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         Math Constant:     more detail
  1. Gamma: Exploring Euler's Constant by Julian Havil, 2003-03-17
  2. Bows, Arrows, and Aircraft Carriers: Moving Bodies with Constant Mass (Math in a Box) by Films for the Humanities & Sciences (DVD), 2004
  3. Take-off: Moving Bodies with Constant Mass (Math in a Box) by Films for the Humanities & Sciences (DVD), 2004
  4. Computing your CADP: any approach plate is a soup of acronyms and abbreviations. Here's the math behind one you've seen but never spoken.(APPROACH CLINIC)(Constant ... Angle Descent Point): An article from: IFR by John Clark, 2007-06-01
  5. Organic Chemistry Laboratory Manual by Paris Svoronos, Edward Sarlo, et all 1996-10-01

41. Shapes Of Constant Width
The length of the boundary of shapes of constant width depends only on R.Honsberger, Ingenuity in mathematics, MAA, New math Library, 1970; H.Rademacher and O
http://www.cut-the-knot.org/do_you_know/cwidth.shtml
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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

42. Math Surprises
math Surprises An Example. In other words, the average number of crossings per 1 unit of relative length L/D is constant and is equal to 2/p. Color one half of
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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 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

43. Feigenbaum's Universal Constant
FEIGENBAUM S UNIVERSAL constant. it. 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
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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=?

44. Math::Symbolic::Constant
NAME. MathSymbolicConstant Constants in symbolic calculations. SYNOPSIS. Returns a MathSymbolicConstant. Constructor zero.
http://steffen-mueller.net/modules/Math-Symbolic/Math-Symbolic-Constant.html
  • NAME SYNOPSIS DESCRIPTION
    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.

45. World Web Math: Calculus Summary
algebraically where in the last equation, c is a constant and in the first two equations, if both limits of f and g exist. integrals For c a constant,.
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

46. World Web Math: Vector Calculus: Partial Differentiation
A partial function is a onevariable function obtained from a function of several variables by assigning constant values to all but one of the independent
http://web.mit.edu/wwmath/vectorc/scalar/partial.html
Partial Differentiation
Prerequisites: Derivatives
Bound as we humans are to three spacial dimensions, multi-variable functions can be very difficult to get a good feel for. (Try picturing a function in the 17th dimension and see how far you get!) We can at least make three-dimensional models of two-variable functions, but even then at a stretch to our intuition. What is needed is a way to cheat and look at multi-variable functions as if they were one-variable functions. We can do this by using partial functions . A partial function is a one-variable function obtained from a function of several variables by assigning constant values to all but one of the independent variables. What we are doing is taking two-dimensional "slices" of the surface represented by the equation. For Example: z x y can be modeled in three dimensional space, but personally I find it difficult to sketch! In the section on critical points a picture of a plot of this function can be found as an example of a saddle point. But by alternately setting x =1 (red)

47. Conic Sections
distance to the origin is constant, sum of distances to each focus is constant, distance to focus = distance to directrix, difference between distances to each
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...

48. S.O.S. Mathematics - Sites Of Interest On The Web
Everything you always wanted to know about mathematical constants like the FransénRobinson constant et al. Temporarily unavailable.; math Humor - Enough of
http://www.sosmath.com/wwwsites.html
S.O.S. Mathematics - Sites of Interest on the World Wide Web
Here is a list of some nice sites on the World Wide Web. If you know of a site that should be listed, please let us know....
General Mathematics Sites

49. World Builders: Math For The Solar Constant In The Biosphere E Viau CSULA
Try to understand the basic idea, and don t use my math numbers on any Important Exams unless you have checked them out! The Solar constant.
http://curriculum.calstatela.edu/courses/builders/lessons/less/biomes/SunEnergy_
Home Science Notes Web Links Biomes ... Lessons Following the Energy Trail Let's see how the sun's energy flows in the Biosphere. Warning: I am making a lot of assumptions and doing a lot of rounding in the math here. My numbers may be off by several thousand percent, but I think the process is all right. Try to understand the basic idea, and don't use my math numbers on any Important Exams unless you have checked them out! Dr Viau says, "Gerald Nordley and Mark Wistey were kind enough to help with this, but I made the mistakes all by myself!" The Solar Constant How much of the sun's energy gets to the surface of the earth, and what does that mean to a lemming? The earth gets only 2 billionths of the sun's energy, but that is still a lot. However, you can see on the chart that life (through photosynthesis) uses only 023% of the energy that reaches the surface of the earth 34% of the sun's energy is reflected back into space by snow and clouds. This reflective quality of a planet is called its

50. Rydberg Constant Definition Meaning Information Explanation
Which gives the Rydberg constant for a certain atom with one electron with the rest mass math m /math and the atomic nucleus mass math M /math .
http://www.free-definition.com/Rydberg-constant.html
A B C D ...
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Rydberg constant
The rydberg constant is named after physicist Janne Rydberg , and is a physical constant discovered when measuring the spectrum of hydrogen , and building upon results from Anders Jonas …ngstr¶m and Johann Balmer. Each chemical element has it's own Rydberg constant, but most commonly referred to is the "infinity" constant. The "infinity" Rydberg constant is: The "infinity" constant appears in the formula: Which gives the Rydberg constant for a certain atom with one electron with the rest mass atomic nucleus As the formula for the Rydberg constant contains no less than five other physical constant s, namely the elementary charge electron rest mass permittivity ... speed of light in vacuum For more information about this formula, see the article on the Rydberg formula
See Also
Books about 'Rydberg constant' at: amazon.com or amazon.co.uk Note: This article from Wikipedia is made available under the terms of the GNU FDL
Further Search within Free-Definition
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from your web site to this article with this HTML tag:
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51. E (mathematical Constant) Definition Meaning Information Explanation
The mathematical constant math e /math (occasionally called Euler s number or Napier s constant in honor of the Scottish mathematician John Napier who
http://www.free-definition.com/E-mathematical-constant.html
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E (mathematical constant)
The mathematical constant Euler's number or Napier's constant in honor of the Scottish mathematician John Napier who introduced logarithms ) is the base of the natural logarithm . It is approximately equal to
e
It is equal to exp(1) where exp is the exponential function and therefore it is the limit and can also be written in a number of ways as an infinite series, the most important of which is: factorial proof of the equivalence of these definitions is given below. The number e is relevant because one can show that the exponential function exp( x derivative and is hence commonly used to model growth or decay processes. The number e is known to be irrational and even transcendental . It was the first number to be proved transcendental without having been specifically constructed; the proof was given by Charles Hermite in . It is conjectured to be normal . It features (along with a few other fundamental constants) in Euler's identity described by Richard Feynman as " the most remarkable formula in mathematics The infinite continued fraction In 1975, the Swiss Felix A. Keller discovered the following formula that converges in e ("Keller's Expression"

52. Netscape DevEdge
You refer to the constant PI as math.PI and you call the sine function as math.sin(x) , where x is the method s argument. constants
http://devedge.netscape.com/library/manuals/2000/javascript/1.3/reference/math.h
DevEdge
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Table of Contents Previous Next Index
Math
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. Core object Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262
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.
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) , where x is the method's argument. Constants are defined with the full precision of real numbers in JavaScript. 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)
Property Summary
Property Description E Euler's constant and the base of natural logarithms, approximately 2.718. Natural logarithm of 10, approximately 2.302.

53. Core JavaScript Reference 1.5:
You refer to the constant PI as math.PI and you call the sine function as math.sin(x), where x is the method s argument. constants
http://devedge.netscape.com/library/manuals/2000/javascript/1.5/reference/math.h
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Previous Contents Index Next Core JavaScript Reference 1.5
Math
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.
Core object Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262
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.
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) , where x is the method's argument. Constants are defined with the full precision of real numbers in JavaScript. 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)
Property Summary Property Description E Euler's constant and the base of natural logarithms, approximately 2.718.

54. Math::BigInt::Constant - Arbitrary Sized Constant Integers
SiteFelix / Toolbox. MathBigIntconstant Arbitrary sized constant integers. MathBigIntconstant - Arbitrary sized constant integers. Update 2003/04/23.
http://www4.kcn.ne.jp/~felix/Softwares/MathPPM/Math-BigInt-Constant.html
Location : Home Softwares Perl Math Packages
Title : Math::BigInt::Constant
Site:Felix / Toolbox
Math::BigInt::Constant - Arbitrary sized constant integers
Math::BigInt::Constant - ”CˆÓ’·‚̐®”’萔
ŠT—v
use Math::BigInt ':constant' ®”’萔‚ªƒRƒ“ƒpƒCƒ‹Žž‚É BigInt ‚̒萔‚ÉŽw’肳‚ê‚邪AƒIƒuƒWƒFƒNƒg‚²‚Æ‚Ì’è‹`‚âA•¶Žš—ñ‚⠂̂悤‚È•‚“®¬”“_‚É‚Í“K—p‚³‚ê‚È‚¢B
Žg—p—á
@ƒ‰ƒ“ƒ^ƒCƒ€ƒ`ƒFƒbƒN‚ðs‚¢A•¶Žš—ñ‰»‚·‚éB
ƒoƒO
¡‚Ì‚Æ‚±‚댩‚‚©‚Á‚Ä‚¢‚È‚¢B
Tels http://bloodgate.com in early 2001. Math::BigInt::Constant - Arbitrary sized constant integers Update : 2003/04/23 Site:Felix / Toolbox
Felix ( felix@m4.kcn.ne.jp

55. Math
. You reference the constant PI as math.PI . constants are defined with the full precision of real numbers in JavaScript....... Navigator 2.0.
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.
  • 56. Constant Field Values (Math 1.0-dev API)
    constant Field Values. Contents org.apache.*. org.apache.*. org.apache.commons.math.random.ValueServer. public static final int, constant_MODE, 5.
    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.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.univariate. DescriptiveStatistics public static final int Overview Package Class Use Tree Deprecated Index Help PREV NEXT FRAMES NO FRAMES All Classes

    57. Constant Problem
    References. Bailey, D. H. ``Numerical Results on the Transcendence of constants Involving , , and Euler s constant. math. Comput. 50, 275281, 1988.
    http://icl.pku.edu.cn/yujs/MathWorld/math/c/c612.htm
    Constant Problem
    Given an expression involving known constants, integration in finite terms, computation of limits, etc., determine if the expression is equal to Zero . The constant problem is a very difficult unsolved problem in Transcendental Number theory. However, it is known that the problem is Undecidable if the expression involves oscillatory functions such as Sine . However, the Ferguson-Forcade Algorithm is a practical algorithm for determining if there exist integers for given real numbers such that
    or else establish bounds within which no relation can exist (Bailey 1988). See also Ferguson-Forcade Algorithm Integer Relation Schanuel's Conjecture
    References Bailey, D. H. ``Numerical Results on the Transcendence of Constants Involving , and Euler's Constant.'' Math. Comput. Sackell, J. ``Zero-Equivalence in Function Fields Defined by Algebraic Differential Equations.'' Trans. Amer. Math. Soc.
    Eric W. Weisstein

    58. Programming Ruby: The Pragmatic Programmer's Guide
    m = math.clone, », math. m.constants, », E , PI . m math, », false. Returns the value of the named constant in mod. math.const_get PI, », 3.141592654.
    http://www.rubycentral.com/book/ref_c_module.html
    Programming Ruby
    The Pragmatic Programmer's Guide
    Contents ^
    class Module Parent: Object Version:
    Index:
    constants nesting new ancestors ... public
    Subclasses: Class A Module is a collection of methods and constants. The methods in a module may be instance methods or module methods. Instance methods appear as methods in a class when the module is included, module methods do not. Conversely, module methods may be called without creating an encapsulating object, while instance methods may not. See Module#module_function on page 346. In the descriptions that follow, the parameter aSymbol refers to a symbol, which is either a quoted string or a Symbol (such as :name module Mod include Math CONST = 1 def meth end end Mod.type Module Mod.constants ["CONST", "E", "PI"] Mod.instance_methods ["meth"] class methods constants anArray Returns an array of the names of all constants defined in the system. This list includes the names of all modules and classes. p Module.constants.sort[1..5] produces: ["ARGV", "ArgumentError", "Array", "Bignum", "Binding"]

    59. Search.cpan.org: Tels / Math-BigInt-Constant-1.05
    Tels mathBigInt-constant-1.05. math-BigInt-constant-1.05. This Release, math-BigInt-constant-1.05, Other Releases, math-BigInt-constant-1.04 11 Feb 2002.
    http://search.cpan.org/~tels/Math-BigInt-Constant-1.05/
    Home Authors Recent News ... Feedback
    in All Modules Distributions Authors Tels > Math-BigInt-Constant-1.05
    Math-BigInt-Constant-1.05
    This Release Math-BigInt-Constant-1.05 Download Browse 13 Jan 2004 Other Releases Math-BigInt-Constant-1.04 11 Feb 2002 Links CPAN Testers View/Report Bugs Tools CPAN Testers PASS (2) [ View Rating Rate this distribution License Unknown Special Files CHANGES
    INSTALL

    LICENSE

    MANIFEST
    ...
    SIGNATURE
    Modules
    Math::BigInt::Constant Arbitrary sized constant integers

    60. Search.cpan.org: Math::Symbolic::Constant - Constants In Symbolic Calculations
    Steffen Müller mathSymbolic-0.132 mathSymbolicConstant. Module Version 0.132 Source mathSymbolicConstant - Constants in symbolic calculations.
    http://search.cpan.org/~smueller/Math-Symbolic-0.132/lib/Math/Symbolic/Constant.
    Home Authors Recent News ... Feedback
    in All Modules Distributions Authors Math-Symbolic-0.132 > Math::Symbolic::Constant Module Version: 0.132 Source Latest Release: Math-Symbolic-0.133
    NAME
    SYNOPSIS
    DESCRIPTION
    This module implements numeric constants for Math::Symbolic trees.
    EXPORT
    None by default.
    METHODS
    Constructor new
    Constructor zero
    Constructor one
    Constructor euler
    Constructor pi
    Method value
    object , not just every named variable.
    Method signature
    Method explicit_signature
    Method special
    Method to_string
    Returns a string representation of the constant.
    Method term_type
    Returns the type of the term. (T_CONSTANT)
    AUTHOR
    List of contributors:
    SEE ALSO
    Math::Symbolic

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