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<div class="doctools">
<h1 class="doctools_title">math::constants(n) 1.0.2 tcllib "Tcl Math Library"</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>math::constants - Mathematical and numerical constants</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>
<li class="doctools_section"><a href="#section1">Description</a></li>
<li class="doctools_section"><a href="#section2">PROCEDURES</a></li>
<li class="doctools_section"><a href="#section3">Constants</a></li>
<li class="doctools_section"><a href="#section4">Bugs, Ideas, Feedback</a></li>
<li class="doctools_section"><a href="#keywords">Keywords</a></li>
<li class="doctools_section"><a href="#category">Category</a></li>
<li class="doctools_section"><a href="#copyright">Copyright</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl <span class="opt">?8.3?</span></b></li>
<li>package require <b class="pkgname">math::constants <span class="opt">?1.0.2?</span></b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">::math::constants::constants</b> <i class="arg">args</i></a></li>
<li><a href="#2"><b class="cmd">::math::constants::print-constants</b> <i class="arg">args</i></a></li>
</ul>
</div>
</div>
<div id="section1" class="doctools_section"><h2><a name="section1">Description</a></h2>
<p>This package defines some common mathematical and numerical constants.
By using the package you get consistent values for numbers like pi and
ln(10).</p>
<p>It defines two commands:</p>
<ul class="doctools_itemized">
<li><p>One for importing the constants</p></li>
<li><p>One for reporting which constants are defined and what values they
actually have.</p></li>
</ul>
<p>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:</p>
<pre class="doctools_example">
variable radtodeg [expr {180.0/(4.0*atan(1.0))}]
</pre>
<p>and use the variable radtodeg whenever you need the conversion.</p>
<p>This has two drawbacks:</p>
<ul class="doctools_itemized">
<li><p>You need to remember the proper formula or value and that is
error-prone.</p></li>
<li><p>Especially with the use of mathematical functions like <em>atan</em>
you assume that they have been accurately implemented. This is seldom or
never the case and for each platform you can get subtle differences.</p></li>
</ul>
<p>Here is the way you can do it with the <em>math::constants</em> package:</p>
<pre class="doctools_example">
package require math::constants
::math::constants::constants radtodeg degtorad
</pre>
<p>which creates two variables, radtodeg and (its reciprocal) degtorad
in the calling namespace.</p>
<p>Constants that have been defined (their values are mostly taken
from mathematical tables with more precision than usually can be
handled) include:</p>
<ul class="doctools_itemized">
<li><p>basic constants like pi, e, gamma (Euler's constant)</p></li>
<li><p>derived values like ln(10) and sqrt(2)</p></li>
<li><p>purely numerical values such as 1/3 that are included for convenience
and for the fact that certain seemingly trivial computations like:</p>
<pre class="doctools_example">
set value [expr {3.0*$onethird}]
</pre>
<p>give <em>exactly</em> the value you expect (if IEEE arithmetic is
available).</p></li>
</ul>
<p>The full set of named constants is listed in section <span class="sectref"><a href="#section3">Constants</a></span>.</p>
</div>
<div id="section2" class="doctools_section"><h2><a name="section2">PROCEDURES</a></h2>
<p>The package defines the following public procedures:</p>
<dl class="doctools_definitions">
<dt><a name="1"><b class="cmd">::math::constants::constants</b> <i class="arg">args</i></a></dt>
<dd><p>Import the constants whose names are given as arguments</p></dd>
<dt><a name="2"><b class="cmd">::math::constants::print-constants</b> <i class="arg">args</i></a></dt>
<dd><p>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.</p></dd>
</dl>
</div>
<div id="section3" class="doctools_section"><h2><a name="section3">Constants</a></h2>
<dl class="doctools_definitions">
<dt><b class="const">pi</b></dt>
<dd><p>Ratio of circle circumference to diameter</p></dd>
<dt><b class="const">e</b></dt>
<dd><p>Base for natural logarithm</p></dd>
<dt><b class="const">ln10</b></dt>
<dd><p>Natural logarithm of 10</p></dd>
<dt><b class="const">phi</b></dt>
<dd><p>Golden ratio</p></dd>
<dt><b class="const">gamma</b></dt>
<dd><p>Euler's constant</p></dd>
<dt><b class="const">sqrt2</b></dt>
<dd><p>Square root of 2</p></dd>
<dt><b class="const">thirdrt2</b></dt>
<dd><p>One-third power of 2</p></dd>
<dt><b class="const">sqrt3</b></dt>
<dd><p>Square root of 3</p></dd>
<dt><b class="const">radtodeg</b></dt>
<dd><p>Conversion from radians to degrees</p></dd>
<dt><b class="const">degtorad</b></dt>
<dd><p>Conversion from degrees to radians</p></dd>
<dt><b class="const">onethird</b></dt>
<dd><p>One third (0.3333....)</p></dd>
<dt><b class="const">twothirds</b></dt>
<dd><p>Two thirds (0.6666....)</p></dd>
<dt><b class="const">onesixth</b></dt>
<dd><p>One sixth (0.1666....)</p></dd>
<dt><b class="const">huge</b></dt>
<dd><p>(Approximately) largest number</p></dd>
<dt><b class="const">tiny</b></dt>
<dd><p>(Approximately) smallest number not equal zero</p></dd>
<dt><b class="const">eps</b></dt>
<dd><p>Smallest number such that 1+eps != 1</p></dd>
</dl>
</div>
<div id="section4" class="doctools_section"><h2><a name="section4">Bugs, Ideas, Feedback</a></h2>
<p>This document, and the package it describes, will undoubtedly contain
bugs and other problems.
Please report such in the category <em>math :: constants</em> of the
<a href="http://core.tcl.tk/tcllib/reportlist">Tcllib Trackers</a>.
Please also report any ideas for enhancements you may have for either
package and/or documentation.</p>
<p>When proposing code changes, please provide <em>unified diffs</em>,
i.e the output of <b class="const">diff -u</b>.</p>
<p>Note further that <em>attachments</em> are strongly preferred over
inlined patches. Attachments can be made by going to the <b class="const">Edit</b>
form of the ticket immediately after its creation, and then using the
left-most button in the secondary navigation bar.</p>
</div>
<div id="keywords" class="doctools_section"><h2><a name="keywords">Keywords</a></h2>
<p><a href="../../../../index.html#constants">constants</a>, <a href="../../../../index.html#degrees">degrees</a>, <a href="../../../../index.html#e">e</a>, <a href="../../../../index.html#math">math</a>, <a href="../../../../index.html#pi">pi</a>, <a href="../../../../index.html#radians">radians</a></p>
</div>
<div id="category" class="doctools_section"><h2><a name="category">Category</a></h2>
<p>Mathematics</p>
</div>
<div id="copyright" class="doctools_section"><h2><a name="copyright">Copyright</a></h2>
<p>Copyright © 2004 Arjen Markus <[email protected]></p>
</div>
</div></body></html>
