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Topic: Number 1729

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	1729 (number) - Wikipedia, the free encyclopedia
		I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen.
		1729 is the third Carmichael number, and a Zeisel number.
		Because in base 10 the number 1729 is divisible by the sum of its digits, it is a Harshad number.
	en.wikipedia.org /wiki/1729_(number) (702 words)

	Notable Properties of Specific Numbers at MROB (Site not responding. Last check: 2007-11-06)
		2520 is the smallest number that is divisible by all the numbers from 1 to 10.
		A square pyramidal number is a number in the sequence 1, 5, 14, 30, 55,...
		There are several similar special properties of numbers (for examples, see 39, 89 and 51381) where the distribution falls off so quickly that it's difficult to see if there are only a finite number of numbers with the property.
	home.earthlink.net /~mrob/pub/math/numbers-9.html (2911 words)

	Unlucky 13 by Shyam Sunder Gupta
		Number 13 is the smallest prime number which can be expressed as the sum of the squares of two prime numbers i.e.
		Sum of the numbers from 1 to 13 gives 91 which is the smallest number which can be expressed as the sum of two cubes and also as the difference of two cubes i.e.
		The concatenation of cubes of numbers from 13 to 1 i.e.
	www.shyamsundergupta.com /unlucky13.htm (998 words)

	The Dullness of 1729
		The famous anecdote is that during one visit to Ramanujan in the hospital at Putney, Hardy mentioned that the number of the taxi cab that had brought him was 1729, which, as numbers go, Hardy thought was "rather a dull one".
		So if anyone ever tells me that 1729 is a dull number, I intend to affect a moment of contemplation and then say "Not at all, it is the first occurrance of all ten digits consecutively in the decimal representation of e".
		In a chapter entitled "Lucky Numbers" he tells of going into a small restaurant in Brazil to eat lunch, and he's the only customer in the place so he has four waiters standing around him, and then a Japanese man enters the restaurant, and he is selling abacuses.
	www.mathpages.com /home/kmath028.htm (853 words)

	A Simple Refutation of Gödel's Theorem
		Thus for example, the number 3 is represented in formal logic by the string of symbols 0 -- meaning "The successor of the successor of the successor of nought".
		So even Gödel's method of assigning numbers to symbols, to strings of symbols, and to strings of strings of symbols, of a formal language, does not overcome the fundamental logical objection to the Liar Paradox: which is, essentially, that self-reference is logically quite impossible.
		But he managed it, and was able to define a relation between numbers which obtained just in case the first (even) number was the Gödel number of a proof-sequence which was in fact a valid proof of the well-formed formula whose Gödel number was the second number in the relation.
	homepage.mac.com /ardeshir/Godel-SimpleRefutation.html (2104 words)

	Wikinfo \| One thousand seven hundred twenty-nine
		1729 is a number known as the Hardy-Ramanujan number, after a famous anecdote of the British Mathematician G.
		During one visit to Ramanujan in the hospital at Putney, Hardy mentioned that the number of the taxi cab that had brought him was 1729, which, as numbers go, Hardy thought was "rather a dull one", and that this was a bad omen.
		A tongue-in-cheek proof by contradiction exists showing that all numbers are "interesting." In a classification of numbers as to whether they had interesting properties or not, there would be a smallest number with no interesting properties (for instance, 38 could be a candidate).
	wikinfo.org /wiki.php?title=One_thousand_seven_hundred_and_twenty_nine (280 words)

	Notable Properties of Specific Numbers at MROB
		The fairly popular numbers 8, 24 and 40 are missing from this list; 1260 is the last number to break the number-of-factors record without having 1 through 8, 24 and 40 among its factors.
		Numbers with lots of factors were popular in ancient civilizations; well-known examples include 12, 24, 60 and 360.
		This number has a property which exemplifies some of the many, obscure and somewhat arbitrary investigations into number theory that can be explored by anyone with the interest (and perhaps a personal computer).
	home.earthlink.net /~mrob/pub/numbers-5.html (2783 words)

	Ivars Peterson's MathTrek - Taxicab Numbers
		The first published reference to this property of the integer 1729 is in the writings of 17th-century French mathematician Bernard Frénicle de Bessy (1605-1670).
		The eighth cabtaxi number is now known, and the ninth must have at least 19 digits.
		Wilson, D.W. The fifth taxicab number is 48988659276962496.
	www.maa.org /mathland/mathtrek_07_22_02.html (734 words)

	The Tribune - Windows - Featured story
		Its number was 1729, rather a dull number.
		It is the smallest number expressible as the sum of two cubes in two different ways." To be accurate, Ramanujan should have said "the sum of two positive cubes in two different ways", but that was what he meant anyhow.
		Numbers of its type (the smallest numbers expressible as the sum of 2 cubes in n ways) are also called taxicab numbers.
	www.tribuneindia.com /2000/20000826/windows/main6.htm (469 words)

	Prime Curios!: 1729 (Site not responding. Last check: 2007-11-06)
		The largest number which is divisible by its prime sum of digits (19) and reversal (91) happens to be Ramanujan's famous taxi-cab number (1729 = 12
		It is the smallest number expressible as the sum of two positive cubes in two different ways.
		The smallest number that is a pseudoprime simultaneously to bases 2, 3 and 5.
	primes.utm.edu /curios/page.php/1729.html (71 words)

	NRICH \| Adam McBride (Site not responding. Last check: 2007-11-06)
		Indeed number theory is one of the oldest areas of mathematics, but at the same time it is one of the most vibrant and lively areas of current mathematical research.
		The basic concepts, such as prime numbers and perfect squares, are accessible to quite young children and this adds to the attractiveness of the subject as a topic for a lecture to any audience.
		Around 25 years ago, it was shown that number theory provided the key (in more senses than one!) to the development of a system that could deliver a high level of security.
	nrich.maths.org /conference/reports/mcbride_printable.shtml (1836 words)

	Carmichael Numbers (Site not responding. Last check: 2007-11-06)
		If a number passes the Fermat test several times then it is prime with a high probability.
		Some numbers that are not prime still pass the Fermat test with every number smaller than themselves.
		For each number in the input, you have to print if it is a Carmichael number or not, as shown in the sample output.
	acm.uva.es /p/v100/10006.html (323 words)

	Search Results for "1729" (Site not responding. Last check: 2007-11-06)
		...NUMBER: 1729 AUTHOR: William Shakespeare (1564–1616) QUOTATION: Poor naked wretches, wheresoe er you are, That bide the pelting of this pitiless storm, How shall...
		...NUMBER: 1729 AUTHOR: William O Douglas, Associate Justice, US Supreme Court QUOTATION: The association promotes a way of life, not causes; a harmony in living, not...
		...NUMBER: 4394 AUTHOR: Edmund Burke (1729–1797) QUOTATION: War, says Machiavel, ought to be the only study of a prince; and by a prince he means every sort of state,...
	www.bartleby.com /cgi-bin/texis/webinator/sitesearch?FILTER=&query=1729 (304 words)

	Previous Questions
		The classic examples of these are the numbers used in hash or CRC functions or the coefficients in a linear congruential generator for pseudo-random numbers.
		Upon greeting Ramanujan, Hardy remarked that 1729 seemed like an exceedingly dull number and he hoped that this would not be taken as a bad omen.
		His tales of whole numbers from one to googolplex, fractions, algebraic, transcendental and imaginary numbers is sure to entertain and inform any reader with an interest in the world of numbers.
	www.gomath.com /Questions/question.php?question=40511 (1455 words)

	Sums of Powers - Ramanujan and his Number 1729 - Text Version
		To see the significance of Ramanujan's Number and one other identity of his in this equality scroll down to the end of the page.
		1729 as we all know is 12^3 + 1^3 = 10^3 + 9^3.
		In the example below, 1729 is contained in a beautiful manner.
	users.tellurian.net /hsejar/maths/1729-SOP/1729-SOPtext.htm (740 words)

	The CTK Exchange Forums
		Hardy remarked that he took note of the number of the taxi in which he had arrived, but unfortunately it appeared to be a rather mundane number: 1729.
		However, fortune smiles on Feynman because the number that is chosen to calculate the cube root of is 1729.03.
		Feynman, who at Los Alamos frequently had to deal with large quantities of water, knew that one cubic foot is 1728 cubic inches, and that therefore the cube root of 1728 is 12.
	www.cut-the-knot.com /htdocs/dcforum/DCForumID4/601.shtml (444 words)

	BBC - Radio 4 - A Further Five Numbers 23/08/2005
		More specifically, the first digit of all numbers is a 1 about 30% of the time, whereas it is 9 just 4% of time.
		1729 sparked one of maths most famous anecdotes: a young Indian, Srinivasa Ramanujan, lay dying of TB in a London hospital.
		"1729 is the smallest number you can write as the sum of two cubes, in two different ways." Most of us would use a computer to figure out that 1³ + 12³ = 9³ + 10³ = 1729.
	www.bbc.co.uk /radio4/science/further5.shtml?rhpimage (1049 words)

	The Fifth Taxicab Number is 48988659276962496
		The nth taxicab number is the least number which can be expressed as a sum of two positive cubes in n distinct ways, up to order of summands.
		A brief history of taxicab numbers is given, along with a description of the computer search used by the author to find the 5th taxicab number, 48988659276962496.
		I had ridden in taxi-cab No. 1729, and remarked that the number (7.13.19) seemed to be rather a dull one, and that I hoped it was not an unfavourable omen.
	www.univie.ac.at /EMIS/journals/JIS/wilson10.html (2186 words)

	Amazon.com: The Kingdom of Infinite Number : A Field Guide: Books: Bryan Bunch (Site not responding. Last check: 2007-11-06)
		This book's playful conceit is that a number is like a bird--something that is interesting to observe and identify in its native habitat, flocks together in groups and has distinct behavior patterns, and may be common or rare.
		In this analogy, finite and infinite numbers are "kingdoms"; natural, rational, real, and complex become "genera" of numbers; and factorials, Fibonacci numbers, and the like turn into "families." A problem with this approach is that it introduces nonstandard terminology to discuss mathematics.
		I loved the numbers games and trivia the author used that both reminded me of the trivia questions we all had in school but the math games our family played and plays while on various trips.
	www.amazon.com /exec/obidos/tg/detail/-/0716744473?v=glance (1872 words)

	Puzzle 90.- The prime version of the taxicab problem (the smallest number expressible as the sum of two [prime] cubes ...
		Puzzle 90.- The prime version of the taxicab problem (the smallest number expressible as the sum of two [prime] cubes in two different ways).
		he smallest number expressible as the sum of two [prime] cubes in two different ways).
		It was, he declared, "rather a dull number," adding that he hoped that wasn't a bad omen.
	www.primepuzzles.net /puzzles/puzz_090.htm (276 words)

	Hope Math Dept Newsletter
		We quantify how much better the condition number of the original ill-conditioned matrix is when using this method in a number of cases.
		We had quite a number of students who picked up the Halloween spirit and found that the number of goblins and werewolves were 55 and 65 respectively.
		4096 is the smallest number with 13 divisors?
	www.math.hope.edu /newsletter/newsletter-11-5-03.html (1035 words)

	Taxicab Numbers (Site not responding. Last check: 2007-11-06)
		It is the smallest number expressible as the sum of two [positive] cubes in two different ways." [1]
		In memory of this incident, the least number which is the sum of two positive cubes in n different ways is called the nth taxicab number, which I will denote Taxicab(n).
		In [2], it is shown that for any n >= 1, there indeed exist numbers which are the sum of two positive cubes in n ways, which guarantees the existence of Taxicab(n) for n >= 1.
	pi.lacim.uqam.ca /eng/problem_en.html (267 words)

	EDGE 28
		I think that the acquisition of a language for numbers is crucial, and it is at that stage that cultural and educational differences appear.
		If we grant that we are all born with a rudimentary number sense that is engraved in the very architecture of our brains by evolution, then clearly numbers should be viewed as a construction of our brains.
		In cases where it does fail, animals clearly have the capacity to solve the problem...these are small number situations, for example, fights between two allies against a third, or an assessment of fruit in a pile, or individuals in one group versus a second.
	www.edge.org /documents/archive/edge28.html (8582 words)

	Fields of Mathematics (Site not responding. Last check: 2007-11-06)
		The concept of number is the obvious distinction between the beast and man. Thanks to number, the cry becomes a song, noise acquires rhythm, the spring is transformed into a dance, force becomes dynamic, and outlines figures.
		The imaginary number is a fine and wonderful recourse of the divine spirit, almost an amphibian between being and not being.
		The second nonabsolute number is the given time of arrival, which is now known to be one of the most bizarre of mathematical concepts, a recipriversexcluson, a number whose existence can only be defined as being anything other than itself.
	www.chemistrycoach.com /fields_of_mathematics.htm (11624 words)

	Edge: ON THE NATURE OF MATHEMATICAL CONCEPTS - by Verena Huber-Dyson [page 3]
		The idea of running through the cubes of all integers from 1 to 12 in order to arrive at Ramanujan's spontaneous recognition of 1729 as the smallest positive integer that can be written in two distinct ways as the sum of two integral cubes is inappropriate and obscures the workings of the naive mathematical mind.
		Upon meeting 1729, your first reaction will probably be to break it up into the sum of 1000 and 729, because of our habit of counting in decimal notation.
		That knowledge, always hovering below the threshold of consciousness, prompts the question whether 1729 might in fact be the LEAST positive integer expressible in distinct ways as the sum of two cubes.
	www.edge.org /3rd_culture/huberdyson/huberdyson_p2.html (1766 words)

	Bastien JANSEN - ticalc.org
		Ranked number 628 in our list of busiest authors with 9 files.
		Ranked number 1719 in our list of most downloaded authors all time with 9226 downloads.
		Ranked number 694 in our list of most downloaded authors for the past seven days with 56 downloads.
	www.ticalc.org /archives/files/authors/78/7874.html (45 words)

	Modular arithmetic
		The Fibonacci numbers are the numbers in the sequence 1, 1, 2, 3, 5, 8, 13, 21,...
		Work modulo a number n which is not a prime and show that in general the order of an element need not divide n - 1.
		Experiment by looking at square roots modulo a number of the form 2p where p is an odd prime.
	www-groups.dcs.st-and.ac.uk /CIRCA/gapstuff/gapfiles/Ex.10.html (721 words)

	Answer to Problem of the Week for 08/23/2004
		Originally, I thought the correct answer was 1729 because I did not consider cubes of negative numbers.
		Hardy remarked that the taxi he had come in had the number 1729, which struck him as not a very interesting number.
		Ramanujan disagreed, pointing out that it is the smallest positive integer that can be written in two different ways as the sum of two cubes (of positive whole numbers).
	www.pen.k12.va.us /Div/Winchester/jhhs/math/probweek/p2004/a082304.html (146 words)

	The Taxicab problem
		To many mathematicians, the mere mention of the number 1729 recalls the following incident involving mathematicians G.H. Hardy and Srinivasa Ramanujan:
		Once, in the taxi from London [to Putney], Hardy noticed its number, 1729.
		It is shown that for any n >= 1, there indeed exist numbers which are the sum of two positive cubes in n ways, which guarantees the existence of Taxicab(n) for n >= 1.
	euler.free.fr /taxicab.htm (313 words)

	CRYONICS Alcor Area Code Change (Site not responding. Last check: 2007-11-06)
		Reflecting on my last posting re the area code change (#1715), I see that I may have given the impression that Alcor would be footing the bill for any bracelet replacements.
		Of course, those Alcor USA/Canada members whose bracelets bear the 714 number may want to get a new one which bears the 800 number anyway.
		Those who would like to order one need only call me with a credit card number or send me a check (payable to Alcor, of course) in the same amount.
	www.cryonet.org /cgi-bin/dsp.cgi?msg=1729 (222 words)

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