1math::constants(n)             Tcl Math Library             math::constants(n)
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NAME

8       math::constants - Mathematical and numerical constants
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SYNOPSIS

11       package require Tcl  ?8.3?
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13       package require math::constants  ?1.0.2?
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15       ::math::constants::constants args
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17       ::math::constants::print-constants args
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DESCRIPTION

22       This  package defines some common mathematical and numerical constants.
23       By using the package you get consistent values for numbers like pi  and
24       ln(10).
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26       It defines two commands:
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28       •      One for importing the constants
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30       •      One  for  reporting  which constants are defined and what values
31              they actually have.
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33       The motivation for this package is that quite often,  with  (mathemati‐
34       cal)  computations, you need a good approximation to, say, the ratio of
35       degrees to radians. You can, of course, define this like:
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38                  variable radtodeg [expr {180.0/(4.0*atan(1.0))}]
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40       and use the variable radtodeg whenever you need the conversion.
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42       This has two drawbacks:
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44       •      You need to remember the proper formula or value and that is er‐
45              ror-prone.
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47       •      Especially  with the use of mathematical functions like atan you
48              assume that they have been accurately implemented. This is  sel‐
49              dom  or  never the case and for each platform you can get subtle
50              differences.
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52       Here is the way you can do it with the math::constants package:
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55                  package require math::constants
56                  ::math::constants::constants radtodeg degtorad
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58       which creates two variables, radtodeg and (its reciprocal) degtorad  in
59       the calling namespace.
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61       Constants  that  have  been defined (their values are mostly taken from
62       mathematical tables with more precision than usually  can  be  handled)
63       include:
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65       •      basic constants like pi, e, gamma (Euler's constant)
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67       •      derived values like ln(10) and sqrt(2)
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69       •      purely numerical values such as 1/3 that are included for conve‐
70              nience and for the fact that certain seemingly trivial  computa‐
71              tions like:
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74                  set value [expr {3.0*$onethird}]
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77              give  exactly the value you expect (if IEEE arithmetic is avail‐
78              able).
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80       The full set of named constants is listed in section Constants.
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PROCEDURES

83       The package defines the following public procedures:
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85       ::math::constants::constants args
86              Import the constants whose names are given as arguments
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89       ::math::constants::print-constants args
90              Print the constants whose names are given as  arguments  on  the
91              screen  (name,  value  and  description) or, if no arguments are
92              given, print all defined constants. This is mainly a convenience
93              procedure.
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CONSTANTS

96       pi     Ratio of circle circumference to diameter
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98       e      Base for natural logarithm
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100       ln10   Natural logarithm of 10
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102       phi    Golden ratio
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104       gamma  Euler's constant
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106       sqrt2  Square root of 2
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108       thirdrt2
109              One-third power of 2
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111       sqrt3  Square root of 3
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113       radtodeg
114              Conversion from radians to degrees
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116       degtorad
117              Conversion from degrees to radians
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119       onethird
120              One third (0.3333....)
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122       twothirds
123              Two thirds (0.6666....)
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125       onesixth
126              One sixth (0.1666....)
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128       huge   (Approximately) largest number
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130       tiny   (Approximately) smallest number not equal zero
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132       eps    Smallest number such that 1+eps != 1
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BUGS, IDEAS, FEEDBACK

135       This  document,  and the package it describes, will undoubtedly contain
136       bugs and other problems.  Please report such in the  category  math  ::
137       constants   of   the   Tcllib  Trackers  [http://core.tcl.tk/tcllib/re‐
138       portlist].  Please also report any ideas for enhancements you may  have
139       for either package and/or documentation.
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141       When proposing code changes, please provide unified diffs, i.e the out‐
142       put of diff -u.
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144       Note further that  attachments  are  strongly  preferred  over  inlined
145       patches.  Attachments  can  be  made  by  going to the Edit form of the
146       ticket immediately after its creation, and  then  using  the  left-most
147       button in the secondary navigation bar.
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KEYWORDS

150       constants, degrees, e, math, pi, radians
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CATEGORY

153       Mathematics
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156       Copyright (c) 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>
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161tcllib                               1.0.2                  math::constants(n)
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