NAME

       math::constants - Mathematical and numerical constants

SYNOPSIS

       package require Tcl  ?8.3?

       package require math::constants  ?1.0.2?

       ::math::constants::constants args

       ::math::constants::print-constants args

_________________________________________________________________________________________________

DESCRIPTION

       This  package  defines  some  common  mathematical  and numerical constants.  By using the
       package you get consistent values for numbers like pi and ln(10).

       It defines two commands:

       •      One for importing the constants

       •      One for reporting which constants are defined and what values they actually have.

       The motivation for this package is that quite often, with (mathematical) computations, you
       need  a  good  approximation to, say, the ratio of degrees to radians. You can, of course,
       define this like:

                  variable radtodeg [expr {180.0/(4.0*atan(1.0))}]

       and use the variable radtodeg whenever you need the conversion.

       This has two drawbacks:

       •      You need to remember the proper formula or value and that is error-prone.

       •      Especially with the use of mathematical functions like atan you  assume  that  they
              have  been  accurately  implemented.  This is seldom or never the case and for each
              platform you can get subtle differences.

       Here is the way you can do it with the math::constants package:

                  package require math::constants
                  ::math::constants::constants radtodeg degtorad

       which creates two variables,  radtodeg  and  (its  reciprocal)  degtorad  in  the  calling
       namespace.

       Constants  that  have been defined (their values are mostly taken from mathematical tables
       with more precision than usually can be handled) include:

       •      basic constants like pi, e, gamma (Euler's constant)

       •      derived values like ln(10) and sqrt(2)

       •      purely numerical values such as 1/3 that are included for convenience and  for  the
              fact that certain seemingly trivial computations like:

                  set value [expr {3.0*$onethird}]

              give exactly the value you expect (if IEEE arithmetic is available).

       The full set of named constants is listed in section Constants.

PROCEDURES

       The package defines the following public procedures:

       ::math::constants::constants args
              Import the constants whose names are given as arguments

       ::math::constants::print-constants args
              Print  the  constants whose names are given as arguments on the screen (name, value
              and description) or, if no arguments are given, print all defined  constants.  This
              is mainly a convenience procedure.

CONSTANTS

       pi     Ratio of circle circumference to diameter

       e      Base for natural logarithm

       ln10   Natural logarithm of 10

       phi    Golden ratio

       gamma  Euler's constant

       sqrt2  Square root of 2

       thirdrt2
              One-third power of 2

       sqrt3  Square root of 3

       radtodeg
              Conversion from radians to degrees

       degtorad
              Conversion from degrees to radians

       onethird
              One third (0.3333....)

       twothirds
              Two thirds (0.6666....)

       onesixth
              One sixth (0.1666....)

       huge   (Approximately) largest number

       tiny   (Approximately) smallest number not equal zero

       eps    Smallest number such that 1+eps != 1

BUGS, IDEAS, FEEDBACK

       This  document,  and  the  package  it  describes, will undoubtedly contain bugs and other
       problems.  Please report such in the category math :: constants  of  the  Tcllib  Trackers
       [http://core.tcl.tk/tcllib/reportlist].  Please also report any ideas for enhancements you
       may have for either package and/or documentation.

       When proposing code changes, please provide unified diffs, i.e the output of diff -u.

       Note further that attachments are strongly preferred over inlined patches. Attachments can
       be  made  by going to the Edit form of the ticket immediately after its creation, and then
       using the left-most button in the secondary navigation bar.

KEYWORDS

       constants, degrees, e, math, pi, radians

CATEGORY

       Mathematics

COPYRIGHT

       Copyright (c) 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>