Physical Sciences - University of Wisconsin-Madison - 2004-2005
		This Table has clearly admirable and extraordinary properties, for beyond what I have already shown of the mystery of combinations hiding within it, it is known to those skilled in the more hidden parts of geometry that the most important secrets of all the rest of mathematics lie concealed within it.
		The lecture will show how Bernoulli numbers themselves are connected with much of the rest of mathematics, pure and applied, and how they unify branches of mathematics as disparate as differential topology and modular forms.
		He is the author of approximately 100 articles and books, including the recent "Imagining Numbers (particularly the square root of minus fifteen)" comparing mathematics with poetry.
	www.secfac.wisc.edu /lectures/hilldale/physical/20042005Mazur.htm (280 words)

	Understanding Large Numbers
		One way to better understand large numbers is to compare the heights of stacks of varying numbers of dollar bills.
		Another way to appreciate large numbers is to consider the area covered by varying numbers of dollar bills.
		Yet another way to understand large numbers is to compare the lengths of varying numbers of dollar bills laid end-to-end.
	www.ehd.org /science_technology_largenumbers.php (1279 words)

	A problem squared \| By genre \| Guardian Unlimited Books
		Imagining Numbers charts the mental journey that the collective mathematical psyche experienced as it came to terms with the shocking idea that a negative number might have a square root.
		Some will relish this invitation to get their hands dirty but the sheer weight of diagrams and equations is sure to leave others in a state of 16th-century denial.
		Despite the effort put in by the reader to learn the time signatures and scales of imaginary numbers, they are not put to more use in explaining the wonderful compositions that mathematicians have written since their creation.
	books.guardian.co.uk /reviews/scienceandnature/0,6121,1065346,00.html (772 words)

	[No title]
		18.03 Class 5, Feb 17, 2006 Complex Numbers, complex exponential Today, or at least 2006, is the 200th anniversary of the birth of complex numbers.
		In 1806 papers by Abb\'e Bul\'ee and by Jean-Robert Argand established the planar representation of complex numbers.
		They had already been in use for several hundred years, but they were kept fairly secret and were regarded as perhaps not entirely real.
	www-math.mit.edu /18.03/spr06/lecs/c05 (767 words)

	On Mathematical Imagination - Harvard Magazine (January-February 2004)
		Those wonderful outworks of the imagination that mathematicians produce rarely make it to the classroom, where mind-numbing drill in what seems a dead language tends to rule instead.
		In his contemplation of modern poetry and his coming to grips with how Renaissance mathematicians made sense of their strange new numbers, it is always the internal structure of the act of imagining that Mazur arrows toward.
		The Math Circle, The Magic of Numbers, and Imagining Numbers are part of a New Instauration that will bring mathematics, at last, into its rightful place in our lives: a source of elation through the questions it puts to us and the answers we shape.
	www.harvardmagazine.com /on-line/010442.html (1436 words)

	Imagining the Next Bill Gates
		It was like watching the first oil well gushing from a Pennsylvania farm in the 1860s -- and imagining 100 million cars and the emergence of John D. Rockefeller as the richest man in America.
		First, they are each attracting huge numbers of very smart scientists and engineers from around the world -- and one should never underestimate the potential of combined intellectual horsepower.
		Engineers and scientists are increasingly able to manipulate an unimaginable combination of molecules with unique electronic and biological attributes, creating a whole new generation of building blocks every bit as malleable, fungible, and extendable as 1s and 0s -- and at increasingly lower cost.
	www.businessweek.com /technology/content/nov2005/tc20051104_013385.htm (1396 words)

	Science Netlinks: Science Updates
		Now imagine that you’re looking at a number line: say, the numbers between one and eight.
		That’s what seems to be happening in these patients, even though they weren’t asked to picture a number line.
		And that suggests that in some way, they were imagining the numbers as points in space, like you might see on a graph in math class.
	www.sciencenetlinks.com /sci_update.cfm?DocID=122 (734 words)

	Minus numbers \| Cosmic Variance
		And when I tried to think of minus one I was trying to imagine an anti-cabbage, an anti-matter cabbage, which was as hard as conceiving of an alternative universe.
		And the “alternative universe” comparison is spot on — the difference between imagining the existence of negative numbers and imagining the existence of extra dimensions of space is one of degree, not of kind.
		I had a similar experience when I was introduced to imaginary numbers by an inept teacher who couldn’t, or didn’t bother, to adequately explain the idea behind the “number” ‘i’.
	cosmicvariance.com /2005/08/03/minus-numbers (1690 words)

	Try this with a slice of pi \| csmonitor.com (Site not responding. Last check: 2007-11-02)
		Mazur explores the history of imaginary numbers, that is, numbers that are some multiple of the square root of minus 1.
		He evocatively recreates the bewilderment of the Renaissance scholars who first grappled with this idea, and through the lens of their imagination, he leads the reader to a deeper comprehension of the realm of numbers.
		Remarkably, the answer seems to be somehow connected to the realm of complex numbers, that is, of numbers that have one real part and one imaginary.
	www.csmonitor.com /2003/0410/p19s02-bogn.html (1088 words)

	Take a Journey Inside Your Imagination
		IMAGINING NUMBERS (particularly the square root of minus fifteen) is an invitation to those who take delight in the creative work of reading poetry but may have no background in math, to take a leap of the imagination in mathematics.
		Imaginary numbers entered into mathematics in sixteenth-century Italy and were used with immediate success, but nevertheless presented an intriguing challenge to the imagination.
		Mazur presents us with a fascinating exploration of how we comprehend and develop ideas both in poetry and in math, from the Renaissance through to the present day, and provides us with a step-by-step guide to how we can begin imagining numbers for ourselves.
	www.mi.sanu.ac.yu /vismath/sg/mazur.htm (375 words)

	Re-Imagining Ireland :: Panels
		Keynote Panel: Re-Imagining Ireland If, as Benedict Anderson has claimed, nations and identities are, to begin with, “imagined communities,” then they are constantly being re-imagined in response to history — to changing political, social and cultural realities.
		century with an imagination and energy which can be of importance globally.
		The public is more than ready for this kind of program. It is long overdue the Re-Imagining Ireland project is the most imaginative and exciting project on the Irish diaspora that has been conceived to date on either side of the Atlantic.
	www.re-imagining-ireland.org /events/panels.asp (1159 words)

	village voice > arts > Education Supplement by Dennis Lim
		A prime is a number perfectly divisible only by itself and the number 1; while every other number can be expressed as the product of at least two primes, the primes themselves are irreducible (11, 89, and 6,971, for instance, are prime; 15, which can be written as 3 x 5, is not).
		The complex numbers for which the zeta function equals zero are called the Riemann zeros; the frequency of the Riemann zeros mirrors the frequency of the primes.
		Ten to the 10th power, to the 10th power, to the 34th power—a strong contender for the most meaningless result in mathematics, since Skewes's number, as it would be called, is so preposterously huge as to be beyond human comprehension (there are fewer atoms in the universe, Goldfeld points out).
	www.villagevoice.com /arts/0316,edlim,43389,12.html (2496 words)

	Imagining Numbers: Particularly the Square Root of Minus Fifteen. - Barry Mazur - book review Science News - Find ...
		Imagining Numbers: Particularly the Square Root of Minus Fifteen.
		In this esoteric tome, Harvard mathematician Mazur addresses what it's like to think creatively like a mathematician and be able to imagine the square root of negative numbers.
		In all, Mazur explains how we comprehend and develop ideas both in poetry and math and helps readers understand how to begin imagining numbers themselves.
	www.findarticles.com /p/articles/mi_m1200/is_8_163/ai_98977997 (182 words)

	Imagining Numbers. (Books).(Book Review)(Brief Article) - The Antioch Review - HighBeam Research
		Author: Holyoke, T.C. Imagining Numbers by Barry Mazur.
		Here he uses poetry and aesthetics to illuminate the role of imagination in the discovery of far-reaching connections among algebra, geometry, and trigonometry.
		The vehicle here is the invention of so-called imaginary numbers and their progeny the complex numbers and their role in the mysterious Dal Ferro formula for the solution of cubic equations that involves non-real numbers when the three solutions are all real.
	www.highbeam.com /doc/1G1-102023941.html (146 words)

	Answers and Explanations -- Do "Imaginary Numbers" Really Exist? (Site not responding. Last check: 2007-11-02)
		An "imaginary number" is a multiple of a quantity called "i" which is defined by the property that i squared equals -1.
		This is puzzling to most people, because it is hard to imagine any number having a negative square.
		At that point in time, people were imagining what it would be like to have a number system that contained square roots of negative numbers, hence the name "imaginary".
	www.math.toronto.edu /mathnet/plain/answers/imaginary.html (343 words)

	An invisible sign of my own by Aimee Bender \| LibraryThing
		Imagining numbers : (particularly the square root of minus fifteen) by Barry Mazur
		Numbers : an introduction and commentary by Gordon J. Wenham
		Number, the language of science by Tobias Dantzig
	www.librarything.com /work.php?book=87457 (488 words)

	Croatia - Historical Military Flags
		What seems odd to me is the high number assigned--somehow I doubt that there were 368 other regiments in the FSC army.
		Comparing with today (imagining numbers for I do not know them exactly), and armoured battalion would be (say) 671th through 679th, while there'd be no other units with numbers of 600 through 700.
		In the catalogue of the exhibition of flags held in 1996, it is indeed stated that the flag in question is made only in 1943, after the new regulations on unit flags was issed on 4-MAY-1943 and new flags were authorized (granted) by Poglavnik.
	www.fotw.net /flags/hr^hist.html (2036 words)

	The meaning of numbers
		Hello my name is John and I'm having a philosophical debate on the meaning of numbers, equations, or the world of math in general.
		Would it be possible if you could help me by giving me a resource that talks about it or if you have your own opinion I would be most grateful.
		Barry Mazur, Imagining Numbers (particularly the square root of minus fifteen), Farrar Straus Giroux, 2003.
	mathcentral.uregina.ca /QQ/database/QQ.02.06/john1.html (151 words)

	Amazon.com: Imagining Numbers: (particularly the square root of minus fifteen): Books: Barry Mazur (Site not responding. Last check: 2007-11-02)
		Fearless Symmetry: Exposing the Hidden Patterns of Numbers by Avner Ash
		"Barry Mazur’s Imagining Numbers is quite literally a charming book; it has brought even me, in a dazed state, to the brink of mathematical play."
		cubic radicals, positive whole numbers, analytic art, three cube roots, minus times, number whose square, imaginary numbers, distributive law, imaginary quantities
	amazon.com /Imagining-Numbers-particularly-square-fifteen/dp/0374174695 (2546 words)

	Imagining large numbers < Marking time < autobio < Peter Marquis-Kyle (Site not responding. Last check: 2007-11-02)
		One thousand, eight hundred and six Americans of Japanese ancestry from Placer County, California were interned during the Second World War.
		I thought we needed to find a way to visually show what the number of citizens from this tiny county looked like, Gill said.
		At the end of the display period each of the cups was given away, with obligations attached.
	www.marquis-kyle.com.au /mt/000097.htm (344 words)

	TeacherSource . Recommended Books . Math \| PBS (Site not responding. Last check: 2007-11-02)
		The book is organized by the numbers 1-10; each number provides practice on a specific part of the multiplication table through scenarios like Noah's Ark, finding clothes in drawers and closets, and much more.
		In the process of exploring imaginary numbers, Mazur examines the role of imagination and imagery in poetry and mathematics, reviewing the work of Girolamo Cardano and Rafael Bombelli.
		Robert, a 12 year old who hates math, has a series of dreams in which a number devil manages to make difficult mathematical principles understandable.
	www.pbs.org /teachersource/recommended/math/bk_basiccomputation.shtm (1375 words)

	Math Digest (Site not responding. Last check: 2007-11-02)
		The idea of the book is to give readers some intuition about that staple of high school algebra courses, imaginary numbers.
		The book is not an easy read: "I found that I needed more than pencil and paper to make these calculations.
		Nevertheless, he found the book to be fascinating and provocative.
	e-math.ams.org /mathmedia/mathdigest/200306-mazur.html (79 words)

	Mental Calculation - Tips & Tricks - Substraction
		When working with these operations it's very useful to picture numbers in groups...
		Visualize a 14 as a group of 10 and a group of 4.
		It's a mater of playing with the numbers, if it were
	www.answermath.com /tips/substraction1.htm (145 words)

	The Harvard Crimson :: Magazine :: Beauty is Math, and Math Beauty
		The Gade University Prof explains that if you ask mathematicians to “talk about a 10-D space and visualize it,” it wouldn’t be a problem.
		But in “Imagining Numbers,” his 2002 book, he hopes to explain such mind-bogglers to scholars outside the TI-83 set.
		Mazur’s book, with the parenthetical subtitle “Particularly the Square Root of Minus Fifteen,” started as a letter explaining imaginary numbers to Michel Chaouli, a professor of German and comparative literature at Indiana University.
	www.thecrimson.com /article.aspx?ref=512656 (207 words)

Try your search on: Qwika (all wikis)