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		<id>http://wiki.karljones.com/index.php?action=history&amp;feed=atom&amp;title=Caustic_%28mathematics%29</id>
		<title>Caustic (mathematics) - Revision history</title>
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		<updated>2026-10-23T22:56:55Z</updated>
		<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>http://wiki.karljones.com/index.php?title=Caustic_(mathematics)&amp;diff=12364&amp;oldid=prev</id>
		<title>Karl Jones at 15:19, 21 April 2016</title>
		<link rel="alternate" type="text/html" href="http://wiki.karljones.com/index.php?title=Caustic_(mathematics)&amp;diff=12364&amp;oldid=prev"/>
				<updated>2016-04-21T15:19:23Z</updated>
		
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				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 15:19, 21 April 2016&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 19:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 19:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [https://en.wikipedia.org/wiki/Caustic_(mathematics) Caustic (mathematics)] @ Wikipedia&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* [https://en.wikipedia.org/wiki/Caustic_(mathematics) Caustic (mathematics)] @ Wikipedia&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
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&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Geometry]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Mathematics]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
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		<author><name>Karl Jones</name></author>	</entry>

	<entry>
		<id>http://wiki.karljones.com/index.php?title=Caustic_(mathematics)&amp;diff=9762&amp;oldid=prev</id>
		<title>Karl Jones: Created page with &quot;In differential geometry and geometric optics, a '''caustic''' is the envelope of rays either reflected or refracted by a [[manifold.  It is...&quot;</title>
		<link rel="alternate" type="text/html" href="http://wiki.karljones.com/index.php?title=Caustic_(mathematics)&amp;diff=9762&amp;oldid=prev"/>
				<updated>2016-03-14T01:01:21Z</updated>
		
		<summary type="html">&lt;p&gt;Created page with &amp;quot;In &lt;a href=&quot;/index.php/Differential_geometry&quot; title=&quot;Differential geometry&quot;&gt;differential geometry&lt;/a&gt; and &lt;a href=&quot;/index.php?title=Geometric_optics&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;Geometric optics (page does not exist)&quot;&gt;geometric optics&lt;/a&gt;, a &amp;#039;&amp;#039;&amp;#039;caustic&amp;#039;&amp;#039;&amp;#039; is the &lt;a href=&quot;/index.php/Envelope_(mathematics)&quot; title=&quot;Envelope (mathematics)&quot;&gt;envelope of rays either reflected or refracted by a [[manifold&lt;/a&gt;.  It is...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;In [[differential geometry]] and [[geometric optics]], a '''caustic''' is the [[Envelope (mathematics)|envelope of rays either reflected or refracted by a [[manifold]].&lt;br /&gt;
&lt;br /&gt;
It is related to the concept of [[Caustic (optics)|caustics in optics]].&lt;br /&gt;
&lt;br /&gt;
== Description ==&lt;br /&gt;
&lt;br /&gt;
The ray's source may be a point (called the radiant) or parallel rays from a point at infinity, in which case a direction vector of the rays must be specified.&lt;br /&gt;
&lt;br /&gt;
== See also ==&lt;br /&gt;
&lt;br /&gt;
* [[Caustic (optics)]]&lt;br /&gt;
* [[Differential geometry]] &lt;br /&gt;
* [[Envelope (mathematics)]]&lt;br /&gt;
* [[Geometric optics]]&lt;br /&gt;
* [[Manifold]]&lt;br /&gt;
* [[Mathematics]]&lt;br /&gt;
&lt;br /&gt;
== External links ==&lt;br /&gt;
&lt;br /&gt;
* [https://en.wikipedia.org/wiki/Caustic_(mathematics) Caustic (mathematics)] @ Wikipedia&lt;/div&gt;</summary>
		<author><name>Karl Jones</name></author>	</entry>

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