81. [math/0209070] Criteria For Irrationality Of Euler's Constant math.NT/0209070. From Jonathan Sondow view email Date Fri, Criteria for Irrationality of Euler s constant. Authors Jonathan Sondow http://arxiv.org/abs/math.NT/0209070/

Mathematics, abstract math.NT/0209070 From: Jonathan Sondow [ view email ] Date ( ): Fri, 6 Sep 2002 15:56:37 GMT (375kb) Date (revised v2): Fri, 4 Oct 2002 00:06:14 GMT (56kb) Criteria for Irrationality of Euler's Constant Authors: Jonathan Sondow Comments: Subj-class: Number Theory; Combinatorics MSC-class: Primary 11J72, Secondary 05A19 Journal-ref: Proc. Amer. Math. Soc. 131 (2003) 3335-3344 Full-text: PostScript PDF References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv math find abs

82. [math/0407514] Geodesically Reversible Finsler 2-spheres Of Constant Curvature math.DG/0407514. From Robert L. Bryant view email Date Thu, 29 Jul 2004 143648 GMT Geodesically reversible Finsler 2spheres of constant curvature http://arxiv.org/abs/math.DG/0407514

Mathematics, abstract math.DG/0407514 From: Robert L. Bryant [ view email ] Date ( ): Thu, 29 Jul 2004 14:36:48 GMT (11kb) Date (revised v2): Mon, 2 Aug 2004 19:25:23 GMT (13kb) Geodesically reversible Finsler 2-spheres of constant curvature Authors: Robert L. Bryant Comments: 11 pages, references added, some arguments improved and exposition rearranged Subj-class: Differential Geometry MSC-class: A Finsler space is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need not be true. In this note, building on recent work of LeBrun and Mason, it is shown that a geodesically reversible Finsler metric of constant flag curvature on the 2-sphere is necessarily projectively flat. As a corollary, using a previous result of the author, it is shown that a reversible Finsler metric of constant flag curvature on the 2-sphere is necessarily a Riemannian metric of constant Gauss curvature, thus settling a long-standing problem in Finsler geometry. Full-text: PostScript PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers?

83. 5.7 Math -- Mathematical Functions e The mathematical constant e. Note The math module consists mostly of thin wrappers around the platform C math library functions. http://www.python.org/doc/current/lib/module-math.html

Python Library Reference Previous: 5.6.7 Recipes Up: 5. Miscellaneous Services Next: 5.8 cmath math Mathematical functions This module is always available. It provides access to the mathematical functions defined by the C standard. These functions cannot be used with complex numbers; use the functions of the same name from the cmath module if you require support for complex numbers. The distinction between functions which support complex numbers and those which don't is made since most users do not want to learn quite as much mathematics as required to understand complex numbers. Receiving an exception instead of a complex result allows earlier detection of the unexpected complex number used as a parameter, so that the programmer can determine how and why it was generated in the first place. The following functions are provided by this module. Except when explicitly noted otherwise, all return values are floats. Number-theoretic and representation functions: ceil x Return the ceiling of x as a float, the smallest integer value greater than or equal to

84. Some Interesting Math Sites One can enter a constant and get in return a list of mathematical expressions that generate that constant. This is a fun math site. Primes! http://orion.ramapo.edu/~ldant/sites.html

A Small Compendium of Interesting Math Sites Mathematics on the Web is a compendium by the A.M.S. of various math Web resources. Erdos number project compiles a list of all mathematicians whose Erdos number is 1 or 2. Math Archives has a wide variety of mathematical resources with a primary emphasis on materials used in the teaching of mathematics. Yahoo Mathematics page is a categorized list of Web sites devoted to mathematics. Directory of math sites on the Web. This Penn State site has a good collection of mathematical associations, journals, and mathematics department Web servers. WWW Virtual Library This Florida State site has the Mathematics section of the Virtual Library, which has extensive links to mathematics resources on the Web. The Inverse Symbolic Calculator This is a set of programs and specialized tables of mathematical constants. One can enter a constant and get in return a list of mathematical expressions that generate that constant. This is a "fun" math site. Primes! This site is an excellent resource about prime numbers. Wondering about the largest currently known prime? Need information on Mersenne primes? Want a good test for primality? For all this and more check out this site. sci.math FAQ

85. Math Unit III: More On The Derivative And Differential Equations math Unit III More on the derivative and differential equations So we get what some people call the ``constanttimes-a-function rule http://dept.physics.upenn.edu/courses/gladney/mathphys/subsection3_1_1.html

Back to Contents! Next: Force Revisited Up: CONSERVING EQUATIONS Previous: CONSERVING EQUATIONS Math Unit III: More on the derivative and differential equations In the last unit, we discussed how mathematicians and scientists deal with quantities that change in ways other than linearly. The key idea turns out to be the rate of change of the quantity. The lowbrow way to measure the rate of change is to compute the average rate of change over a small interval. The high-class way to talk about change is to try to compute the derivative , or instantaneous rate of change In real-world situations, when one deals with measured data, it is often the case that the data has been measured only for certain specific values of the independent variable. Then, one can only compute average rates of change between the data points. But in mathematics, when one deals with abstractly-defined functions, it is possible to compute derivatives. Often, mathematical models are developed using derivatives, predictions are made based upon these mathematical models, and then experimental results are compared to the predictions to see how well the models reflect reality. 1. Review and extensions

86. Graham, Knuth, And Patashnik: Concrete Mathematics line 4 from the bottom change constant $\alpha$ to constant $\alpha\ne0$ page 609, lines 3 and 4 of reference 77 change math ematische to http://www-cs-faculty.stanford.edu/~knuth/gkp.html

Concrete Mathematics, Second Edition by Ronald L. Graham, Donald E. Knuth, and Oren Patashnik (Reading, Massachusetts: Addison-Wesley, 1994), xiii+657pp. ISBN 0-201-55802-5 Chinese translation by Lai FeiPei, Ju Ti Shu Xue (Taipei: Dong Hua Publishing Co., 1990), xv+731pp. Chinese translation by Chen YanWen, Ju Ti Shu Xue (Taipei: Ru Lin Publishing Co., 1991), xii+695pp. Chinese translation by Xingu Zhuang, Ju Ti Shu Xue (Xi'an: Xi An Dian Zi Ke Ji Da Xue Chu Ban She, 1992), xii+539pp. Chinese translation by somebody (Beijing: China Machine Press), in preparation. Italian translation edited by Giovanni Monegato, Matematica Discreta (Milan: Editore Ulrico Hoepli, 1992), xviii+607pp. Japanese translation by Makoto Arisawa, Michiaki Yasumura, Tatsuya Hagino, and Kiyoshi Ishihata, Kompyuta no Suugaku (Tokyo: Kyoritsu-Shuppan, 1993), xvi+606pp. Russian translation by A. B. Khodulev and B. B. Pokhodzei, with foreword by V. Arnol'd, Konkretnaya matematika (Moscow: Mir, 1999), 704pp. Polish translation by P. Chrzastowski, A. Czumaj, L. Gasieniec, and M. Raczunac, Matematyka Konkretna (Warszawa: Polskie Wydawnictwa Naukowe, 1996), 718pp.

87. MathFiction: Tigor (aka The Snowflake Constant) (Peter Stephan Jungk) Professor Giacopo Tigor s idea of a snowflake constant seems to be something which he came up with arbitrarily, and rather than attempting to mathematically http://math.cofc.edu/faculty/kasman/MATHFICT/mfview.php?callnumber=mf449

88. Astronomy And Numerical Software Source Codes It prevents folding of floating point constant expressions. This version of the patch is Cephes C and C++ language special functions math library http://www.moshier.net/

Astronomy and numerical software source codes Astronomy Programs Cephes Mathematical Library Hexadecimal floating constants in C Language Complex Variables in C Language ... The Rubidium PC Mirrors This site has a European mirror at http://www.mirrorservice.org/sites/www.moshier.net/. Please try that if you experience slow downloading speed. Also, for Cephes files you can try one of the Netlib mirrors listed at http://www.netlib.org/bib/mirrors.html. Ephemerides aa200c.zip : JPL ephemeris reader; size 300 KB. AA200 reads astronomical ephemerides, in the data format produced by Jet Propulsion Laboratory, and reduces the barycentric coordinates to printouts of geocentric and topocentric place. Specific configurations for the DE406 CD-ROM from Willmann-Bell, DE406, DE405, DE404, DE403, DE400, DE245, DE200, DE102, and DE118I.ZIP ephemerides are supplied. The ephemeris data files themselves are not supplied; get them from Willmann-Bell or from JPL's ftp site. Answers for DE200 from this program should agree with Astronomical Almanac tabulations from about 1984 onward. Additionally, the program can reduce star catalogue positions given in either the FK4 or FK5 system. It can also find positions from heliocentric orbital elements. Source code listings in C language are supplied with MSDOS (Microsoft and Borland compilers) and Unix make files. The archive includes an MSDOS executable program configured for the new Willmann-Bell CD ROM. Latest update 2005-02-26. Previous version aa200b.zip

89. Feigenbaum's Universal Constant FEIGENBAUM S UNIVERSAL constant Last updated 191197. Send comments to berland(a)stud.math.ntnu.no © 1997 Back to homepage. http://www.stud.ntnu.no/~berland/math/feigenbaum/feigconstant.html

F EIGENBAUM'S UNIVERSAL CONSTANT Back to main page Back to homepage Send comment The short answer: However, noone should be satisfied by that. In fact, this number is perhaps the most fantastic aspect of this fractal. There are many many formulas that produce the same tree, but the number is always the same. It is said that mr. Mitchell Feigenbaum called home to his mother when he discovered this universality and said this was going to make him famous. The famous value, comes when you compare the length of one part of the tree, that is a parts between the line divisions/bifurcations. See illustration at right. The first part is from -0.25 to 0.75, and has a length of 1.00. The next part is from 0.75 to 1.25, and has a length of 0.50. The relationship between the two lengths is 1.00/0.50=2.00. Now that is far from the Feigenbaumvalue, but the exact value springs up when you compare two parts as far right as possible, as long as x follows a periodic orbit. I have graphically found the values for the first 6 bifurcations: Bifurc no. Divides at Length This length/next length -0.25 - - 1 0.75 L1=1.0 L1/L2=2.0 2 1.25 L2=0.5 L2/L3=4.25 3 1.3677 L3=0.1147 L3/L4=4.492 4 1.3939 L4=0.0262 L4/L5=4.6208 5 1.39957 L5=0.00567 L5/L6=4.536 6 1.40082 L6=0.00125 L6/L7=?

90. Math You reference the constant PI as math.PI . constants are defined with the full precision Because PI is a constant, it is a readonly property of math. http://members.ozemail.com.au/~phoenix1/html/ref_m-q.htm

[Previous reference file] Math Object. A built-in object that has properties and methods for mathematical constants and functions. For example, the Math object's PI property has the value of pi. Syntax To use a Math object: 1. Math. propertyName 2. Math. methodName parameters Parameters propertyName is one of the properties listed below. methodName is one of the methods listed below. Property of None. The Math object is a top-level, built-in JavaScript object. Implemented in Navigator 2.0 Description You reference the constant PI as Math.PI . Constants are defined with the full precision of real numbers in JavaScript. Similarly, you reference Math functions as methods. For example, the sine function is Math.sin(argument) , where argument is the argument. It is often convenient to use the with statement when a section of code uses several Math constants and methods, so you don't have to type "Math" repeatedly. For example, a = PI * r*r y = r*sin(theta) x = r*cos(theta) Properties The Math object has the following properties: E PI Methods The Math object has the following methods: abs acos asin atan ... valueOf Event handlers None.

91. Welcome To TCEAP.co.uk: The Site For Constants And Equations Expanding reference resource for science, math and astronomy http://www.tcaep.co.uk/

Search TCAEP Welcome to TCAEP .co.uk Science Maths Constants - Over alphabetically listed Topics - Explanations of the more common entries aspects of maths. Over links Equations - Some entries Number Conversions - Interactive log tables, metric prefixes and more conversion of over units Algebra - All the common algebraic SI Units - Details on all the standard SI units identities, including complex numbers of measurement Trigonometry - Identities Calculus - Integral and differential functions Symbols - Greek alphabet, electronic symbols and mathematical symbols Astronomy Planets - Details on all the currently known planets and their satellites Constellations - Table of constellations with info on 3164 stars - Times for 231 locations around the world Moon phases - Tables of moon phases for the next 20 years If you have any problems with this site help can be found on the about page or you can contact us at editor@scenta.co.uk or alternatively call us on (+44) 0207470 4800 These pages make extensive use of XML There is a non-XML version of these pages available For help with physics questions try www.physics.org

92. SCI.SPACE FAQ No. 04 - Space/math SPACE/math Constants and Equations for Calculations. Last-modified $Date 94/03/01 172439 $. CONSTANTS AND EQUATIONS FOR CALCULATIONS http://www.ksc.nasa.gov/facts/faq04.html

SPACE/MATH - Constants and Equations for Calculations Last-modified: $Date: 94/03/01 17:24:39 $ CONSTANTS AND EQUATIONS FOR CALCULATIONS This list was originally compiled by Dale Greer. Additions would be appreciated. Numbers in parentheses are approximations that will serve for most blue-skying purposes. Unix systems provide the 'units' program, useful in converting between different systems (metric/English, CGS/MKS etc.) NUMBERS 7726 m/s (8000) Earth orbital velocity at 300 km altitude 3075 m/s (3000) Earth orbital velocity at 35786 km (geosync) 6371 km (6400) Mean radius of Earth 6378 km (6400) Equatorial radius of Earth 1738 km (1700) Mean radius of Moon 5.974e24 kg (6e24) Mass of Earth 7.348e22 kg (7e22) Mass of Moon 1.989e30 kg (2e30) Mass of Sun 3.986e14 m^3/s^2 (4e14) Gravitational constant times mass of Earth 4.903e12 m^3/s^2 (5e12) Gravitational constant times mass of Moon 1.327e20 m^3/s^2 (13e19) Gravitational constant times mass of Sun 384401 km ( 4e5) Mean Earth-Moon distance 1.496e11 m (15e10) Mean Earth-Sun distance (Astronomical Unit)

93. Mathematical Constant - Wikipedia, The Free Encyclopedia A list of constants with links to more detailed information. http://en.wikipedia.org/wiki/Mathematical_constant

Mathematical constant From 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. Unlike physical constants , mathematical constants are defined independently of any physical measurement. For example, up to multiplication with nonzero complex numbers, there is a unique holomorphic function f with f' f . Therefore, f f (0) is a mathematical constant, the constant e f is also a periodic function , and the absolute value of its period is another mathematical constant, 2π. Mathematical constants are typically elements of the field of real numbers or complex numbers . Mathematical constants that one can talk about are definable numbers (and almost always also computable However, there are still some mathematical constants for which only very rough estimates are known. An alternate sorting may be found at Mathematical constant (sorted by continued fraction representation) edit Table of selected mathematical constants Abbreviations used: I - irrational number , A - algebraic number , T - transcendental number Gen - General , NuT - Number theory , ChT - Chaos theory , Com - Combinatorics , Inf - Information theory , Ana - Mathematical analysis Symbol Approximate Value Name Field N First Described # of Known Digits Pi Archimedes ' constant or Ludolph 's number Gen Ana T e Napier's constant , base of Natural logarithm Gen Ana T ... Pythagoras ' constant

94. Xalan-Java 2.6.0 API Reference: Class ExsltMath The mathconstant function returns the specified constant to a set precision. static double, cos(double num) The mathcos function returns cosine of the http://www.stylusstudio.com/api/xalan-j_2_6_0/org/apache/xalan/lib/ExsltMath.htm

Overview Package Class Use Tree Deprecated Index ... METHOD org.apache.xalan.lib Class ExsltMath org.apache.xalan.lib.ExsltBase org.apache.xalan.lib.ExsltMath public class ExsltMath extends ExsltBase This class contains EXSLT math extension functions. It is accessed by specifying a namespace URI as follows: xmlns:math="http://exslt.org/math" The documentation for each function has been copied from the relevant EXSLT Implementer page. See Also: EXSLT Usage: Constructor Summary ExsltMath Method Summary static double abs (double num) The math:abs function returns the absolute value of a number. static double acos (double num) The math:acos function returns the arccosine value of a number. static double asin (double num) The math:asin function returns the arcsine value of a number. static double atan (double num) The math:atan function returns the arctangent value of a number. static double (double num1, double num2) The math:atan2 function returns the angle ( in radians ) from the X axis to a point (y,x). static double constant (java.lang.String name, double precision)

95. Mathematics Archives - Topics In Mathematics - Number Theory KEYWORDS Number theory, utility, constants, interactive page; The Jewel of Arithmetic TECHNOLOGY Javascript; Number Theory Section of sci.math FAQ http://archives.math.utk.edu/topics/numberTheory.html

Topics in Mathematics Number Theory Absolute Primes ADD. KEYWORDS: Article, Repunits SOURCE: Arkadii Slinko, University of Auckland and Mathematics Olympiad Learning Centre TECHNOLOGY: Adobe Acrobat Reader Aesthetics of the Prime Sequence Algorithmic Number Theory - Bibliography AMS - Fermat's Last Theorem ADD. KEYWORDS: Number theory, Fermat's Last Theorem, History, Reports, Articles AMS's Materials Organized by Mathematical Subject Classification ADD. KEYWORDS: Electronic Journals, Preprints, Web Sites, Databases Arithmetic properties of Binomial Coefficients ADD. KEYWORDS: Elementary Number Theory, Lucas' Theorem, Pascal's triangle via cellular automata, Bernoulli numbers and polynomials, Theorems of Morley and Emma Lehmer and their generalizations, Some useful p-adic numbers Bernoulli (Beta) and Integer Part Sequences ADD. KEYWORDS: Article SOURCE: Rod Nillsen, Keith Tognetti and Graham Winley, University of Wollongong TECHNOLOGY: Adobe PDF, Postscript and DVI readers

96. Polynomial Functions The constant term of a polynomial is the term of degree 0; it is the term Name the degree, the leading coefficient, and the constant term of (5x + 1)(3x http://www.themathpage.com/aPreCalc/polynomial.htm

Topics in P R E C A L C U L U S Table of Contents Home THE VOCABULARY OF POLYNOMIAL FUNCTIONS Terms and factors Variables versus constants Definition of a polynomial in x ... Domain and range F UNCTIONS CAN BE CATEGORIZED , and the simplest type is a polynomial function. We will define it below. We will begin with vocabulary. 1. When numbers are added or subtracted, they are called terms . This x x is a sum of three terms. When numbers are multiplied, they are called factors . This x x x is a product of three factors. 2. A variable is a symbol that takes on values. A value is a number. 3. A constant is a symbol that has a single value. Example. The symbols '5' and ' ' are constants. The beginning letters of the alphabet a, b, c , etc. are typically used to denote constants, while the letters x y z , are typically used to denote variables. For example, if we write y a x b x c we mean that a b c are constants (i.e. fixed numbers), and that x and y are variables. 4. A polynomial in x is a sum of whole number powers of the variable x Example.

97. Hamilton - Math To Build On: Variables & Constants Constants are letters or symbols that represent one number. The math Forum is a research and educational enterprise of Drexel University. http://mathforum.org/~sarah/hamilton/ham.variables.html

Variables and Constants About Math To Build On Contents On to Squaring Numbers Back to Circles, Triangles... ... Glossary Variables Some people get uncomfortable every time they see a letter of the alphabet mixed with numbers. They understand what to do with the numbers, but not those letters. The letters represent numbers that change in value or are unknown. They are called variables since the numbers those letters represent vary from time to time. A good example is pay. If a person is paid $20 per hour, to find his weekly pay, you would multiply $20 by the number of hours he works each week. The problem is that you may not know how many hours he will work each week. It may be 40 hours one week and 37 the next. However, if you represent the amount of hours with an h, you can say The h is a variable that represents a real number that varies from week to week. The $20 represents the hourly rate of pay. To work with any variable, you must know exactly what it represents. There are many variables in this book. As you work with them, you will learn what they represent. Constants Constants are letters or symbols that represent one number. A well known constant is

98. Constants How many of these dimensionless fundamental constants are there? John Archibald Wheeler. baez@math.ucr.edu. © 2000 John Baez http://math.ucr.edu/home/baez/constants.html

How Many Fundamental Constants Are There? John Baez June 15, 2002 You might at first think that the speed of light, Planck's constant and Newton's gravitational constant are great examples of fundamental physical constants. But in fundamental physics, these constants are so important that lots of people use units where they all equal 1! The point is that we can choose units of length, time and mass however we want. That's three independent choices, so with a little luck we can use them to get our favorite three constants to equal 1. Planck was the first to notice this, so these units are called "Planck units". Planck units are great for quantum gravity. They are not so convenient for other purposes, however. The Planck length, for example, is ridiculously small: about 2 x 10 meters. The Planck time looks even worse: about 5 x 10 seconds. The Planck mass is 2 x 10 kilograms. In ordinary life, and even in nuclear physics, Planck units can be a real nuisance. But in the grand scheme of things, units are not very important. They are arbitrary human conventions. As long as you stick with some choice or other you will do okay.

99. Mathematical Resources: Constants And Interesting Numbers (Math Links By Bruno K Constans and Interesting Numbers Mathematical Resources. http://mathres.kevius.com/constans.html

Mathematical Constans and Interesting Numbers not a complete list, only what I happened to see... Big Number Names Catalan Number Conversion of Units / Umrechnung von Einheiten CSU Maths Interesting Numbers, Facts Page Charles Sturt University Data Powers of Ten by Roy Williams Clickery Dictionary of Number Words The Euler Number (Geometry and the Imagination) The Euler's Number Home Page Feigenbaum's universal constant by Håvard Berland Fibonacci bases and other ways of representing integers The Fibonacci Numbers by David L. Schweizer Fibonacci Numbers and the Golden Section by Dr Ron Knott The Fibonacci numbers The Fibonacci numbers in a formula for Pi Fibonacci Numbers and Nature Fibonacci Rabbit Sequence ... Fun with Numbers Malka Numbers Fun With Numbers: The Home Page by Sage Weil Fundamental Physical Constants from NIST The Garden of Eden (the famous Eve Astrid Andersson) Number - Pi The Golden Ratio, or Phi The Golden Section In Art, Architecture and Music The Great Internet Mersenne Prime Search I Love Binary, Primes, and Factors Page ... Infinity (Bellevue Community College) Interesting Numbers by Owen Courtis Ivan Panin's - Bible Numerics God is A Mathematician By Keith Newman Largest Known Primes The Largest Known Primes by Chris Caldwell Learn About Cool Numbers Lehmer's Problem by Michael Mossinghoff Linear periodization theory by Artur Mos Mathsoft Constants - Mathcad Library - S. Finch at MathSoft, Inc.

100. Experimental Mathematics: Table Of Contents: Volume 8 New Representations for the Madelung constant Richard E. Crandall Abstract in Postscript or DVI Full text (Postscript) http://www.expmath.org/expmath/volumes/8/8.html

Home Table of Contents / Volume 8 Subscription Information Submission Guidelines Articles Editorial Board For subscription or editorial inquiries, please contact us by email , telephone, or mail. A K Peters, Ltd. 888 Worcester Street Suite 230 Wellesley, MA 02482 Tel: 781.416.2888 or 800.450.2210 Fax: 781.416.2889 http://www.akpeters.com/ Are characters missing or replaced by rectangles? Experimental Mathematics Volume 8 (1999) Next Volume All Volumes Previous Volume Volume 8, issue 1 Singular Separatrix Splitting and the Melnikov Method: An Experimental Study Amadeu Delshams Abstract in Postscript or DVI Full text (Postscript) The Topology of the Relative Character Varieties of a Quadruply-Punctured Sphere Robert L. Benedetto William M. Goldman Abstract in Postscript or DVI Full text (Postscript) Alain Joets Roland Ribotta Abstract in Postscript or DVI Full text (Postscript) Spectral Properties of High Contrast Band-Gap Materials and Operators on Graphs Peter Kuchment Leonid A. Kunyansky

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