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Topic: Mathematical constants


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  Mathematical constant - Wikipedia, the free encyclopedia
A mathematical constant is a quantity, usually a real number or a complex number, that arises naturally in mathematics and does not change.
Therefore, f(1)/f(0) is a mathematical constant, the constant e.
Mathematical constants are typically elements of the field of real numbers or complex numbers.
en.wikipedia.org /wiki/Mathematical_constant   (336 words)

  
 Encyclopedia: Mathematical constant
The Euler-Mascheroni constant is a mathematical constant, used mainly in number theory, and is defined as the limiting difference between the harmonic series and the natural logarithm: Intriguingly, the constant is also given by the integral: Its value is approximately γ ≈ 0.
The Meissel-Mertens constant is a mathematical constant, used mainly in number theory, and is defined as the limiting difference between the harmonic series summed only over the primes and the natural logarithm of the natural logarithm: Its value is approximately M ≈ 0.
The Sierpińskis constant is a mathematical constant usually denoted as K. One way of defining it is by limiting the expression: where r2(k) is a number of representations of k as a sum of the form a2 + b2 for natural a and b.
www.nationmaster.com /encyclopedia/Mathematical-constant   (3463 words)

  
 Mathematical constants   (Site not responding. Last check: 2007-11-06)
Numbers, Constants and Computation Mathematical, historical and algorithmic aspects of some classical mathematical constants.
Tables of Mathematical Constants A list of known constants with a precision of 16 digits.
Enumeration Constants vs. Constant Objects Presents insights on choosing between symbolic constants as either enumeration constants or constant objects.
www.serebella.com /encyclopedia/article-Mathematical_constants.html   (218 words)

  
 Buecher Kaufempfehlung: Mathematical Constants (Encyclopedia of Mathematics and Its Applications) von Steven R. Finch ...   (Site not responding. Last check: 2007-11-06)
Famous mathematical constants include the ratio of circular circumference to diameter, pi=3.14..., and the natural logarithmic base, e=2.178...Students and professionals usually can name at most a few others, but there are many more buried in the literature and awaiting discovery.
This book will be helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example combinatorial enumeration or geometric optimization.
This is an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
www.buchtipp.schnellsuchmaschine.de /0521818052-Mathematical_Constants_Encyclopedia_of_Mathematics_and_Its_Applications_von_Steven_R_Finch_bei_Cambridge_Univ_Pr_Sd_.html   (276 words)

  
 Mathematical Constants - Cambridge University Press
Famous mathematical constants include the ratio of circular circumference to diameter, pi=3.14 …, and the natural logarithmic base, e=2.178 … Students and professionals usually can name at most a few others, but there are many more buried in the literature and awaiting discovery.
Constants associated with the approximation of functions; 5.
The aim is always to be clear and complete, to motivate why a particular constant of idea is important, and to indicate exactly where in the literature one should look for rigorous proofs and further elaboration.
www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521818052   (475 words)

  
 Constants
Named constants can be assigned a data type with the ordinary data type declarations, but are not variables, in the sense that memory storage is allocated differently (?).
The data type of the constant is determined either by an explicit declaration, or by an implicit one (not recommended), not by the constant's form.
Ambiguity in representing "mathematical" constants -------------------------------------------------- A "mathematical" constant may be represented internally in several different ways according to the formal data type it belongs to.
www.ibiblio.org /pub/languages/fortran/ch2-2.html   (1436 words)

  
 A search for a mathematical expression
Using a database of 610 millions mathematical constants and expressions a search was conducted in order to find a reasonable expression based on simplicity and length for the mass ratios of fundamental particles.
On-line Encyclopaedia of Integer sequences of [Sloane] and a subset of 797 mathematical constants from Steven Finch’s Mathematical Constants [Finch].
Recognizing means to propose a mathematical expression from a series of known digits, usually in mathematics we go from left to right, a mathematical expression is equal to a certain number to a given precision.
www.lacim.uqam.ca /~plouffe/Search.htm   (2045 words)

  
 Read This: Mathematical Constants
While I might quibble with how well known some of these constants (such as Madelung's constant, -1.615542..., which describes the electrostatic potential at the origin due to placing unit charges of alternating sign at all non-zero integral points of the plane) are, these essays set the very accessible tone that is found throughout the book.
The final chapter is about constants that arise in geometry, including the so-called 'coverage constants', such as the area of the smallest square which would cover any path of length one, and the Moving Sofa constant which calculates the largest area of a sofa which can be moved around a corner.
These three chapters, as well as the two on constants from analysis, are shorter than the ones on number theory and combinatorics, both in terms of the number and the length of the essays they contain.
www.maa.org /reviews/constants.html   (1046 words)

  
 Numerical Constants - Mathematics & Physics - Numericana
Planck's constant: The ratio of a photon's energy to its frequency.
The attribution of this irrational constant to Ramanujan was made by Simon Plouffe, as a monument to a famous 1975 April fools column by Martin Gardner in Scientific American (where it was claimed that the above had been proven to be exactly an integer, as conjectured by Ramanujan in 1914 [sic!]).
Some other set of independent constants could have been used to define the 7 basic units (for example, a conventional value of the electron's charge could replace the conventional permeability of the vacuum) but the following one was chosen after careful considerations.
home.att.net /~numericana/answer/constants.htm   (4599 words)

  
 More About Mathematical Constants
Famous mathematical constants include the ratio of circular circumference to diameter, pi=3.14..., and the natural logarithmic base, e=2.178....
Finch organizes these numbers in chapters by the mathematical disciplines from which they arise, so individual chapters will have special interest for students of number theory, analysis, approximation theory, combinatorics, dynamics, complex analysis, and geometry.
Numerical constants are one of them and they are here, for the first time, the object of a systematic investigation...
pauillac.inria.fr /algo/csolve/constant.html   (717 words)

  
 constants
Constants that aren't dimensionless can be regarded as relating one sort of unit to another.
The electromagnetic coupling constant is just another name for the fine structure constant; it describes the strength of the electromagnetic field.
Instead of the electromagnetic coupling constant together with the masses of the W, Z, and Higgs, we could have used 4 other constants: the U(1) coupling constant, the SU(2) coupling constant, the mass of the Higgs, and the expectation value of the Higgs field.
math.ucr.edu /home/baez/constants.html   (1705 words)

  
 Mathematical Constants (Encyclopedia of Mathematics and its Applications)   (Site not responding. Last check: 2007-11-06)
Until I read this book, I had no perspective on the number of significant constants there are in mathematics.
Finch describes in complete detail a large number of constants of interest in mathematics, I didnt count how many are covered, but a list of one per line covers twenty four pages.
This is an instant classic of mathematical exposition, a superb addition to the series Encyclopedia of Mathematics and Its Applications.
www.medicine-book.com /Mathematical_Constants_Encyclopedia_of_Mathematics_and_its_Applications_0521818052.html   (465 words)

  
 Mathematical Constants (Encyclopedia of Mathematics and its Applications) Review and price
The coverage of each constant or group of constants follows the pattern of an explanation of how the constant arose, the formulas that are used to define it and an extensive set of references.
From the Preface: "Material about well-known constants appears early and carefully, for the sake of readers without much mathematical background." The well-known constants include Pythagoras' square root of 2, the Golden Mean, Euler's e and gamma, Archimedes' pi, Apery's zeta(3), Catalan's G, Khintchine's K, Feigenbaum's delta, Madelung's M, and Chaitin's Omega.
There are chapters on constants associated with the fields of number theory, real and complex analysis, approximation of functions, enumeration of discrete structures (some from physics), functional iteration (e.g., paper folding), and geometry.
www.wi-fitechnology.com /Wi-Fi-Products-0521818052.html   (805 words)

  
 Earliest Uses of Symbols for Constants   (Site not responding. Last check: 2007-11-06)
The first symbol used for the constant mentioned by Cajori is the letter b used by Leibniz in letters to Huygens in 1690 and 1691.
Leonhard Euler (1707-1783) introduced e for this constant in a manuscript, Meditatio in Experimenta explosione tormentorum nuper instituta (Meditation on experiments made recently on the firing of cannon), written at the end of 1727 or the beginning of 1728 (when Euler was just 21 years old).
The name Euler's constant may be inappropriate for this number, as the number was known before Euler's birth and Euler's constant more frequently is used to refer to 0.577....
members.aol.com /jeff570/constants.html   (3847 words)

  
 Specific Numbers Science, Directory   (Site not responding. Last check: 2007-11-06)
Brun's Constant Description of the constant, some related work and links to some further reading.
Inverse Symbolic Calculator A set of programs and specialized tables of mathematical constants dedicated to the identification of real numbers.
Ap+¬ry's Constant Describes the definition of the constant and some interpretations as well as a list of references to further work about the constant.
www.wacofdn.org /d2RjXzI2OTMy.aspx   (640 words)

  
 The educational encyclopedia, mathematics tables and constants   (Site not responding. Last check: 2007-11-06)
Favorite mathematical constants the constants are organized by topic and well explained
Mathematical reference tables trigonometric identities and properties, hyperbolic trigonometry, differential and integral calculus, properties of limits, rules for differentiation, rules for integration, vectors and matrices
Mathematical tables and formulas mathematical tables, formulas, algebra, trigonometry, calculus, differential equations, college mathematics, units and conversion, constants, Laplace,
users.telenet.be /educypedia/education/mathematicstables.htm   (278 words)

  
 Some number-theoretical constants
Twin Prime Constant is the first member, and which therefore appear immediately after it.
Density of the set of primes q, relative to the set of all primes, such that a given positive integer (not a proper power and with squarefree part incongruent 1 mod 4) is a primitive root modulo q.
This, as well as the next two 0.85654 and 0.93127, are higher analogues of Artin's Constant, and are related to (among other things) the generation of prime residue class groups modulo a prime
www.gn-50uma.de /alula/essays/Moree/Moree.en.shtml   (1108 words)

  
 The constant $e$ and its computation
It should be pointed out that Leibniz (1646-1716) was the first, in 1690, to recognize e as a constant and he used the notation b (more about the early origins of e may be found in [4]).
Hence the constant e is defined by the monotone increasing sequence :
Links between the definition (1) and the law of compound interest in financial calculations are given in [13] which is a nice book completely dedicated to the constant e and its mathematical background.
numbers.computation.free.fr /Constants/E/e.html   (2300 words)

  
 Math Constants Home Page   (Site not responding. Last check: 2007-11-06)
You will find lots of mathematical constants at Plouffe's Inverter, which is highly recommended.
Mathematical sequences from ISC is found here and explanations to the mathematical constants are found at Mathsoft.
The constants from ISC are partly mirrored at the Swedish SUNET, where they also are compressed for faster download.
www.geocities.com /CapeCanaveral/6204   (137 words)

  
 Mathematical Constants -- Steven R. Finch
Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic.
This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization.
This work represents a scholarly attempt to bring together all significant mathematical constants in one place.
www.frontlist.com /detail/0521818052   (93 words)

  
 [No title]   (Site not responding. Last check: 2007-11-06)
In the Mathematical Laboratory of the University Museum of Natural History and Scientific Instruments there are about 160 mathematical machines built by teachers of Liceo A.Tassoni in the scope of an innovation project for the teaching of geometry developed by the Nucleo di Ricerca in Storia e Didattica della Matematica (University of Modena).
Steven Finch, Research and Development Team, MathSoft, Inc. All numbers are not created equal; that certain constants appear at all and then echo throughout mathematics, in seemingly independent ways, is a source of fascination.
Just as physical constants provide "boundary conditions" for the physical universe, mathematical constants somehow characterize the structure of mathematics.
www.mccallie.org /myates/2historyandconstants.htm   (567 words)

  
 USF+AngSysWis: info (octave)Mathematical Constants   (Site not responding. Last check: 2007-11-06)
Mathematical Constants ====================== - Built-in Variable: I - Built-in Variable: J - Built-in Variable: i - Built-in Variable: j A pure imaginary number, defined as `sqrt (-1)'.
The `I' and `J' forms are true constants, and cannot be modified.
The constant E satisfies the equation `log' (E) = 1.
www.usf.uni-osnabrueck.de /cgi-bin/info?(octave)Mathematical+Constants   (261 words)

  
 Tables of Constants
Keywords : constants, Pi, gamma, sqrt(2), real numbers, digits, tables, digits of Pi.
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.
pi.lacim.uqam.ca /eng/table_en.html   (106 words)

  
 Class jnt.util.Constants
Mathematical constants and constants related to the arithmetic environment.
These constants are available as final class variables.
The mathematical constant the square root of 2.
math.nist.gov /jnt/api/jnt.util.Constants.html   (136 words)

  
 Mathematics Archives - Numbers
All numbers are not created equal; that certain constants appear at all and then echo throughout mathematics, in seemingly independent ways, is a source of fascination.
Three dimensional mathematical depictions are used in the beginning of the film to illustrate the meaning of the mathematical ideas involved.
PI Mathematics, a collaborative project, using the concept of PI as the focus, is a home page on the WWW.
archives.math.utk.edu /subjects/numbers.html   (1310 words)

  
 Reference/Data and constants resources - PhysicsWeb
The value of the constant "alpha" is deduced as statistical limit, compatibily with the quantistic hypotesis E=hf and a slight interaction among electric charges.
Fine Structure Constant, alpha - Solution to a 20th Century Mystery Feynmans conjecture of a relation between alpha, the fine structure constant, and pi.
The Constants and Equations Pages - The Constants and Equations Pages are an on-going project to list as many constants and equations as possible, although it now includes much more than just constants and equations.
www.physicsweb.org /resources/Reference/Data_and_constants   (1792 words)

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