
	Where results make sense

Topic: Champernowne constant

	Champernowne constant - Wikipedia, the free encyclopedia
		Computing Champernowne's constant can be done by concatenation of bit strings on a computer, but this may not necessarily be the fastest way of computation.
		Clearly Champernowne's constant is irrational, since rational numbers have a repeating or terminating expansion into digits to the right of the "decimal" (radix) point.
		Champernowne, The construction of decimals normal in the scale of ten, Journal of the London Mathematical Society, vol.
	en.wikipedia.org /wiki/Champernowne_constant (746 words)

	Champernowne constant -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-06)
		In (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics, the Champernowne constant C
		is a certain (Any rational or irrational number) real number, named after (A person skilled in mathematics) mathematician D. Champernowne.
		It is a simple number to construct, which has some important properties.
	www.absoluteastronomy.com /encyclopedia/c/ch/champernowne_constant.htm (765 words)

	D. G. Champernowne - tScholars.com (Site not responding. Last check: 2007-11-06)
		David Gawen Champernowne (july 9,1912 - august 19,2000, Professor of Statistical Economics at Oxford (1948 -1959), and professor of Economics and Statistics at Cambridge (1970-2000).
		Published Champernowne's Number in 1933 while still an undergraduate at Cambridge.
		After academic work at Cambridge and the London School of Economics, he worked in the Prime Minister's Statistical department and helped to supply quantitative information to help Churchill make decsions.
	www.tscholars.com /encyclopedia/D._G._Champernowne (277 words)

	Champernowne Constant (Site not responding. Last check: 2007-11-06)
		Continued Fraction of the Champernowne constant is [0, 8, 9, 1, 149083, 1, 1, 1, 4, 1, 1, 1, 3, 4, 1, 1, 1, 15,
		Copeland-Erdös Constant, which is the decimal obtained by concatenating the
		Champernowne, D. ``The Construction of Decimals Normal in the Scale of Ten.'' J.
	mathserver.sdu.edu.cn /mathency/math/c/c209.htm (146 words)

	Lost Boy: Champernowne's Constant
		Sequences that meet this restriction are apparently known as "normal numbers".
		The first explicit (rather than theoretical) example of a normal number is Champernowne's Constant which was produced (discovered?) in 1933.
		David Champernowne pointed out that if one starts with zero, then one then string together all possible pairings, then all eight triples, an so on you end up with a number which must, by construction, contain all possible patterns, and is therefore "normal".
	www.ldodds.com /blog/archives/000154.html (305 words)

	Champernowne constant - Encyclopedia, History, Geography and Biography
		Champernowne constant - Encyclopedia, History, Geography and Biography
		D. Champernowne, The construction of decimals normal in the scale of ten, Journal of the London Mathematical Society, vol.
		This encyclopedia, history, geography and biography article about Champernowne constant contains research on
	www.arikah.net /encyclopedia/Champernowne_constant (874 words)

	xTalk: Proposal: Constants
		A constant without the value is to be looked up in a built-in table of well-known constants.
		If the constant is not found in said table, the line is in error.
		The following constants are "well known constants": pi e i (this is going to open a can of worms...) any others that we think of adding The main two goals are to: a) Allow the user to create symbolic names for numbers b) Allow the addition of constants without breaking scripts.
	www.mail-archive.com /xtalk@metacard.com/msg00099.html (327 words)

	Citations: Note on normal numbers - Copeland, Erdos (ResearchIndex)
		....fractions, noting for the moment that the Champernowne constant has some gargantuan elements in its simple continued fraction, as can be seen by simple numerical experiments.
		....Champernowne proved that for b = 10 the above sequence is normal 3 in the scale of ten, so it is disjunctive.
		More recently Schi er [Sc] and Nakai and Shiokawa [NS] proved that for a non constant, eventually increasing polynomial p, the number 0: p(1) p(2) p(3) is also a normal number.
	citeseer.ist.psu.edu /context/273562/0 (654 words)

	[No title]
		Copeland and Erdos proved in 1945 that this number is normal (in all bases), and it is therefore called the Copland-Erdos constant.
		But then it wouldn't be a constant, as it would depend on the base.
		The constant I gave originally is called Champernowne's > constant, which is stated to be normal in base 10.
	www.math.niu.edu /~rusin/known-math/99/copeland (818 words)

	Numbers and Functions as Continued Fractions - Numericana
		The number known to recreational mathematicians as Champernowne Constant has a decimal expansion consisting of the successive digits of all the integers: 0.123456789101112131415161718192021...
		Champernowne Constant is thus "almost" equal to 60499999499 / 490050000000: The two decimal expansions match for the part corresponding to the integers 0 to 97, (0.123456...899091929394959697) after which point the fraction goes on 99000102030405...
		There is an attractive flavor of universality about continued fractions: Every number has one and only one representation as a continued fraction (if we rule out unity as the last element of a finite continued fraction of two or more elements).
	home.att.net /~numericana/answer/fractions.htm (3614 words)

	Champernowne constant (Site not responding. Last check: 2007-11-06)
		is a certain normal realnumber, named after mathematician D. Champernowne.
		Similar constants can be defined for bases other than 10; for example,
		Champernowne, The construction of decimals normal in the scale of ten, Journal of the London MathematicalSociety, vol.
	www.therfcc.org /champernowne-constant-218287.html (56 words)

	[No title]
		Evaluation of Artin's constant and the twin-prime constant.
		0.123456789101112131415161718192021222324252627282930313233343536373839404142434 445464748495051525354555657585960616263646566676869707172737475767778798081828 384858687888990919293949596979899100101102103104105106107108109110111112113114 115116117118119120121122123124125126127128129130131132133134135136137138139140 141142143144145146147148149150151152153154155156157158159160161162163164165166 167168169170171172173174175176177178179180181182183184185186187188189190191192 193194195196197198199200201202203204205206207208209210211212213214215216217218 219220221222223224225226227228229230231232233234235236237238239240241242243244 245246247248249250251252253254255256257258259260261262263264265266267268269270 271272273274275276277278279280281282283284285286287288289290291292293294295296 297298299300301302303304305306307308309310311312313314315316317318319320321322 323324325326327328329330331332333334335336337338339340341342343344345346347348 349350351352353354355356357358359360361362363364365366367368369370371372373374 375376377378379380381382383384385386387388389390391392393394395396397398399400 401402403404405406407408409410411412413414415416417418419420421422423424425426 427428429430431432433434435436437438439440441442443444445446447448449450451452 453454455456457458459460461462463464465466467468469470471472473474475476477478 479480481482483484485486487488489490491492493494495496497498499500501502503504 505506507508509510511512513514515516517518519520521522523524525526527528529530 531532533534535536537538539540541542543544545546547548549550551552553554555556 557558559560561562563564565566567568569570571572573574575576577578579580581582 583584585586587588589590591592593594595596597598599600601602603604605606607608 609610611612613614615616617618619620621622623624625626627628629630631632633634 635636637638639640641642643644645646647648649650651652653654655656657658659660 661662663664665666667668669670671672673674675676677678679680681682683684685686 687688689690691692693694695696697698699700701702703704705706707708709710711712 713714715716717718719720721722723724725726727728729730731732733734735736737738 739740741742743744745746747748749750751752753754755756757758759760761762763764 765766767768769770771772773774775776777778779780781782783784785786787788789790 791792793794795796797798799800801802803804805806807808809810811812813814815816 817818819820821822823824825826827828829830831832833834835836837838839840841842 843844845846847848849850851852853854855856857858859860861862863864865866867868 869870871872873874875876877878879880881882883884885886887888889890891892893894 895896897898899900901902903904905906907908909910911912913914915916917918919920 921922923924925926927928929930931932933934935936937938939940941942943944945946 947948949950951952953954955956957958959960961962963964965966967968969970971972 973974975976977978979980981982983984985986987988989990991992993994995996997998 999 ----------------------------------------------------------------------------- Copeland-Erdos constant, the primes concatenated.
		1.0303455242162108324415524375441423913311674535426350477520603769436858333367 078466536634299653186541372113411215861485309267528306708178141431148217377434 464491473535305791217064585171952378312515789548509946623397488705415787396598 914128956695347553752512638550318082771091427083769596910701526504657102657014 692869502510623838492054960512997771472559153485184037328476999471131102482175 108766705405357550641075673536209065070065612083371548796051824396699408865713 070119453591522563130261505375573780321442206315118412633701828205392108525782 413195330127295606671997427108097591179860083444244927443504416473570457716741 027361944790276285858904376391561055460513844056484484786473059281875288705999 618242118516344206637486889073335672784807640819659793662267947301826094178286 628556298718293181640871018794887107215120378358047902368736163774600113536888 571530806116406546769959374670822838831591995246739397760825519219044581209189 563299741163333901285277924920149254250155930276721158235118621942060338299354 365607743394171754382061635835272405348932946679933596759506206130017828475418 918307145 ----------------------------------------------------------------------------- Feigenbaum reduction parameter 2.502907875095892822283902873218215786381271376727149977336192056 Feigenbaum bifurcation velocity constant 4.669201609102990671853203820466201617258185577475768632745651343 00413433021131473 References : Briggs, Keith A precise calculation of the Feigenbaum constants.
	www.lacim.uqam.ca /~plouffe/articles/Miscellaneous.txt (869 words)

	CONSTANT (Site not responding. Last check: 2007-11-06)
		Search the CONSTANT Family Message Boards at Ancestry.com (if available).
		Search the CONSTANT Family Resource Center at RootsWeb.com (if available).
		Find graves of people named CONSTANT at Find-a-Grave.com (or add one that you know).
	www.worldhistory.com /surname/US/C/CONSTANT.htm (73 words)

	Miscellaneous Mathematical Constants - Table of Contents (Site not responding. Last check: 2007-11-06)
		The Backhouse constant calculated by Philippe Flajolet INRIA Paris to 1300 places.
		Si(Pi) or the Gibbs Constant to 1024 places.
		The Varga constant, also known to be the 1/(one-ninth constant).
	www.worldwideschool.org /library/books/sci/math/MiscellaneousMathematicalConstants/toc.html (153 words)

	MathGroup Archive: April 1999 [00186]
		A quite artificial but nevertheless interesting construction in recreational maths is the Champernowne Constant, defined in Eric Weisstein's Concise Encyc.
		I suppose that rounding errors and inadequate precision are coming into play with this situation as it is now.
		So I wonder if anyone knows a workable method of obtaining the correct continued fraction period of a difficult case like the Champernowne const.
	forums.wolfram.com /mathgroup/archive/1999/Apr/msg00186.html (186 words)

	MathGroup Archive: April 1999 [00273]
		Alan W.Hopper wrote: > A quite artificial but nevertheless interesting construction > in recreational maths is the Champernowne Constant, defined > in Eric Weisstein's Concise Encyc.
		In[2]:= x = Champernowne[ 17000 ];//Timing Out[2]= {3.06 Second, Null} Next find the continued fraction, which is a kernel function in version 4.0.
		In[3]:= cf = ContinuedFraction[ x ];//Timing Out[3]= {1.96 Second, Null} The ContinuedFraction function will take care of error control for inexact numbers by only returning partial quotients that are justified by the precision of the input value - this was not the case in the NumberTheory package in version 3.0.
	forums.wolfram.com /mathgroup/archive/1999/Apr/msg00273.html (315 words)

	Tables of Constants
		The following is a list of known constants with a precision of 16 digits.
		If you would like more information on these constants, please refer to the list (classified by subject area) at the end of the page.
		1.002008392826082 Zeta(9) 1.008349277381922 Zeta(7) 1.030345524216210 exp(Pi)/Pi^E 1.030640834100712 Continued Fractions constant (base 10).
	pi.lacim.uqam.ca /eng/table_en.html (106 words)

	On the Random Character of Fundamental Constant Expansions - Bailey, Crandall (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		Here normal to a given base b means that all m long base b digit strings occur with a limiting frequency that is precisely what one...
		Bailey, R. Crandall, On the random character of fundamental constant expansions, manuscript, http://www.perfsci.com/free/techpapers.
		On the Khintchine Constant - Bailey, Borwein, Crandall (1997)
	citeseer.ist.psu.edu /481409.html (575 words)

	MATHEWS: Smarandache Concatenated Sequences
		Interpret the sequence as the digits of a constant.
		There are no primes in the first 8000 terms (note that the 8000nd term has more than 30000 digits).
		The sequence gives the digits of the Champernowne constant which is normal in base 10.
	www.wschnei.de /sequences/smarandache-concatenated-sequences.html (346 words)

	Omega constant -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-06)
		Omega constant -- Facts, Info, and Encyclopedia article
		The Omega (A number representing a quantity assumed to have a fixed value in a specified mathematical context) constant is the value of W(1) where W is (Click link for more info and facts about Lambert's W function) Lambert's W function.
		The name is derived from the alternate name for Lambert's W function, viz., the Omega function.
	www.absoluteastronomy.com /encyclopedia/O/Om/Omega_constant.htm (145 words)

	[No title]
		Once discovered, the {\it proof} is an elementary calculus exercise, but the haystack of such formulas is infinitely large, and to find the `just right' formula requires ingenious experimental mathematics, that the authors generously share with the readers.
		There is also has a very interesting chapter on {\it normality}, that attempts to tackle the famous, notoriously difficult, problem of proving that the decimal (or any base) expansion of famous constants like $e$ and $\pi$ behave `randomly'.
		Aside from some constructive-but-contrived numbers (the {\it Champernowne constant} $0.12\dots891011\dots9899100101102\dots$ and natural-but-non-constructive numbers (like Chaitin's $\Omega$), there are no known examples.
	www.math.rutgers.edu /~zeilberg/mamarim/mamarimTeX/mathexp.tex (905 words)

	Welcome to Mathsoft (Site not responding. Last check: 2007-11-06)
		Flajolet and B. Vallée, Continued fraction algorithms, functional operators, and structure constants, Theoret.
		Mukherjee and G. Karner, Irrational numbers of constant type – a new characterization, New York J. Math.
		Guangheng Ji and Hongwen Lu, On dispersion and Markov constants, Monatsh.
	www.mathsoft.com /mathsoft_resources/mathsoft_constants/ref/2122.asp (531 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		%H A087491 Eric Weisstein's World of Mathematics, Khinchin's Constant %H A087491 Eric Weisstein's World of Mathematics, Khnichin Harmonic Mean %e A087491 1.74540566...
		%H A050996 S. Plouffe, The Parking or Renyi constant %H A050996 S. Plouffe, The Parking or Renyi constant %H A050996 E. Weisstein, Link to a section of The World of Mathematics.
		%H A072558 Steven Finch, The One-Ninth Constant %H A072558 Alphonse P. Magnus, Jean Meinguet, The elliptic functions and integrals of the '1/9' problem %H A072558 Simon Plouffe, The One-ninth constant %H A072558 Eric Weisstein's World of Mathematics, One-Ninth Constant %e A072558 0.1076539192264845766153234450909471905879...
	akpublic.research.att.com /~njas/sequences/eisBTfry00077.txt (7012 words)

	MathGroup Archive (2000/04) - Maxim Rytin / Champernowne (Site not responding. Last check: 2007-11-06)
		Maxim Rytin is the author of the delightful "Champernowne Constant and Its Continued Fraction Expansion" ...
		Don't really understand the math well enough to know if this is fixable.
		Defined as the decimal number having after the decimal point the digits of consecutive natural numbers beginning with one: 0.12345678910111213..., the simple continued fraction expansion of Champernowne is [0; 8, 9, 1, 149083, 1, 1, 1, 4, 1, 1, 1, 3, 4, 1, 1, 1, 15, 457540111391031076483646628242956118599603939710457555000662004393090262 659256314937953207747128656313864120937550355209460718308998457580146986 3148833592141783010987, 6,...].
	hilbert.math.hr /arhive/mathgroup/2000/04/0099.html (168 words)

	hwx.html (Site not responding. Last check: 2007-11-06)
		Find a z whose orbit comes within e of both x and y.
		Champernowne's constant is the number C = 0.123456789101112131415....
		Show that for any e > 0 and any x and y, the orbit of Champernowne's constant comes within e of both x and y.
	www.sju.edu /~rhall/Chaos/hw6.html (488 words)

	Miscellaneous Mathematical Constants, Equations, Derivations... - Full Text Free Book (Part 1/4)
		An index of high precision tables of functions can be found at:
		for his kind permission to distribute this collection of constants.
		The Backhouse constant calculated by Philippe Flajolet INRIA Paris to
	www.fullbooks.com /Miscellaneous-Mathematical-Constants1.html (231 words)

	Oddly Irrational (Site not responding. Last check: 2007-11-06)
		= = Alex = = Thanks, sorry, I was still thinking of Champerowne's constant rather than Louiville when I challenged the result...
		On Sun, 8 Aug 2004 14:03:10 -0500, "amcwill417" Champernowne constant has an obvious rule generating it.
		The Champernowne constant has an obvious rule generating it.
	www.thehelparchive.com /new-2304030-278.html (1264 words)

Try your search on: Qwika (all wikis)