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    <title>Sun Coast Amateur &lt;br&gt;Radio Club Society - blog:2020-11-08</title>
    <tagline></tagline>
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    <id>https://scarcs.ca/</id>
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    <entry>
        <title>geogebra_plugin</title>
        <link rel="alternate" type="text/html" href="https://scarcs.ca/blog/2020-11-08/geogebra_plugin"/>
        <created>2024-11-24T20:38:14+00:00</created>
        <issued>2024-11-24T20:38:14+00:00</issued>
        <modified>2024-11-24T20:38:14+00:00</modified>
        <id>https://scarcs.ca/blog/2020-11-08/geogebra_plugin</id>
        <author>
            <name>Anonymous</name>
        </author>
        <summary>
&lt;h1 class=&quot;sectionedit1&quot; id=&quot;geogebra_plugin&quot;&gt;Geogebra Plugin&lt;/h1&gt;
&lt;div class=&quot;level1&quot;&gt;

&lt;p&gt;
&lt;a href=&quot;https://www.geogebra.org/&quot; class=&quot;urlextern&quot; title=&quot;https://www.geogebra.org/&quot; rel=&quot;ugc nofollow&quot;&gt;Geogebra&lt;/a&gt; is a graphing and geometry tool I&amp;#039;ve been using since my teaching days.  I always found it to be very useful to display concepts that are hard to visualize on a static page.  However, it is a lot more than a simple animation since people can interact with it and move things around.
&lt;/p&gt;

&lt;p&gt;
In the past, I had to export Geogbra files to html5 to embed them, but the process was pretty clunky and time consuming. I searched the Dokuwiki plugins but all the ones listed are too old and don&amp;#039;t work anymore.  Finally, I created my own using some general instructions for &lt;a href=&quot;https://wiki.geogebra.org/en/Reference:GeoGebra_Apps_Embedding&quot; class=&quot;urlextern&quot; title=&quot;https://wiki.geogebra.org/en/Reference:GeoGebra_Apps_Embedding&quot; rel=&quot;ugc nofollow&quot;&gt;embedding Geogebra files&lt;/a&gt;.  This is my first plugin and a bit of a cheat: I basically took the existing &lt;a href=&quot;https://www.dokuwiki.org/plugin:color&quot; class=&quot;urlextern&quot; title=&quot;https://www.dokuwiki.org/plugin:color&quot; rel=&quot;ugc nofollow&quot;&gt;Color plugin&lt;/a&gt; which is pretty simple, studied it to learn a bit of the syntax and modified it until it did what I needed.  However, there&amp;#039;s still a lot of code that I don&amp;#039;t really understand and a few features that are missing.
&lt;/p&gt;

&lt;p&gt;
Here&amp;#039;s what I got so far.  If anyone has experience writing Dokuwiki plugin, please &lt;a href=&quot;mailto:&amp;#112;&amp;#97;&amp;#116;&amp;#111;&amp;#111;&amp;#64;&amp;#114;&amp;#98;&amp;#111;&amp;#120;&amp;#46;&amp;#109;&amp;#101;&quot; class=&quot;mail&quot; title=&quot;&amp;#112;&amp;#97;&amp;#116;&amp;#111;&amp;#111;&amp;#64;&amp;#114;&amp;#98;&amp;#111;&amp;#120;&amp;#46;&amp;#109;&amp;#101;&quot;&gt;reach out&lt;/a&gt;.
&lt;/p&gt;

&lt;p&gt;
Here&amp;#039;s how to installed it:
&lt;/p&gt;
&lt;div class=&quot;hiddenGlobal  hiddenActive&quot;&gt;&lt;div class=&quot;hiddenElements&quot;&gt;&lt;/div&gt;&lt;div class=&quot;hiddenHead  hiddenSinceBeginning&quot;&gt;&lt;div class=&quot;hiddenOnHidden&quot;&gt;
&lt;p&gt;
Click to display ⇲
&lt;/p&gt;
&lt;/div&gt;&lt;div class=&quot;hiddenOnVisible&quot;&gt;
&lt;p&gt;
Click to hide ⇱
&lt;/p&gt;
&lt;/div&gt;&lt;/div&gt; &lt;!-- .hiddenHead --&gt;&lt;div class=&quot;hiddenBody&quot;&gt;&lt;ul&gt;
&lt;li class=&quot;level1&quot;&gt;&lt;div class=&quot;li&quot;&gt;
 Add the following three files in the wiki folder: &lt;code&gt;./lib/plugins/ggb2/&lt;/code&gt;
&lt;/div&gt;&lt;/li&gt;
&lt;li class=&quot;level1&quot;&gt;&lt;div class=&quot;li&quot;&gt;
 &lt;code&gt;manager.dat&lt;/code&gt;&lt;pre class=&quot;code&quot;&gt;installed=Sun, 08 Nov 2020 08:20:00 -0800&lt;/pre&gt;

&lt;p&gt;

&lt;/div&gt;&lt;/li&gt;
&lt;li class=&quot;level1&quot;&gt;&lt;div class=&quot;li&quot;&gt;
 &lt;code&gt;plugin.info.txt&lt;/code&gt;
&lt;/p&gt;
&lt;pre class=&quot;code&quot;&gt;base   ggb2
author Patrick Truchon
email  patoo@rbox.me
date   2020-11-08
name   geogebra6 syntax plugin
desc   Embeds GeoGebra 6 files into Dokuwiki&lt;/pre&gt;

&lt;p&gt;

&lt;/div&gt;&lt;/li&gt;
&lt;li class=&quot;level1&quot;&gt;&lt;div class=&quot;li&quot;&gt;
 &lt;code&gt;syntax.php&lt;/code&gt;
&lt;/p&gt;
&lt;pre class=&quot;code php&quot;&gt;&lt;span class=&quot;kw2&quot;&gt;&amp;lt;?php&lt;/span&gt;
&lt;span class=&quot;co4&quot;&gt;/**
 * Plugin ggb2: Embeds Geogebra files into Dokuwiki.
 *
 * @license    GPL 3 (http://www.gnu.org/licenses/gpl.html)
 * @author     Patrick Truchon &amp;lt;patoo@rbox.me&amp;gt;
 * See: https://wiki.geogebra.org/en/Reference:GeoGebra_Apps_Embedding
 */&lt;/span&gt;
&amp;nbsp;
&lt;span class=&quot;co1&quot;&gt;// must be run within DokuWiki&lt;/span&gt;
&lt;span class=&quot;kw1&quot;&gt;if&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;!&lt;/span&gt;&lt;a href=&quot;http://www.php.net/defined&quot;&gt;&lt;span class=&quot;kw3&quot;&gt;defined&lt;/span&gt;&lt;/a&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;st_h&quot;&gt;'DOKU_INC'&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt; &lt;a href=&quot;http://www.php.net/die&quot;&gt;&lt;span class=&quot;kw3&quot;&gt;die&lt;/span&gt;&lt;/a&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
&lt;span class=&quot;kw1&quot;&gt;if&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;!&lt;/span&gt;&lt;a href=&quot;http://www.php.net/defined&quot;&gt;&lt;span class=&quot;kw3&quot;&gt;defined&lt;/span&gt;&lt;/a&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;st_h&quot;&gt;'DOKU_PLUGIN'&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt; &lt;a href=&quot;http://www.php.net/define&quot;&gt;&lt;span class=&quot;kw3&quot;&gt;define&lt;/span&gt;&lt;/a&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;st_h&quot;&gt;'DOKU_PLUGIN'&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt;DOKU_INC&lt;span class=&quot;sy0&quot;&gt;.&lt;/span&gt;&lt;span class=&quot;st_h&quot;&gt;'lib/plugins/'&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
&lt;span class=&quot;kw1&quot;&gt;require_once&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;DOKU_PLUGIN&lt;span class=&quot;sy0&quot;&gt;.&lt;/span&gt;&lt;span class=&quot;st_h&quot;&gt;'syntax.php'&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
&amp;nbsp;
&amp;nbsp;
&lt;span class=&quot;co4&quot;&gt;/**
 * All DokuWiki plugins to extend the parser/rendering mechanism
 * need to inherit from this class
 */&lt;/span&gt;
&lt;span class=&quot;kw2&quot;&gt;class&lt;/span&gt; syntax_plugin_ggb2 &lt;span class=&quot;kw2&quot;&gt;extends&lt;/span&gt; DokuWiki_Syntax_Plugin &lt;span class=&quot;br0&quot;&gt;&amp;#123;&lt;/span&gt;
&amp;nbsp;
    &lt;span class=&quot;kw2&quot;&gt;function&lt;/span&gt; &lt;a href=&quot;http://www.php.net/gettype&quot;&gt;&lt;span class=&quot;kw3&quot;&gt;getType&lt;/span&gt;&lt;/a&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#123;&lt;/span&gt; &lt;span class=&quot;kw1&quot;&gt;return&lt;/span&gt; &lt;span class=&quot;st_h&quot;&gt;'substition'&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt; &lt;span class=&quot;br0&quot;&gt;&amp;#125;&lt;/span&gt;
    &lt;span class=&quot;kw2&quot;&gt;function&lt;/span&gt; getSort&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#123;&lt;/span&gt; &lt;span class=&quot;kw1&quot;&gt;return&lt;/span&gt; &lt;span class=&quot;nu0&quot;&gt;306&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt; &lt;span class=&quot;br0&quot;&gt;&amp;#125;&lt;/span&gt;
    &lt;span class=&quot;kw2&quot;&gt;function&lt;/span&gt; connectTo&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$mode&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt; &lt;span class=&quot;br0&quot;&gt;&amp;#123;&lt;/span&gt; &lt;span class=&quot;re0&quot;&gt;$this&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;-&amp;gt;&lt;/span&gt;&lt;span class=&quot;me1&quot;&gt;Lexer&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;-&amp;gt;&lt;/span&gt;&lt;span class=&quot;me1&quot;&gt;addSpecialPattern&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;st_h&quot;&gt;'{{ggb&amp;gt;.*?}}'&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$mode&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;st_h&quot;&gt;'plugin_ggb2'&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt; &lt;span class=&quot;br0&quot;&gt;&amp;#125;&lt;/span&gt;
&amp;nbsp;
&amp;nbsp;
    &lt;span class=&quot;co4&quot;&gt;/**
     * Handle the match
     */&lt;/span&gt;
    &lt;span class=&quot;kw2&quot;&gt;function&lt;/span&gt; handle&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$match&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;re0&quot;&gt;$state&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;re0&quot;&gt;$pos&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt; Doku_Handler &lt;span class=&quot;re0&quot;&gt;$handler&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#123;&lt;/span&gt;
        &lt;span class=&quot;re0&quot;&gt;$match&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;=&lt;/span&gt; &lt;a href=&quot;http://www.php.net/html_entity_decode&quot;&gt;&lt;span class=&quot;kw3&quot;&gt;html_entity_decode&lt;/span&gt;&lt;/a&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;a href=&quot;http://www.php.net/substr&quot;&gt;&lt;span class=&quot;kw3&quot;&gt;substr&lt;/span&gt;&lt;/a&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$match&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;nu0&quot;&gt;6&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;-&lt;/span&gt;&lt;span class=&quot;nu0&quot;&gt;2&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
        &lt;a href=&quot;http://www.php.net/list&quot;&gt;&lt;span class=&quot;kw3&quot;&gt;list&lt;/span&gt;&lt;/a&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$ggbfile&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;re0&quot;&gt;$index&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;=&lt;/span&gt; &lt;a href=&quot;http://www.php.net/explode&quot;&gt;&lt;span class=&quot;kw3&quot;&gt;explode&lt;/span&gt;&lt;/a&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;st_h&quot;&gt;'|'&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$match&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;nu0&quot;&gt;2&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
        &lt;span class=&quot;kw1&quot;&gt;if&lt;/span&gt; &lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;a href=&quot;http://www.php.net/preg_match&quot;&gt;&lt;span class=&quot;kw3&quot;&gt;preg_match&lt;/span&gt;&lt;/a&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;st_h&quot;&gt;'/(.*) ([0-9]+,[0-9]+)$/'&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt;&lt;a href=&quot;http://www.php.net/trim&quot;&gt;&lt;span class=&quot;kw3&quot;&gt;trim&lt;/span&gt;&lt;/a&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$ggbfile&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$matches&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt; &lt;span class=&quot;br0&quot;&gt;&amp;#123;&lt;/span&gt;
            &lt;span class=&quot;re0&quot;&gt;$ggbfile&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;re0&quot;&gt;$matches&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#91;&lt;/span&gt;&lt;span class=&quot;nu0&quot;&gt;1&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#93;&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
        &lt;span class=&quot;kw1&quot;&gt;if&lt;/span&gt; &lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;a href=&quot;http://www.php.net/strpos&quot;&gt;&lt;span class=&quot;kw3&quot;&gt;strpos&lt;/span&gt;&lt;/a&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$matches&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#91;&lt;/span&gt;&lt;span class=&quot;nu0&quot;&gt;2&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#93;&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;st_h&quot;&gt;','&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;!==&lt;/span&gt; &lt;span class=&quot;kw4&quot;&gt;false&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt; &lt;span class=&quot;br0&quot;&gt;&amp;#123;&lt;/span&gt;
            &lt;a href=&quot;http://www.php.net/list&quot;&gt;&lt;span class=&quot;kw3&quot;&gt;list&lt;/span&gt;&lt;/a&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$w&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;re0&quot;&gt;$h&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;=&lt;/span&gt; &lt;a href=&quot;http://www.php.net/explode&quot;&gt;&lt;span class=&quot;kw3&quot;&gt;explode&lt;/span&gt;&lt;/a&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;st_h&quot;&gt;','&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$matches&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#91;&lt;/span&gt;&lt;span class=&quot;nu0&quot;&gt;2&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#93;&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt;&lt;span class=&quot;nu0&quot;&gt;2&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
            &lt;span class=&quot;br0&quot;&gt;&amp;#125;&lt;/span&gt;
        &lt;span class=&quot;kw1&quot;&gt;else&lt;/span&gt; &lt;span class=&quot;br0&quot;&gt;&amp;#123;&lt;/span&gt;
            &lt;span class=&quot;re0&quot;&gt;$w&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;st_h&quot;&gt;'800'&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
            &lt;span class=&quot;re0&quot;&gt;$h&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;re0&quot;&gt;$matches&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#91;&lt;/span&gt;&lt;span class=&quot;nu0&quot;&gt;2&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#93;&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
            &lt;span class=&quot;br0&quot;&gt;&amp;#125;&lt;/span&gt;
            &lt;span class=&quot;br0&quot;&gt;&amp;#125;&lt;/span&gt;
        &lt;span class=&quot;kw1&quot;&gt;else&lt;/span&gt; &lt;span class=&quot;br0&quot;&gt;&amp;#123;&lt;/span&gt;
            &lt;span class=&quot;re0&quot;&gt;$w&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;st_h&quot;&gt;'800'&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
            &lt;span class=&quot;re0&quot;&gt;$h&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;st_h&quot;&gt;'400'&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
            &lt;span class=&quot;br0&quot;&gt;&amp;#125;&lt;/span&gt;
&amp;nbsp;
        &lt;span class=&quot;kw1&quot;&gt;if&lt;/span&gt; &lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;!&lt;/span&gt;&lt;a href=&quot;http://www.php.net/isset&quot;&gt;&lt;span class=&quot;kw3&quot;&gt;isset&lt;/span&gt;&lt;/a&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$index&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt; &lt;span class=&quot;re0&quot;&gt;$index&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;st_h&quot;&gt;''&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
        &lt;span class=&quot;kw1&quot;&gt;return&lt;/span&gt; &lt;a href=&quot;http://www.php.net/array&quot;&gt;&lt;span class=&quot;kw3&quot;&gt;array&lt;/span&gt;&lt;/a&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$ggbfile&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt; hsc&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;a href=&quot;http://www.php.net/trim&quot;&gt;&lt;span class=&quot;kw3&quot;&gt;trim&lt;/span&gt;&lt;/a&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$index&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt; hsc&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;a href=&quot;http://www.php.net/trim&quot;&gt;&lt;span class=&quot;kw3&quot;&gt;trim&lt;/span&gt;&lt;/a&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$w&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt; hsc&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;a href=&quot;http://www.php.net/trim&quot;&gt;&lt;span class=&quot;kw3&quot;&gt;trim&lt;/span&gt;&lt;/a&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$h&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt; 
        &lt;span class=&quot;br0&quot;&gt;&amp;#125;&lt;/span&gt;
&amp;nbsp;
    &lt;span class=&quot;co4&quot;&gt;/**
     * Create output
     */&lt;/span&gt;
    &lt;span class=&quot;kw2&quot;&gt;function&lt;/span&gt; render&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$mode&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt; Doku_Renderer &lt;span class=&quot;re0&quot;&gt;$renderer&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;re0&quot;&gt;$data&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt; &lt;span class=&quot;br0&quot;&gt;&amp;#123;&lt;/span&gt;
        &lt;a href=&quot;http://www.php.net/list&quot;&gt;&lt;span class=&quot;kw3&quot;&gt;list&lt;/span&gt;&lt;/a&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$ggbfile&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;re0&quot;&gt;$index&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;re0&quot;&gt;$w&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;re0&quot;&gt;$h&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;re0&quot;&gt;$data&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
        &lt;span class=&quot;kw1&quot;&gt;if&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$mode&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;==&lt;/span&gt; &lt;span class=&quot;st_h&quot;&gt;'xhtml'&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#123;&lt;/span&gt;
            &lt;span class=&quot;re0&quot;&gt;$slash&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;=&lt;/span&gt; &lt;a href=&quot;http://www.php.net/strrpos&quot;&gt;&lt;span class=&quot;kw3&quot;&gt;strrpos&lt;/span&gt;&lt;/a&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$ggbfile&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;st0&quot;&gt;&amp;quot;/&amp;quot;&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
            &lt;span class=&quot;kw1&quot;&gt;if&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$slash&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;&amp;gt;&lt;/span&gt; &lt;span class=&quot;nu0&quot;&gt;0&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#123;&lt;/span&gt;
               &lt;span class=&quot;re0&quot;&gt;$slash&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;=&lt;/span&gt; &lt;span class=&quot;re0&quot;&gt;$slash&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;+&lt;/span&gt; &lt;span class=&quot;nu0&quot;&gt;1&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
               &lt;span class=&quot;br0&quot;&gt;&amp;#125;&lt;/span&gt;
            &lt;span class=&quot;re0&quot;&gt;$ggbid&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;=&lt;/span&gt; &lt;a href=&quot;http://www.php.net/substr&quot;&gt;&lt;span class=&quot;kw3&quot;&gt;substr&lt;/span&gt;&lt;/a&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#40;&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$ggbfile&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;re0&quot;&gt;$slash&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;,&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;-&lt;/span&gt;&lt;span class=&quot;nu0&quot;&gt;4&lt;/span&gt;&lt;span class=&quot;br0&quot;&gt;&amp;#41;&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
            &lt;span class=&quot;re0&quot;&gt;$renderer&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;-&amp;gt;&lt;/span&gt;&lt;span class=&quot;me1&quot;&gt;doc&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;.=&lt;/span&gt; &lt;span class=&quot;st_h&quot;&gt;'&amp;lt;script src=&amp;quot;https://www.geogebra.org/apps/deployggb.js&amp;quot;&amp;gt;&amp;lt;/script&amp;gt;'&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
            &lt;span class=&quot;re0&quot;&gt;$renderer&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;-&amp;gt;&lt;/span&gt;&lt;span class=&quot;me1&quot;&gt;doc&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;.=&lt;/span&gt; &lt;span class=&quot;st_h&quot;&gt;'&amp;lt;div id=&amp;quot;'&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;.&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$ggbid&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;.&lt;/span&gt;&lt;span class=&quot;st_h&quot;&gt;'&amp;quot;&amp;gt;&amp;lt;/div&amp;gt;'&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
            &lt;span class=&quot;re0&quot;&gt;$renderer&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;-&amp;gt;&lt;/span&gt;&lt;span class=&quot;me1&quot;&gt;doc&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;.=&lt;/span&gt; &lt;span class=&quot;st_h&quot;&gt;'&amp;lt;script&amp;gt;'&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
            &lt;span class=&quot;re0&quot;&gt;$renderer&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;-&amp;gt;&lt;/span&gt;&lt;span class=&quot;me1&quot;&gt;doc&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;.=&lt;/span&gt; &lt;span class=&quot;st_h&quot;&gt;'window.addEventListener(&amp;quot;load&amp;quot;, function() {'&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
            &lt;span class=&quot;re0&quot;&gt;$renderer&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;-&amp;gt;&lt;/span&gt;&lt;span class=&quot;me1&quot;&gt;doc&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;.=&lt;/span&gt; &lt;span class=&quot;st_h&quot;&gt;'new GGBApplet({&amp;quot;width&amp;quot;: '&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;.&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$w&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;.&lt;/span&gt;&lt;span class=&quot;st_h&quot;&gt;', &amp;quot;height&amp;quot;: '&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;.&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$h&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;.&lt;/span&gt;&lt;span class=&quot;st_h&quot;&gt;', '&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
            &lt;span class=&quot;re0&quot;&gt;$renderer&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;-&amp;gt;&lt;/span&gt;&lt;span class=&quot;me1&quot;&gt;doc&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;.=&lt;/span&gt; &lt;span class=&quot;st_h&quot;&gt;'&amp;quot;showToolBar&amp;quot;: false, &amp;quot;showAlgebraInput&amp;quot;: false,'&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
            &lt;span class=&quot;re0&quot;&gt;$renderer&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;-&amp;gt;&lt;/span&gt;&lt;span class=&quot;me1&quot;&gt;doc&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;.=&lt;/span&gt; &lt;span class=&quot;st_h&quot;&gt;'&amp;quot;showMenuBar&amp;quot;: false, &amp;quot;filename&amp;quot;: &amp;quot;/_media/'&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
            &lt;span class=&quot;re0&quot;&gt;$renderer&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;-&amp;gt;&lt;/span&gt;&lt;span class=&quot;me1&quot;&gt;doc&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;.=&lt;/span&gt; &lt;span class=&quot;st0&quot;&gt;&amp;quot;&lt;span class=&quot;es4&quot;&gt;$ggbfile&lt;/span&gt;&lt;span class=&quot;es1&quot;&gt;\&amp;quot;&lt;/span&gt;},true).inject(&lt;span class=&quot;es4&quot;&gt;$ggbid&lt;/span&gt;) })&amp;quot;&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
            &lt;span class=&quot;re0&quot;&gt;$renderer&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;-&amp;gt;&lt;/span&gt;&lt;span class=&quot;me1&quot;&gt;doc&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;.=&lt;/span&gt; &lt;span class=&quot;st_h&quot;&gt;'&amp;lt;/script&amp;gt;'&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
            &lt;span class=&quot;re0&quot;&gt;$renderer&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;-&amp;gt;&lt;/span&gt;&lt;span class=&quot;me1&quot;&gt;doc&lt;/span&gt; &lt;span class=&quot;sy0&quot;&gt;.=&lt;/span&gt; &lt;span class=&quot;st_h&quot;&gt;'Download &amp;lt;a href=&amp;quot;/_media/'&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;.&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$ggbfile&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;.&lt;/span&gt;&lt;span class=&quot;st_h&quot;&gt;'&amp;quot;&amp;gt;'&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;.&lt;/span&gt;&lt;span class=&quot;re0&quot;&gt;$ggbid&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;.&lt;/span&gt;&lt;span class=&quot;st_h&quot;&gt;'.ggb&amp;lt;/a&amp;gt;'&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
            &lt;span class=&quot;kw1&quot;&gt;return&lt;/span&gt; &lt;span class=&quot;kw4&quot;&gt;true&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
        &lt;span class=&quot;br0&quot;&gt;&amp;#125;&lt;/span&gt;
        &lt;span class=&quot;kw1&quot;&gt;return&lt;/span&gt; &lt;span class=&quot;kw4&quot;&gt;false&lt;/span&gt;&lt;span class=&quot;sy0&quot;&gt;;&lt;/span&gt;
    &lt;span class=&quot;br0&quot;&gt;&amp;#125;&lt;/span&gt;
&lt;span class=&quot;br0&quot;&gt;&amp;#125;&lt;/span&gt;
&lt;span class=&quot;sy1&quot;&gt;?&amp;gt;&lt;/span&gt;&lt;/pre&gt;

&lt;/div&gt;&lt;/li&gt;
&lt;/ul&gt;

&lt;/div&gt;&lt;/div&gt;
&lt;p&gt;
The syntax is:
&lt;/p&gt;
&lt;pre class=&quot;code&quot;&gt;{{ggb&amp;gt;/path/to/geogebrafile.ggb 740,300}}&lt;/pre&gt;

&lt;p&gt;
Note that at the moment, if a path is used, it must use &lt;code&gt;/&lt;/code&gt; instead of &lt;code&gt;:&lt;/code&gt;.  The default dimensions are 800&amp;times;400 if they are omitted.
&lt;/p&gt;

&lt;p&gt;
Here&amp;#039;s an example from one of &lt;a href=&quot;https://scarcs.ca/hambasics/sections/wavemodulation#wave_addition&quot; class=&quot;wikilink1&quot; title=&quot;hambasics:sections:wavemodulation&quot; data-wiki-id=&quot;hambasics:sections:wavemodulation&quot;&gt;Ham Basics&lt;/a&gt; pages showing how different waves add and what SWR looks like:
&lt;/p&gt;

&lt;/div&gt;
&lt;!-- EDIT{&amp;quot;target&amp;quot;:&amp;quot;section&amp;quot;,&amp;quot;name&amp;quot;:&amp;quot;Geogebra Plugin&amp;quot;,&amp;quot;hid&amp;quot;:&amp;quot;geogebra_plugin&amp;quot;,&amp;quot;codeblockOffset&amp;quot;:0,&amp;quot;secid&amp;quot;:1,&amp;quot;range&amp;quot;:&amp;quot;1-4675&amp;quot;} --&gt;
&lt;h2 class=&quot;sectionedit2&quot; id=&quot;wave_addition&quot;&gt;Wave Addition&lt;/h2&gt;
&lt;div class=&quot;level2&quot;&gt;

&lt;p&gt;
When two waves overlap, they add up together at every point.  Here, the &lt;span style=&quot;color:#4682b4;&quot;&gt;blue&lt;/span&gt; and &lt;span style=&quot;color:#008000;&quot;&gt;green&lt;/span&gt; waves are generated and add up together to form the &lt;span style=&quot;color:#ff0000;&quot;&gt;red&lt;/span&gt; wave.  You can move the blue and green waves and see the result.  To convince yourself that the red wave is really the sum of the blue and green waves, look at points &lt;span style=&quot;color:#4682b4;&quot;&gt;A&lt;/span&gt;, &lt;span style=&quot;color:#008000;&quot;&gt;B&lt;/span&gt;, and &lt;span style=&quot;color:#ff0000;&quot;&gt;C&lt;/span&gt;.  You  can move the blue or green waves by sliding their phase (&lt;span style=&quot;color:#4682b4;&quot;&gt;φ&lt;/span&gt; and &lt;span style=&quot;color:#008000;&quot;&gt;Φ&lt;/span&gt;) around.  You&amp;#039;ll see that point &lt;span style=&quot;color:#ff0000;&quot;&gt;C&lt;/span&gt; is always the sum of &lt;span style=&quot;color:#4682b4;&quot;&gt;A&lt;/span&gt; and &lt;span style=&quot;color:#008000;&quot;&gt;B&lt;/span&gt;.
&lt;/p&gt;

&lt;p&gt;
&lt;script src=&quot;https://www.geogebra.org/apps/deployggb.js&quot;&gt;&lt;/script&gt;&lt;div id=&quot;waveaddition&quot;&gt;&lt;/div&gt;&lt;script&gt;window.addEventListener(&quot;load&quot;, function() {new GGBApplet({&quot;width&quot;: 800, &quot;height&quot;: 500, &quot;showToolBar&quot;: false, &quot;showAlgebraInput&quot;: false,&quot;showMenuBar&quot;: false, &quot;filename&quot;: &quot;/_media//hambasics/sections/waveaddition.ggb&quot;},true).inject(waveaddition) })&lt;/script&gt;Download &lt;a href=&quot;https://scarcs.ca/_media//hambasics/sections/waveaddition.ggb&quot;&gt;waveaddition.ggb&lt;/a&gt;
&lt;/p&gt;

&lt;p&gt;
Where do the blue and green waves need to be so that...
&lt;/p&gt;
&lt;ul&gt;
&lt;li class=&quot;level1&quot;&gt;&lt;div class=&quot;li&quot;&gt;
 the red wave is the biggest?
&lt;/div&gt;&lt;/li&gt;
&lt;li class=&quot;level1&quot;&gt;&lt;div class=&quot;li&quot;&gt;
 the red wave is cancelled out?&lt;sup&gt;&lt;a href=&quot;#fn__1&quot; id=&quot;fnt__1&quot; class=&quot;fn_top&quot;&gt;1)&lt;/a&gt;&lt;/sup&gt;
&lt;/div&gt;&lt;/li&gt;
&lt;/ul&gt;


&lt;p&gt;
If you press the play button on the bottom left corner, you&amp;#039;ll see the blue wave travel to the right and the green wave travel to the left.  The red wave, which is the sum of the forward and reflected waves, oscillates up and down but doesn&amp;#039;t travel anywhere, which means it&amp;#039;s not going into the antenna.
&lt;/p&gt;

&lt;p&gt;
While the animation is running, slowly decrease the amplitude of the reflected wave (&lt;span style=&quot;color:#008000;&quot;&gt;V&lt;sub&gt;B&lt;/sub&gt;&lt;/span&gt;) and you&amp;#039;ll see that the red wave will start moving to the right.  As you do that, notice how the SWR (Standing Wave Ratio) decreases toward 1:1.  At this point, there is no reflected wave and all of the energy is going to the antenna (assuming no loss in the feedline).  
&lt;/p&gt;

&lt;/div&gt;
&lt;!-- EDIT{&amp;quot;target&amp;quot;:&amp;quot;section&amp;quot;,&amp;quot;name&amp;quot;:&amp;quot;Wave Addition&amp;quot;,&amp;quot;hid&amp;quot;:&amp;quot;wave_addition&amp;quot;,&amp;quot;codeblockOffset&amp;quot;:4,&amp;quot;secid&amp;quot;:2,&amp;quot;range&amp;quot;:&amp;quot;4676-&amp;quot;} --&gt;&lt;div class=&quot;footnotes&quot;&gt;
&lt;div class=&quot;fn&quot;&gt;&lt;sup&gt;&lt;a href=&quot;#fnt__1&quot; id=&quot;fn__1&quot; class=&quot;fn_bot&quot;&gt;1)&lt;/a&gt;&lt;/sup&gt; 
&lt;div class=&quot;content&quot;&gt;Fun fact: This is how &lt;a href=&quot;https://en.wikipedia.org/wiki/Active_noise_control&quot; class=&quot;interwiki iw_wp&quot; title=&quot;https://en.wikipedia.org/wiki/Active_noise_control&quot;&gt;noise cancelling headphones&lt;/a&gt; work.  The headset has a microphone that picks up the noise, inverts the waves, and plays them back in the ear piece.  The combination of the real life noise and the inverted noise being played in the speaker cancel out (somewhat).&lt;/div&gt;&lt;/div&gt;
&lt;/div&gt;
</summary>
    </entry>
</feed>
