41. Mathematical Constants Subject Re How did we come by e? From Matthew P Wiener Date 1998/08/12 Newsgroups sci.math http://pauillac.inria.fr/algo/bsolve/constant/e/wiener.html

Mathematical Constants by Steven R. Finch Clay Mathematics Institute Book Fellow My website is smaller than it once was. Please visit again, however, since new materials will continue to appear occasionally. * My book Mathematical Constants is now available for online purchase from Cambridge University Press (in the United Kingdom and in North America ). It is far more encompassing and detailed than my website ever was. It is also lovingly edited and beautifully produced - many thanks to Cambridge! - please support us in our publishing venture. Thank you. (If you wish, see several very kind reviews . You can also search the book via Amazon and Google by keyword.) Here are errata and addenda to the book (last updated 8/11/2005), as well sample essays from the book about integer compositions optimal stopping and Reuleaux triangles . Here also are recent supplementary materials, organized by topic: Number Theory and Combinatorics Bipartite, k-colorable and k-colored graphs Transitive relations, topologies and partial orders Series-parallel networks Two asymptotic series ... Quadratic Dirichlet L-series Elliptic curves over Q Inequalities and Approximation Hardy-Littlewood maximal inequalities Bessel function zeroes Nash's inequality Uncertainty inequalities ... Moduli of continuity Real and Complex Analysis Radii in geometric function theory Numerical radii of linear operators Coefficient estimates for univalent functions Planar harmonic mappings ... Constant of interpolation Probability and Stochastic Processes

42. EXSLT - Math:constant - Implementer Page The mathconstant function returns the specified constant to a set precision. Builtin support for mathconstant is available in the following XSLT http://www.exslt.org/math/functions/constant/math.constant.html

EXSLT math constant - Implementer Page User Page How To Downloads Modules Dates and Times Dynamic Common Functions ... Contact Version: Status: implemented User Page: index.html XML Definition: math.constant.xml Function Package: math.constant.zip Function Syntax number math:constant string number Template Syntax math:constant string number The math:constant function returns the specified constant to a set precision. The possible constants are: PI E An implementation of this extension function in the EXSLT math namespace must conform to the behaviour described in this document. Implementations Built-in support for math:constant is available in the following XSLT processors: Processor Processor Version Implemented Version 4XSLT, from 4Suite. libxslt from Daniel Veillard et al. The following implementations of math:constant are available: Language Implemented Version Creator Date Download XSLT Template James Fuller math.constant.template.xsl Javascript ... math.constant.function.xsl Change History Submitted: Creator: James Fuller http://www.ruminate.co.uk

43. Curl 3.0: Package CURL.LANGUAGE.MATH-CONSTANT CURL.LANGUAGE.mathconstant. Variables e half-pi infinity inv-half-pi inv-pi inv-quarter-pi inv-sqrt-2 ln-of-10 ln-of-2 log10-of-e http://km0330.keymachine.de/friedger/doc/CURL.LANGUAGE.MATH-CONSTANT.html

CURL.LANGUAGE.MATH-CONSTANT Variables e half-pi infinity inv-half-pi ... sqrt-2

44. Curl 3.0: Package CURL.LANGUAGE.MATH-CONSTANT Package CURL.LANGUAGE.mathconstant. Variables. double, e = 2.71828. double, half-pi = 1.5708. double, infinity =. double, inv-half-pi = 0.63662 http://km0330.keymachine.de/friedger/doc/CURL.LANGUAGE.MATH-CONSTANT/

Overview Package Class Index Help Curl TM Package CURL.LANGUAGE.MATH-CONSTANT Variables double e double half-pi double infinity double inv-half-pi double inv-pi double inv-quarter-pi double inv-sqrt-2 double ln-of-10 double ln-of-2 double log10-of-e double log2-of-e double nan double pi double quarter-pi double sqrt-2

45. GSL-- 0.6 - GSL--: Constant.hh File Reference mathematical constants. Author Christian Holm. Date Wed Mar 12 152419 2003. include gsl/gsl_math.h . Include dependency graph for math/constant.hh http://cholm.home.cern.ch/cholm/misc/gslmm/math_2constant_8hh.html

Examples Modules Namespaces Hierarchy ... math math/constant.hh File Reference Detailed Description Mathematical constants. Author: Christian Holm Date: Wed Mar 12 15:24:19 2003 Include dependency graph for math/constant.hh: Namespaces namespace gslmm Top of page Last update Wed Jun 1 11:39:14 2005 Christian Holm Created by DoxyGen 1.4.2

46. GSL-- 0.6 - GSL--: Gslmm::constant Struct Reference Physical constants. include gslmm/math/constant.hh . Collaboration diagram for gslmmconstant. Collaboration graph. legend. List of all members. http://cholm.home.cern.ch/cholm/misc/gslmm/structgslmm_1_1constant.html

Examples Modules Namespaces Hierarchy ... constant gslmm::constant Struct Reference Physical Constants Collaboration diagram for gslmm::constant: legend List of all members. Detailed Description Mathematical contants. Static Public Attributes static const double e static const double static const double static const double static const double static const double static const double pi static const double static const double static const double static const double static const double static const double static const double static const double static const double static const double euler static const double static const double static const double Member Data Documentation const double gslmm::constant::e [static] The base of exponentials, const double gslmm::constant::euler [static] Euler's static constant, const double gslmm::constant::half_of_pi [static] divided by two, const double gslmm::constant::log10_of_e [static] The base-10 logarithm of e, const double gslmm::constant::log2_of_e [static] The base-2 logarithm of e, const double gslmm::constant::log_of_10 [static] The natural logarithm of ten

47. E -- From MathWorld e, and Euler s constant. math. Comput. 50, 275281, 1988. HJ and Knox, JA New Closed-Form Approximations to the Logarithmic constant e. math. http://mathworld.wolfram.com/e.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Number Theory Constants e ... Sondow e The constant is base of the natural logarithm , whose symbol honors Euler . This means that is the unique number with the property that the area of the region bounded by the hyperbola , the x -axis , and the vertical lines and is 1. In other words, With the possible exception of is the most important constant in mathematics since it appears in myriad mathematical contexts involving limits and derivatives . The numerical value of is (Sloane's can be defined by the limit (illustrated above), or by the infinite series as first published by Newton (1669; reprinted in Whitehead 1968, p. 225). also has a surprising connection with the product-of-primes primorial function, and is given by the unusual limit (Brothers and Knox 1998). Euler proved that is irrational by proving that has an infinite simple continued fraction ( ; Nagell 1951), and

48. Feigenbaum Constant -- From MathWorld Briggs, K. A Precise Calculation of the Feigenbaum Constants. math. Comput. 57, 435439, 1991. Briggs, KM Feigenbaum Scaling in Discrete Dynamical http://mathworld.wolfram.com/FeigenbaumConstant.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Applied Mathematics Complex Systems Chaos ... Trott Feigenbaum Constant The Feigenbaum constant is a universal constant for functions approaching chaos via period doubling . It was discovered by Feigenbaum in 1975 (Feigenbaum 1979) while studying the fixed points of the iterated function and characterizes the geometric approach of the bifurcation parameter to its limiting value as the parameter is increased for fixed several hundred times for a series of discrete but closely spaced values of , discarding the first hundred or so points before the iteration has settled down to its fixed points, and then plotting the points remaining. A similar plot that more directly shows the cycle may be constructed by plotting as a function of . The plot above (Trott) shows the resulting curves for , 2, and 4.

49. Mathematical Constants This is the most well known mathematical constant, and is the ratio of the circumference of a circle to its Mudd math Fun Facts Continuum Hypothesis http://dspace.dial.pipex.com/town/way/po28/maths/constant.htm

Mathematical Constants This is the most well known mathematical constant, and is the ratio of the circumference of a circle to its diameter - the fact that this is the same for all circles is amazing in itself. The value has been estimated since biblical times, Pi through the ages , and a (wrong) value was almost written into a law You will know that can be approximated by which only gives the value correct to 2 decimal places. is correct to 6 decimal places, and to 9 decimal places. has been calculated to over 50 billion digits . See Table of current records for the computation of constants for the current record for and other constants. is not only irrational (it cannot be written exactly as the ratio of two integers) it is also transcendental (it is not the solution of any polynomial equation with rational coefficients). You will find proofs in Transcendence of Pi and in T E X format Not many transcendental numbers are known ( e and Liouville's number are another two examples) but in fact in 1874 Cantor showed that almost all real numbers are transcendental. You can see some of the proofs if you follow the links at

50. Kaprekar's Constant Kaprekar s constant. 6174 is Kaprekar s constant. Russian mathematician. Recreational math became his hobby as a child he enjoyed spending time solving http://math.about.com/od/recreationalmath/a/kaprekar.htm

var zLb=8; var zIoa2 = new Array('Elsewhere on the Web','From Wolfram Research: Kaprekar','http://mathworld.wolfram.com/KaprekarNumber.html','University of Waterloo','http://www.cs.uwaterloo.ca/journals/JIS/VOL3/iann2a.html'); zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') About Homework Help Mathematics Recreational Math Kaprekar's Constant Homework Help Mathematics Essentials Grade By Grade Goals ... Help zau(256,140,140,'el','http://z.about.com/0/ip/417/C.htm','');w(xb+xb+' ');zau(256,140,140,'von','http://z.about.com/0/ip/496/7.htm','');w(xb+xb); FREE Newsletter Sign Up Now for the Mathematics newsletter! See Online Courses Search Mathematics Stay up to date! Compare Prices Email to a friend ... Print this page Elsewhere on the Web From Wolfram Research: Kaprekar University of Waterloo Most Popular Area and Surface Formulas Worksheets in PDF and Word multiplication table tricks Multiplication Chart, Multiplication Table ... Facts to 20 - PDF What's Hot Exponents 11th grade math, Eleventh grade math Polygons Shape Book ... What's Needed? Related Topics Physics Chemistry Teen Advice Homework / Study Tips ... Homeschooling Kaprekar's Constant From Deb Russell Your Guide to Mathematics FREE Newsletter.

51. Calculus I (Math 2413) - Extras - Constant Of Integration Online Notes / Calculus I (math 2413) / Extras / constant of Integration So, without a proper understanding of the constant of integration, http://tutorial.math.lamar.edu/AllBrowsers/2413/ConstantOfIntegration.asp

MPBodyInit('ConstantOfIntegration_files') Paul's Online Math Notes Online Notes / Calculus I (Math 2413) / Extras / Constant of Integration Constants of Integration In this section we need to address a couple of topics about the constant of integration.  Throughout most calculus classes we play pretty fast and loose with it and because of that many students don’t really understand it or how it can be important. First, let’s address how we play fast and loose with it.  Recall that technically when we integrate a sum or difference we are actually doing multiple integrals.  For instance, MPSetEqnAttrs('eq0001','',3,[[178,18,6,-1,-1],[237,24,8,-1,-1],[297,29,10,-1,-1],[],[],[],[743,75,25,-3,-3]]) MPSetEqnAttrs('eq0001','',3,[[178,18,6,-1,-1],[237,24,8,-1,-1],[297,29,10,-1,-1],[],[],[],[743,75,25,-3,-3]]); MPNNCalcTopLeft(document.mpeq0001ph,'1') MPDeleteCode('eq0001') Upon evaluating each of these integrals we should get a constant of integration for each integral since we really are doing two integrals. MPSetEqnAttrs('eq0002','',3,[[178,54,20,-1,-1],[237,73,26,-1,-1],[297,90,33,-1,-1],[],[],[],[743,226,82,-3,-3]])

52. 3.1416 = Number Pi. Squaring The Circle. Mathematics. SUBJECT A New Approach to the Universal constant pi math. I will appreciate any comments. With absolute respect to those who strive to uncover the http://www.alkyone.com/mak-pi-gr/en/

SUBJECT : A New Approach to the Universal Constant "pi" Dear Sirs, Attached you will find an original, I would like to believe, research study, concerning «A new approach to the area of a circle» and thus a new approach to the Universal Constant "pi". The innovative aspect of the new approach is attributed to avoid the insurmountable obstacles presented by the intervention of square roots and infinite series when we try to calculate the circumference as the Upper Limit of the perimeter of a regular Polygon inscribed in the circle, according to the relevant "deceptive" definition, i.e. o The New Theory considers the above way as an "impasse", which makes us to believe that the so derived number pi' = 3.14159 2 6535 .... is an irrational and trancendental number. By the new way we approach the area of the circle as the "Lower Limit" of the area of the Superscribed Regular Polygon, coming from the square of side ao = 2R , and we use as main tool the "tangent", the values of which can be easily calculated, with the desirable accuracy, using as algorithm the formula q which defines the circle.

53. JavaScript: The Math Object var my_pie=math.PI;. This returns the pi constant, a number with lots of decimals, PI, Returns the constant pi. math.SQRT2, Returns the square root of 2 http://www.pageresource.com/jscript/jmath.htm

The Math Object Helpful methods for calculations JS Main Basics Advanced Complete List ... Advanced /The Math Object Browser Compatibility: NS 4+, IE 4+ The Math object of JavaScript allows you to perform certain calculations by using method functions of the Math object. Also, it provides a few constants such as pi. The easiest way to get a value is to define a variable and set its value to a property or function of the Math Object. If you want to use a property, which returns a constant value (such as pi), you would write something like this: var my_car=Math.property; You would replace the word "property" with the property you want to use. So, if you want to use the value of pi in a variable, you would use the PI property of the Math object. You would write: var my_pie=Math.PI; This returns the pi constant, a number with lots of decimals, or 3.14..... If you want to use a member function, which performs a calculation, you would write something like this: var my_house=Math.function(x); Most of the member functions have one or more parameters, which is what the "x" is for. You can replace x with a number or variable. You would replace the word "function" with the function you want to use. For instance, if you want the square root of a number, you can call the square root member function of the Math object with the number as the parameter: var my_money=Math.sqrt(2);

54. Is The Speed Of Light Constant? If it wasn t zero, the speed of light would not be constant; but from a theoretical point Can we tell if the speed of light is constant in those units? http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.htm

[Physics FAQ] Updated 1997 by Steve Carlip. Original by Philip Gibbs 1996. Is The Speed of Light Constant? There are a number of senses to the meaning of this question and so there are a number of different answers. Firstly . . . Does the speed of light change in air or water? Yes. Light is slowed down in transparent media such as air, water and glass. The ratio by which it is slowed is called the refractive index of the medium and is always greater than one. This was discovered by Jean Foucault in 1850. When people talk about "the speed of light" in a general context, they usually mean the speed of light in a vacuum. This quantity is also referred to as c Is c , the speed of light in vacuum, constant? At the 1983 Conference Generale des Poids et Mesures , the following SI (Systeme International) definition of the metre was adopted: The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. This defines the speed of light in vacuum to be exactly 299,792,458 m/s. This provides a very short answer to the question "Is

55. Constant Field Values (Math 1.0 API) constant Field Values org.apache.commons.math.analysis.PolynomialSplineFunction. static final long, serialVersionUID, 7011031166416885789l http://jakarta.apache.org/commons/math/api/constant-values.html

Overview Package Class Use Tree Deprecated Index Help PREV NEXT FRAMES NO FRAMES All Classes Constant Field Values Contents org.apache.* org.apache.* org.apache.commons.math. ConvergenceException static final long serialVersionUID org.apache.commons.math. FunctionEvaluationException static final long serialVersionUID org.apache.commons.math. MathConfigurationException static final long serialVersionUID org.apache.commons.math. MathException static final long serialVersionUID org.apache.commons.math.analysis. BisectionSolver static final long serialVersionUID org.apache.commons.math.analysis. BrentSolver static final long serialVersionUID org.apache.commons.math.analysis. NewtonSolver static final long serialVersionUID org.apache.commons.math.analysis. PolynomialFunction static final long serialVersionUID org.apache.commons.math.analysis. PolynomialSplineFunction static final long serialVersionUID org.apache.commons.math.analysis. SecantSolver static final long serialVersionUID org.apache.commons.math.analysis. UnivariateRealSolverImpl static final long serialVersionUID org.apache.commons.math.complex.

56. Constant Field Values (Math 1.2-dev API) constant Field Values org.apache.commons.math.stat.descriptive. DescriptiveStatistics. public static final int, INFINITE_WINDOW, 1 http://jakarta.apache.org/commons/math/apidocs/constant-values.html

Overview Package Class Use Tree Deprecated Index Help PREV NEXT FRAMES NO FRAMES All Classes Constant Field Values Contents org.apache.* org.apache.* org.apache.commons.math.random. ValueServer public static final int public static final int public static final int public static final int public static final int public static final int org.apache.commons.math.stat.descriptive. DescriptiveStatistics public static final int org.apache.commons.math.util. ResizableDoubleArray public static final int public static final int Overview Package Class Use Tree Deprecated Index Help PREV NEXT FRAMES NO FRAMES All Classes

57. Math::Symbolic::Constant DESCRIPTION. This module implements numeric constants for MathSymbolic trees. Returns a MathSymbolicConstant with value of e, the Euler number. http://steffen-mueller.net/modules/Math-Symbolic/Math-Symbolic-Constant.html

NAME SYNOPSIS DESCRIPTION EXPORT ... SEE ALSO NAME Math::Symbolic::Constant - Constants in symbolic calculations SYNOPSIS DESCRIPTION This module implements numeric constants for Math::Symbolic trees. EXPORT None by default. METHODS Constructor new Takes hash reference of key-value pairs as argument. Special case: a value for the constant instead of the hash. Returns a Math::Symbolic::Constant. Constructor zero Arguments are treated as key-value pairs of object attributes. Returns a Math::Symbolic::Constant with value of 0. Constructor one Arguments are treated as key-value pairs of object attributes. Returns a Math::Symbolic::Constant with value of 1. Constructor euler Arguments are treated as key-value pairs of object attributes. Returns a Math::Symbolic::Constant with value of e, the Euler number. The object has its 'special' attribute set to 'euler'. Constructor pi Arguments are treated as key-value pairs of object attributes. Returns a Math::Symbolic::Constant with value of pi. The object has its 'special' attribute set to 'pi'. Method value object , not just every named variable.

58. Math Forum - Ask Dr. Math The constant function f(x) = 0 will give zero no matter what function g(x) it is integrated with. Ask Dr. math Questions and Answers from our Archives http://mathforum.org/library/drmath/view/52141.html

Associated Topics Dr. Math Home Search Dr. Math Constant Function Zero and Orthogonal Functions Date: 02/08/2002 at 10:56:01 From: Neeraj Subject: Constant function zero and orthogonal functions We're currently learning about orthogonal functions. Two functions are said to be orthogonal over a given interval if integrating their product (over that interval) equals zero. Here's where I'm confused: I) The constant function f(x) = will give zero no matter what function g(x) it is integrated with. Does this mean that the constant function zero is orthogonal to all functions?-(1) II) Also, what could be the geometrical interpretation of orthogonal functions? Orthogonal implies perpendicular. Does this mean that at their point of intersection, tangents to orthogonal functions are mutually perpendicular? If that is so, then from (1) above, zero should act as a normal to any curve. http://mathforum.org/dr.math/problems/queenie.11.14.01.html - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ Associated Topics College Calculus High School Calculus High School Functions Search the Dr. Math Library:

59. Math Forum - Ask Dr. Math Ask Dr. math Questions and Answers from our Archives The surface of a sphere is one good example; it has a constant curvature. http://mathforum.org/library/drmath/view/55198.html

Associated Topics Dr. Math Home Search Dr. Math Einstein, Curved Space, and Pi Date: 10/09/1999 at 13:35:35 From: Steve Subject: Pi and curved space... I am in 8th grade and recently became interested in Einstein's General and Special Relativity theories. (Just so you know my question is NOT about Einstein's Relativity but how it relates to pi). In Einstein's general relativity, space is described as being curved. If space is curved, then Euclidean geometry doesn't apply. And since one of the parts to Euclidean Geometry is that the relation between a circle's circumference and its diameter (pi) is always 3.1415926535897923... doesn't that mean that the value of pi changes when space is curved? Doesn't that also mean that sometimes the value of pi can actually be rational? Do you know of any methods to calculate pi in curved space? Thanks for your help. http://mathforum.org/dr.math/ Associated Topics High School Geometry High School Higher-Dimensional Geometry Middle School Geometry Middle School Higher-Dimensional Geometry ... Middle School Pi Search the Dr. Math Library: Find items containing (put spaces between keywords): Click only once for faster results: [ Choose "whole words" when searching for a word like age.

60. AoPS Math Forum :: View Topic - 6174=Kaprekar's Constant 1 Deutsch D. and Goldman B. ,Kaprekar s constant, math. Teacher 98,(2004) 234242. 7 Kiyoshi Iseki , Note on Kaprekar s constant, math. Japon. http://www.artofproblemsolving.com/Forum/topic-29532.html

Do you have a weblog? If so, add it to our ring of blogs by clicking here View our community members' blogs by clicking here Font Size: The time now is Fri Sep 16, 2005 2:32 pm All times are GMT - 7 Hours 6174=Kaprekar's constant Mark the topic unread Math Forum Olympiad Section ... Number Theory Theorems and Formulas Moderators: amfulger Arne harazi Megus ... pbornsztein Page of [4 Posts] Printer View Tell a Friend View previous topic View next topic Author Message Riemann Hypothesis Joined: 18 Jul 2004 Posts: 398 Posted: Wed Mar 09, 2005 9:19 pm Post subject: 6174=Kaprekar's constant Source: Internet The number arises in the following famous problem : Take any 4-digit number which uses more than one digit and find the difference between the numbers formed by writing the digits in descending order and ascending order. For example, starting with yields . Iterate this process using the difference x_2 as the new 4-digit number. In other words, The Indian mathematician D.R. Kaprekar discovered that this process leads in at most 7 steps to the number Kaprekar's constant , a fixed point of the iteration.

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