61. Core JavaScript 1.5 Reference:Global Objects:Math - Devmo All properties and methods of math are static. You refer to the constant pi as math.PI and you call the sine function as math.sin(x) , where x is the http://developer.mozilla.org/en/docs/Core_JavaScript_1.5_Reference:Objects:Math

Skip to main content Visit Mozilla.org Mozilla Developer Network Create an account or log in ... Webwatch Hide Sidebar Show Sidebar Related Navigation Main Page Community portal Current events Recent changes ... Donations Views Article Discussion Edit History Toolbox What links here Related changes Upload file Special pages ... Printable version In other languages Polski Core JavaScript 1.5 Reference:Global Objects:Math From Devmo (Redirected from Core JavaScript 1.5 Reference:Objects:Math Main Page Core JavaScript 1.5 Reference Global Objects Math Contents Summary Created by Description Properties ... edit Summary Core 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. edit Created by The Math object is a top-level, predefined JavaScript object. You can automatically access it without using a constructor or calling a method. edit Description All properties and methods of Math are static. You refer to the constant pi as Math.PI and you call the sine function as Math.sin(x)

62. World Web Math: Calculus Summary where in the last equation, c is a constant and in the first two equations is called Euler s constant and is defined to be the unique real number e such http://web.mit.edu/wwmath/calculus/summary.html

Calculus Summary Calculus has two main parts: differential calculus and integral calculus. Differential calculus studies the derivative and integral calculus studies (surprise!) the integral. The derivative and integral are linked in that they are both defined via the concept of the limit: they are inverse operations of each other (a fact sometimes known as the fundamental theorem of calculus): and they are both fundamental to much of modern science as we know it. Derivatives The limit of a function f x ) as x approaches a is equal to b if for every desired closeness to b , you can find a small interval around (but not including) a that acheives that closeness when mapped by f . Limits give us a firm mathematical basis on which to examine both the infinite and the infinitesmial. They are also easy to handle algebraically: where in the last equation, c is a constant and in the first two equations, if both limits of f and g exist. One important fact to keep in mind is that doesn't depend at all on f a ) in fact

63. 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

WOOT - Olympiad training with many top students worldwide. Sponsored by D. E. Shaw group and Google Click here for more information. Font Size: The time now is Fri Sep 16, 2005 4:46 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.

64. AoPS Math Forum :: View Topic - Catalan, Euler Constant Mandelbrot Competition math Jam Wednesday, Aug 24 at 730 PM ET Post Posted Tue Mar 29, 2005 1008 am Post subject Euler s constant, 3 Mark this post http://www.artofproblemsolving.com/Forum/topic-18240.html

Register now for the 2005-06 USA Mathematical Talent Search. Click here to go to the USAMTS website Font Size: The time now is Fri Sep 16, 2005 4:46 pm All times are GMT - 7 Hours Catalan, Euler constant Mark the topic unread Math Forum Olympiad Section ... Number Theory Open Questions Moderators: amfulger Arne harazi Megus ... pbornsztein Page of [3 Posts] Printer View Tell a Friend View previous topic View next topic Author Message Moubinool Navier-Stokes Equations Joined: 27 Aug 2003 Posts: 1979 Posted: Sun Oct 17, 2004 1:35 pm Post subject: Catalan, Euler constant Source: web Are they irrational ? m.o. Paris Back to top djimenez Navier-Stokes Equations Joined: 08 Feb 2005 Posts: 1411 Posted: Wed Mar 23, 2005 9:10 am Post subject: Wow! how ignorant one can be... or how missinformed. I had been always told that was for sure, not only irrational but transcendental. Nevertheless, doing a small research along the web, it seems like both constants are not known to be irrational, those are open problem!!! Does any one wants to give it a try? There is just one thing that is easier to get than to lose, WEIGHT

65. 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.

66. Math Surprises math Surprises An Example. August 2001 These are the so called shapes of constant width. For the width equal to the distance D between the cracks, http://www.cut-the-knot.org/ctk/August2001.shtml

Username: Password: Sites for teachers Sites for parents Awards Interactive Activities ... Sites for parents Cut The Knot! An interactive column using Java applets by Alex Bogomolny Math Surprises: An Example August 2001 Compte de Buffon (1707-1788) in the 18 th century posed and solved the very first problem of geometric probability. A needle of a given length L is tossed on a wooden floor with evenly spaced cracks, distance D apart. What is the probability of the needle hitting a crack? (The problem is nowadays known as Buffon's Needle problem.) The answer he discovered with the help of integral calculus is given by the simple formula [ Beckmann Eves Kasner Paulos ... Stein P = 2L/ p D With P approximated by the ratio of hits to the total number of tosses, the formula offers a way of evaluating p , an observation that eventually led Pierre Simon Laplace (1749-1827) to propose a method, known today as the Monte Carlo Method, for numerical evaluation of various quantities by realizing appropriate random events. History records several names of people who applied the method manually to approximate p . A Captain Fox [ Beckmann , p. 77] mentions Wolf from Zurich (1850) who obtained

67. Shapes Of Constant Width Shapes of constant width, definition, animation, discussion, there are Shapes of R.Honsberger, Ingenuity in mathematics, MAA, New math Library, 1970 http://www.cut-the-knot.org/do_you_know/cwidth.shtml

Username: Password: Sites for teachers Sites for parents Awards Interactive Activities ... Sites for parents Shapes of constant width Yes there are shapes of constant width other than the circle No - you can't drill square holes. But saying this was not just an attention catcher. As the applet on the right illustrates, you can drill holes that are almost square - drilled holes whose border includes straight line segments! Now then let us define the subject of our discussion. First we need a notion of width. Let there be a bounded shape. Pick two parallel lines so that the shape lies between the two. Move each line towards the shape all the while keeping it parallel to its original direction. After both lines touched our figure, measure the distance between the two. This will be called the width of the shape in the direction of the two lines. A shape is of constant width if its (directional) width does not depend on the direction. This unique number is called the width of the figure. For the circle, the width and the diameter coincide. The curvilinear triangle above is built the following way. Start with an equilateral triangle. Draw three arcs with radius equal to the side of the triangle and each centered at one of the vertices. The figure is known as the

68. Math You reference the constant PI as math.PI . constants are defined with the full precision of real numbers in JavaScript. Similarly, you reference math http://home.netscape.com/eng/mozilla/3.0/handbook/javascript/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.

69. Havil, J.: Gamma: Exploring Euler's Constant. of the book Gamma Exploring Euler s constant by Havil, J., Sure to be popular with not only students and instructors but all math...... http://www.pupress.princeton.edu/titles/7494.html

SEARCH: Keywords Author Title More Options Power Search Search Hints E-MAIL NOTICES NEW IN PRINT E-BOOKS ... HOME PAGE Gamma: Exploring Euler's Constant Julian Havil With a foreword by Freeman Dyson Shopping Cart Reviews Table of Contents Introduction [in PDF format] ... Search within this book at Google Print Among the myriad of constants that appear in mathematics, p, e, and i are the most familiar. Following closely behind is g, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . up to 1/n, minus the natural logarithm of nthe numerical value being 0.5772156. . .. But unlike its more celebrated colleagues p and e, the exact nature of gamma remains a mysterywe don't even know if gamma can be expressed as a fraction. Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics todaythe Riemann Hypothesis (though no proof of either is offered!).

70. 1 Introduction 4 JWL Glaisher, History of Euler s constant, Messenger of math., (1872), vol. 1, p. 2530 8 DE Knuth, Euler s constant to 1271 places, math. http://numbers.computation.free.fr/Constants/Gamma/gamma.html

The Euler constant : g g (Postcript version of this page : gamma.ps , pdf version : gamma.pdf . Versions of Formulas on the Euler constant are also available : gammaFormulas.ps gammaFormulas.pdf Introduction Euler's Constant was first introduced by Leonhard Euler (1707-1783) in 1734 as g lim n n log(n) It is also known as the Euler-Mascheroni constant . According to Glaisher [ ], the use of the symbol g is probably due to the geometer Lorenzo Mascheroni (1750-1800) who used it in 1790 while Euler used the letter C. The constant g is deeply related to the Gamma function G (x) thanks to the Weierstrass formula G (x) =xexp( g x) x n exp x n This identity entails the relation G g It is not known if g is an irrational or a transcendental number. The question of its irrationality has challenged mathematicians since Euler and remains a famous unresolved problem. By computing a large number of digits of g and using continued fraction expansion, it has been shown that if g is a rational number p/q then the denominator q must have at least 242080 digits. Even if g is less famous than the constants p and e, it deserves a great attention since it plays an important role in

71. The Constant $e$ And Its Computation 3 Brothers, Harlan J. and JA Knox, New closedform approximations to the logarithmic constant e, math. Intelligencer, (1998) http://numbers.computation.free.fr/Constants/E/e.html

The constant e and its computation e (Click here for a Postscript version of this page.) e i p , all analysis lies here - Felix Klein (1849-1925). Gentlemen, we have not the slightest idea what this equation means, but we may be sure that it means something very important (to his students about the formula i i e p - Benjamin Peirce (1809-1880). Introduction A function equal to it's own derivative Let a be a real positive number, the exponential function a x (in base a) is a differentiable function, that is the following limit exists (a x lim h a x+h a x h lim h a h h a x =Ca x A very important case is given when the derivative of the exponential function is equal to itself, which implies C=1= lim h a h h and this may also be written as a= lim h ( 1+h) 1/h This limit is well defined and it was denoted by the letter e by the Swiss mathematician Leonhard Euler (1707-1783), first around the end of year 1727 in a manuscript entitled Meditatio in Experimenta explosione tormentorum nuper instituta (Meditation upon experiments made recently on the firing of Canon, [ ]), then in a letter to a friend Goldbach (1690-1764) in 1731 and later in 1748 in his work [

72. Mudd Math Fun Facts: Kaprekar's Constant hosted by the Harvey Mudd College math Department Kaprekar s constant. Take any four digit number (whose digits are not all identical), http://www.math.hmc.edu/funfacts/ffiles/10002.5-8.shtml

hosted by the Harvey Mudd College Math Department Francis Su Any Easy Medium Advanced Search Tips List All Fun Facts Fun Facts Home About Math Fun Facts ... Other Fun Facts Features 181937294.184684 Fun Facts viewed since 20 July 1999. Francis Edward Su From the Fun Fact files, here is a Fun Fact at the Easy level: Kaprekar's Constant Take any four digit number (whose digits are not all identical), and do the following: Rearrange the string of digits to form the largest and smallest 4-digit numbers possible. Take these two numbers and subtract the smaller number from the larger. Use the number you obtain and repeat the above process. What happens if you repeat the above process over and over? Let's see... Suppose we choose the number 3141. The process eventually hits 6174 and then stays there! But the more amazing thing is this: every four digit number whose digits are not all the same will eventually hit 6174, in at most 7 steps, and then stay there! Presentation Suggestions: Remember that if you encounter any numbers with fewer than has fewer 4 digits, it must be treated as though it had 4 digits, using leading zeroes. Example: if you start with 3222 and subtract 2333, then the difference is 0999. The next step would then consider the difference 9990-0999=8991, and so on. You might ask students to investigate what happens for strings of other lengths or in other bases.

73. Notable Properties Of Specific Numbers At MROB This is the Omega constant, which satisfies each of these simple Expressed as a continued fraction, the constant is 0 + 1/(20 + 1/(21 + 1/(21 + 1/(22 + http://home.earthlink.net/~mrob/pub/math/numbers.html

Notable Properties of Specific Numbers Introduction These are some numbers with notable properties. (Most of the less notable properties are listed here .) Other people have compiled similar lists, but this is my I think are important A few rules I used in this list: Everything can be understood by a typical undergraduate college student. If multiple numbers have a shared property, that property is described under one "representative" number with that property. I try to choose the smallest representative that is not also cited for another property. When a given number has more than one type of property, the properties are listed in this order: 1. Purely mathematical properties unrelated to the use of base 10 (example: 137 is prime.) 2. Base-10-specific mathematical properties (example: 137 is a prime with all-prime digits) 3. Things related to the physical world but outside human culture (example: 137 is close to the reciprocal of the fine-structure constant, once thought to be exact but later found to be closer to 137.036...) 4. All other properties (example: 137 has often been given almost mystical significance due to its proximity to the fine-structure constant, most famously by Eddington)

74. Writing In Math Classes Fieldtested Learning Assessment Guide for science, math, engineering, The third problem compares constant velocity with constant deceleration. http://server1.fandm.edu/departments/Mathematics/writing_in_math/writing_index.h

75. Conic Sections distance to the origin is constant, sum of distances to each focus is constant difference between distances to each foci is constant http://www.math2.org/math/algebra/conics.htm

Conic Sections Circle Ellipse (h) Parabola (h) Hyperbola (h) Definition: A conic section is the intersection of a plane and a cone. Ellipse (v) Parabola (v) Hyperbola (v) By changing the angle and location of intersection, we can produce a circle, ellipse, parabola or hyperbola; or in the special case when the plane touches the vertex: a point, line or 2 intersecting lines. Point Line Double Line The General Equation for a Conic Section: Ax + Bxy + Cy + Dx + Ey + F = The type of section can be found from the sign of: B If B - 4AC is... then the curve is a... ellipse, circle, point or no curve. parabola, 2 parallel lines, 1 line or no curve. hyperbola or 2 intersecting lines. The Conic Sections. For any of the below with a center (j, k) instead of (0, 0), replace each x term with (x-j) and each y term with (y-k). Circle Ellipse Parabola Hyperbola Equation (horiz. vertex): x + y = r x / a + y / b 4px = y x / a - y / b Equations of Asymptotes: Equation (vert. vertex): x + y = r y / a + x / b 4py = x y / a - x / b Equations of Asymptotes: Variables: r = circle radius a = major radius (= 1/2 length major axis) b = minor radius (= 1/2 length minor axis) c = distance center to focus p = distance from vertex to focus (or directrix) a = 1/2 length major axis b = 1/2 length minor axis c = distance center to focus Eccentricity: c/a c/a Relation to Focus: p = a - b = c p = p a + b = c Definition: is the locus of all points which meet the condition...

76. Most Frequently Linked Pages In The MathSearch Index mathSoft constants, www.mathsoft.com/asolve/constant/constant.html University of Michigan Department of mathematics, www.math.lsa.umich.edu/ http://www.maths.usyd.edu.au/MS-freq-link.html

Most frequently linked pages in the MathSearch index As the the MathSearch index is compiled, the robot which generates it keeps count of off-domain cross-links, that is, how many times a given indexed page is referred to by a link in an indexed page on a server in a different domain. The pages with the most links leading to them are those most frequently recommended by the authors of all the pages in the index, excluding recommendations by authors and local colleagues for their own pages. These most linked pages form a list of English-language reference pages on mathematics and statistics, which have been popularly selected by mathematicians and statisticians who author Web pages. Below is a list of the 60 most frequently linked pages in the index, each with its HTML title and its URL. Title URL AMS Website www.ams.org/ MathSciNet Home Page www.ams.org/mathscinet/ Mathematical Association of America: MAA Online www.maa.org/ Society for Industrial and Applied Mathematics www.siam.org/ MSRI Home Page www.msri.org/

77. Density Constant - Physics Help And Math Help - Physics Forums Physics Forums is a science and physics community. http://www.physicsforums.com/showthread.php?threadid=84137

78. Math Games: Evil Numbers math Games. Evil Numbers. Ed Pegg Jr. and Chris Lomont, October 4, 2004 The first 59 numbers in the CF of the Bloch constant sum to 666. (0, 2, 8, 2, 1, http://www.maa.org/editorial/mathgames/mathgames_10_04_04.html

Search MAA Online MAA Home Math Games Evil Numbers Ed Pegg Jr. and Chris Lomont, October 4, 2004 This calls for wisdom. If anyone has insight, let them calculate the number of the beast, for it is man's number. His number is (Revelations 13:18) The number 666 pops up a lot in recreational mathematics. Mike Keith has a whole page devoted to this number of the beast . Among the many tidbits recorded by Mike are the following: sin Golden Ratio Euler Totient Function The first 144 decimal digits of sum to 666. The first 146 decimal digits of sum to 666. (new, found by Ilan Honig) Many of these items are also listed at the Beast Number entry for MathWorld evil numbers . Evil numbers have the despicable property that if the digits following the decimal point are added one at a time, 666 will be hit exactly. It's like the game of 21, where you want to hit 21, without going over. How common are evil numbers? This actually turns out to be a nice puzzle, which I put on mathpuzzle.com . (and answer below stop reading now if you wish to solve this on your own). There are 905 constants listed at the back of Steven Finch's marvelous book Mathematical Constants how many of them would be needed to make the list of evil constants complete? How much of a can of worms would it be to list all the evil constants?

79. Search.cpan.org: Tels / Math-BigInt-Constant-1.06 mathBigInt-constant-1.05 13 Jan 2004. Links, CPAN Testers Discussion Forum View/Report Bugs Tools . CPAN Testers, PASS (2) View http://search.cpan.org/~tels/Math-BigInt-Constant-1.06/

Home Authors Recent News ... Feedback in All Modules Distributions Authors Tels > Math-BigInt-Constant-1.06 Math-BigInt-Constant-1.06 This Release Math-BigInt-Constant-1.06 Download Browse 01 Jan 2005 Other Releases Math-BigInt-Constant-1.05 13 Jan 2004 Links CPAN Testers Discussion Forum View/Report Bugs Tools CPAN Testers PASS (2) [ View Rating Rate this distribution License Perl ( Artistic and GPL Special Files CHANGES INSTALL LICENSE MANIFEST ... SIGNATURE Modules Math::BigInt::Constant Arbitrary sized constant integers hosted by perl.org , hardware provided by

80. Search.cpan.org: Math::Big - Routines (cos,sin,primes,hailstone,euler,fibbonaci use MathBigInt constant; use MathBig qw/base/; print base ( 2 ** 150 + 42,2);. This will print 150 and 42. to_base(). $string = to_base($number,$base); http://search.cpan.org/perldoc/Math::Big

Home Authors Recent News ... Feedback in All Modules Distributions Authors Tels Math-Big-1.11 > Math::Big Module Version: 1.11 Source Download: math/Math-Big-1.11.tar.gz NAME SYNOPSIS REQUIRES ... AUTHOR NAME SYNOPSIS REQUIRES perl5.005, Exporter, Math::BigInt, Math::BigFloat EXPORTS Exports nothing on default, but can export bernoulli euler sin cos tan cosh sinh arctan arcsin arcsinh pi log and factorial DESCRIPTION This module contains some routines that may come in handy when you want to do some math with really, really big (or small) numbers. These are primarily examples. METHODS @primes = primes($n); $primes = primes($n); Calculates all the primes below N and returns them as array. In scalar context returns the number of primes below N. This uses an optimized version of the Sieve of Eratosthenes , which takes half of the time and half of the space, but is still O(N). Or in other words, quite slow. @fib = fibonacci($n); $fib = fibonacci($n); Calculates the first N fibonacci numbers and returns them as array. In scalar context returns the Nth number of the Fibonacci series. @hail = hailstone($n); # sequence $hail = hailstone($n); # length of sequence

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