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class="vector-toc-numb">2</span> <span>Recent deletion</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">1 comment</span> <ul id="toc-Recent_deletion-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rigid_Motion_or_Translation_+_Rotation?" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Rigid_Motion_or_Translation_+_Rotation?"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Rigid Motion or Translation + Rotation?</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">1 comment</span> <ul id="toc-Rigid_Motion_or_Translation_+_Rotation?-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Equivalence_Class_or_Quotient_Set?" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Equivalence_Class_or_Quotient_Set?"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Equivalence Class or Quotient Set?</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">2 comments</span> <ul id="toc-Equivalence_Class_or_Quotient_Set?-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Huh?" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Huh?"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Huh?</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">13 comments</span> <ul id="toc-Huh?-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Isometric_scaling_paragraph_in_lead" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Isometric_scaling_paragraph_in_lead"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Isometric scaling paragraph in lead</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">5 comments</span> <ul id="toc-Isometric_scaling_paragraph_in_lead-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-What_is_the_relationship_between_Isometric_and_"angle_and_distance_preserving"?" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#What_is_the_relationship_between_Isometric_and_"angle_and_distance_preserving"?"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>What is the relationship between Isometric and "angle and distance preserving"?</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">3 comments</span> <ul id="toc-What_is_the_relationship_between_Isometric_and_"angle_and_distance_preserving"?-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Citations" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Citations"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Citations</span> 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Quantum Unitarity research.</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">1 comment</span> <ul id="toc-Isometry_in_Quantum_Unitarity_research.-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Proposed_merge_of_Isometry_(disambiguation)_into_Isometry" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Proposed_merge_of_Isometry_(disambiguation)_into_Isometry"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Proposed merge of Isometry (disambiguation) into Isometry</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">1 comment</span> <ul id="toc-Proposed_merge_of_Isometry_(disambiguation)_into_Isometry-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" 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Mathematics</a></b>, a collaborative effort to improve the coverage of <a href="/wiki/Mathematics" title="Mathematics">mathematics</a> on Wikipedia. If you would like to participate, please visit the project page, where you can join <a href="/wiki/Wikipedia_talk:WikiProject_Mathematics" title="Wikipedia talk:WikiProject Mathematics">the discussion</a> and see a list of open tasks.<span class="metadata wpb-metadata"><span class="wpb-project">Mathematics</span><span class="wpb-project_link">Wikipedia:WikiProject Mathematics</span><span class="wpb-banner_name">Template:WikiProject Mathematics</span><span class="wpb-assessment_cat">mathematics</span></span></td><td class="mbox-empty-cell"></td></tr><tr><td class="assess import-high"><a href="/wiki/Category:High-priority_mathematics_articles" title="Category:High-priority mathematics articles">High</a></td><td class="mbox-text" colspan="2">This article has been rated as <b>High-priority</b> on the <a href="/wiki/Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Assessment#Priority_scale" class="mw-redirect" title="Wikipedia:WikiProject Mathematics/Wikipedia 1.0/Assessment">project's priority scale</a>.</td></tr></tbody></table></td></tr></tbody></table></td></tr></tbody></table> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Early_thread" data-mw-thread-id="h-Early_thread"><span data-mw-comment-start="" id="h-Early_thread"></span>Early thread<span data-mw-comment-end="h-Early_thread"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Isometry&action=edit&section=1" title="Edit section: Early thread"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Is f:x->|x| an path isometry from R->R? f(1)-f(-1)=0 but 1-(-1)=2. </p> <dl><dd>Right, but that's not the length of the curve. I assume you're talking about defining <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma :[-1,1]\to \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> <mo>:</mo> <mo stretchy="false">[</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> <mo stretchy="false">→</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma :[-1,1]\to \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a18ae9ee27086b6562fa0795236a0b50e0761ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.952ex; height:2.843ex;" alt="{\displaystyle \gamma :[-1,1]\to \mathbb {R} }" /></span> by <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma (t)=t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma (t)=t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a58a4eceddad934315565d900d8397bf141a24db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.849ex; height:2.843ex;" alt="{\displaystyle \gamma (t)=t}" /></span>. Then <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{Length}}(\gamma )=\int _{-1}^{1}\left|\,{d\gamma \over dt}\,\right|dt=\int _{-1}^{1}|1|dt=2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Length</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>γ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msubsup> <mrow> <mo>|</mo> <mrow> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>γ</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace"></mspace> </mrow> <mo>|</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{Length}}(\gamma )=\int _{-1}^{1}\left|\,{d\gamma \over dt}\,\right|dt=\int _{-1}^{1}|1|dt=2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/56a9f7908eec96be8c94c73ea56f84bb9bb43f26" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:41.028ex; height:6.343ex;" alt="{\displaystyle {\mbox{Length}}(\gamma )=\int _{-1}^{1}\left|\,{d\gamma \over dt}\,\right|dt=\int _{-1}^{1}|1|dt=2}" /></span></dd></dl></dd> <dd>But <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{Length}}(f\circ \gamma )=\int _{-1}^{0}\left|\,{d(f\circ \gamma ) \over dt}\,\right|dt+\int _{0}^{1}\left|\,{d(f\circ \gamma ) \over dt}\,\right|dt=\int _{-1}^{0}|-1|dt+\int _{0}^{1}|1|dt=2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Length</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>f</mi> <mo>∘</mo> <mi>γ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msubsup> <mrow> <mo>|</mo> <mrow> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mo stretchy="false">(</mo> <mi>f</mi> <mo>∘</mo> <mi>γ</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace"></mspace> </mrow> <mo>|</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msubsup> <mrow> <mo>|</mo> <mrow> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mo stretchy="false">(</mo> <mi>f</mi> <mo>∘</mo> <mi>γ</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace"></mspace> </mrow> <mo>|</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>−</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{Length}}(f\circ \gamma )=\int _{-1}^{0}\left|\,{d(f\circ \gamma ) \over dt}\,\right|dt+\int _{0}^{1}\left|\,{d(f\circ \gamma ) \over dt}\,\right|dt=\int _{-1}^{0}|-1|dt+\int _{0}^{1}|1|dt=2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36fb88511885b0ebfd093e5ee0deeaed16818930" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:83.735ex; height:6.509ex;" alt="{\displaystyle {\mbox{Length}}(f\circ \gamma )=\int _{-1}^{0}\left|\,{d(f\circ \gamma ) \over dt}\,\right|dt+\int _{0}^{1}\left|\,{d(f\circ \gamma ) \over dt}\,\right|dt=\int _{-1}^{0}|-1|dt+\int _{0}^{1}|1|dt=2}" /></span></dd></dl></dd> <dd>So that's not a counterexample.</dd></dl> <p>IMHO, the second paragraph should be moved to much later in the article. It's definitely way too involved to be part of the initial summary.--<a href="/wiki/User:Pdelong" title="User:Pdelong">Paul</a> 17:07, September 11, 2005 (UTC) </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Recent_deletion" data-mw-thread-id="h-Recent_deletion-2005-10-09T04:05:00.000Z"><span data-mw-comment-start="" id="h-Recent_deletion-2005-10-09T04:05:00.000Z"></span>Recent deletion<span data-mw-comment-end="h-Recent_deletion-2005-10-09T04:05:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Isometry&action=edit&section=2" title="Edit section: Recent deletion"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Oleg_Alexandrov-2005-10-09T04:05:00.000Z-Recent_deletion"></span>The example I just <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Isometry&diff=25109123&oldid=24801751">deleted</a> does not belong either in this article or even in <a href="/wiki/Isometry_group" title="Isometry group">isometry group</a>, it rather belongs in <a href="/wiki/Euclidean_group" title="Euclidean group">Euclidean group</a> and there only. It is way too specific to provide any useful illustration anywhere else. A good example in the right article is invaluable, a good example in the wrong article is useless ranting distracting form the point of the article. <a href="/wiki/User:Oleg_Alexandrov" title="User:Oleg Alexandrov">Oleg Alexandrov</a> (<a href="/wiki/User_talk:Oleg_Alexandrov" title="User talk:Oleg Alexandrov">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Oleg_Alexandrov-2005-10-09T04:05:00.000Z-Recent_deletion" class="ext-discussiontools-init-timestamplink">04:05, 9 October 2005 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Oleg_Alexandrov-2005-10-09T04:05:00.000Z-Recent_deletion"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Oleg_Alexandrov-2005-10-09T04:05:00.000Z-Recent_deletion"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Rigid_Motion_or_Translation_+_Rotation?" data-mw-thread-id="h-Rigid_Motion_or_Translation_+_Rotation?-2013-11-22T22:01:00.000Z"><span id="Rigid_Motion_or_Translation_.2B_Rotation.3F"></span><span data-mw-comment-start="" id="h-Rigid_Motion_or_Translation_+_Rotation?-2013-11-22T22:01:00.000Z"></span>Rigid Motion or Translation + Rotation?<span data-mw-comment-end="h-Rigid_Motion_or_Translation_+_Rotation?-2013-11-22T22:01:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Isometry&action=edit&section=3" title="Edit section: Rigid Motion or Translation + Rotation?"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-24.233.151.201-2013-11-22T22:01:00.000Z-Rigid_Motion_or_Translation_+_Rotation?"></span>I see the term "rigid motion" used on this page repeatedly, but when I click the link for the definition it takes me to the page for "rigid body". I glean that "rigid motion" as used here is just another word for translation and/or rotation. I propose using those terms instead. One reason I propose this is that, although used by physicists, this is clearly a general mathematics concept. There needn't actually be any kind of literal movement involved, and referring to "motion" without reference to precise meaning suggests to me we are restricting the concept of isometry to contexts involving positions and times. Alternatively, a nice mathematically general definition for "rigid motion" could be provided, so as to make it clear we are not making such a restriction. Thanks. <a href="/wiki/Special:Contributions/24.233.151.201" title="Special:Contributions/24.233.151.201">24.233.151.201</a> (<a href="/w/index.php?title=User_talk:24.233.151.201&action=edit&redlink=1" class="new" title="User talk:24.233.151.201 (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-24.233.151.201-2013-11-22T22:01:00.000Z-Rigid_Motion_or_Translation_+_Rotation?" class="ext-discussiontools-init-timestamplink">22:01, 22 November 2013 (UTC)</a> (PS: The first two words of the <a href="/wiki/Rigid_body" title="Rigid body">rigid body</a> page are "In physics...")<span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-24.233.151.201-2013-11-22T22:01:00.000Z-Rigid_Motion_or_Translation_+_Rotation?"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-24.233.151.201-2013-11-22T22:01:00.000Z-Rigid_Motion_or_Translation_+_Rotation?"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Equivalence_Class_or_Quotient_Set?" data-mw-thread-id="h-Equivalence_Class_or_Quotient_Set?-2006-02-16T14:37:00.000Z"><span id="Equivalence_Class_or_Quotient_Set.3F"></span><span data-mw-comment-start="" id="h-Equivalence_Class_or_Quotient_Set?-2006-02-16T14:37:00.000Z"></span>Equivalence Class or Quotient Set?<span data-mw-comment-end="h-Equivalence_Class_or_Quotient_Set?-2006-02-16T14:37:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Isometry&action=edit&section=4" title="Edit section: Equivalence Class or Quotient Set?"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Jpawloski-2006-02-16T14:37:00.000Z-Equivalence_Class_or_Quotient_Set?"></span>I clicked through quotient set because I was not familiar with the term. I was expecting something similar to quotient group, but it redirects equivalence class. I have a hard time believing quotient set is the wikipedia standard. Surely equivalence class is more common?? (This may be a US-centric view). --<a href="/w/index.php?title=User:Jpawloski&action=edit&redlink=1" class="new" title="User:Jpawloski (page does not exist)">Jpawloski</a> <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Jpawloski-2006-02-16T14:37:00.000Z-Equivalence_Class_or_Quotient_Set?" class="ext-discussiontools-init-timestamplink">14:37, 16 February 2006 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Jpawloski-2006-02-16T14:37:00.000Z-Equivalence_Class_or_Quotient_Set?"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Jpawloski-2006-02-16T14:37:00.000Z-Equivalence_Class_or_Quotient_Set?"></span> </p> <dl><dd><span data-mw-comment-start="" id="c-Jpawloski-2006-02-16T14:38:00.000Z-Jpawloski-2006-02-16T14:37:00.000Z"></span>Okay, well, never mind. Next time I'll read the page first. I will continue, however, to post without thinking. --<a href="/w/index.php?title=User:Jpawloski&action=edit&redlink=1" class="new" title="User:Jpawloski (page does not exist)">Jpawloski</a> <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Jpawloski-2006-02-16T14:38:00.000Z-Jpawloski-2006-02-16T14:37:00.000Z" class="ext-discussiontools-init-timestamplink">14:38, 16 February 2006 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Jpawloski-2006-02-16T14:38:00.000Z-Jpawloski-2006-02-16T14:37:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Jpawloski-2006-02-16T14:38:00.000Z-Jpawloski-2006-02-16T14:37:00.000Z"></span></dd></dl> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Huh?" data-mw-thread-id="h-Huh?-2010-06-09T11:12:00.000Z"><span id="Huh.3F"></span><span data-mw-comment-start="" id="h-Huh?-2010-06-09T11:12:00.000Z"></span>Huh?<span data-mw-comment-end="h-Huh?-2010-06-09T11:12:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Isometry&action=edit&section=5" title="Edit section: Huh?"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <ul><li><span data-mw-comment-start="" id="c-Mike_Rosoft-2010-06-09T11:12:00.000Z-Huh?"></span>The map <b>R</b><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \to }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">→</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \to }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1daab843254cfcb23a643070cf93f3badc4fbbbd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \to }" /></span><b>R</b> defined by <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\mapsto |x|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo stretchy="false">↦</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\mapsto |x|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04f7cb7bcc9c126b2d18614065cfeeb20f8e5514" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.567ex; height:2.843ex;" alt="{\displaystyle x\mapsto |x|}" /></span> is a path isometry but not a global isometry.</li></ul> <p>Am I missing something? The map x->abs(x) is not an isometry (under Euclidean metric); it doesn't preserve the distance between 1 and -1. (It isn't even injective.) - <a href="/wiki/User:Mike_Rosoft" title="User:Mike Rosoft">Mike Rosoft</a> (<a href="/wiki/User_talk:Mike_Rosoft" title="User talk:Mike Rosoft">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Mike_Rosoft-2010-06-09T11:12:00.000Z-Huh?" class="ext-discussiontools-init-timestamplink">11:12, 9 June 2010 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Mike_Rosoft-2010-06-09T11:12:00.000Z-Huh?"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Mike_Rosoft-2010-06-09T11:12:00.000Z-Huh?"></span> </p><p><span data-mw-comment-start="" id="c-Mike_Rosoft-2010-06-09T11:23:00.000Z-Huh?"></span>Removed the example completely. (It's been there for quite a bit of time; see <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Isometry&diff=2442950&oldid=2441295">this</a> revision.) As for "path isometry", note that length of a curve isn't defined in a general metric space. - <a href="/wiki/User:Mike_Rosoft" title="User:Mike Rosoft">Mike Rosoft</a> (<a href="/wiki/User_talk:Mike_Rosoft" title="User talk:Mike Rosoft">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Mike_Rosoft-2010-06-09T11:23:00.000Z-Huh?" class="ext-discussiontools-init-timestamplink">11:23, 9 June 2010 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Mike_Rosoft-2010-06-09T11:23:00.000Z-Huh?"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Mike_Rosoft-2010-06-09T11:23:00.000Z-Huh?"></span> </p> <ul><li><span data-mw-comment-start="" id="c-Mike_Rosoft-2010-06-09T11:45:00.000Z-Mike_Rosoft-2010-06-09T11:23:00.000Z"></span>Turns out, I wasn't quite right with the final statement; see <a href="/wiki/Intrinsic_metric" title="Intrinsic metric">Intrinsic metric</a>. - <a href="/wiki/User:Mike_Rosoft" title="User:Mike Rosoft">Mike Rosoft</a> (<a href="/wiki/User_talk:Mike_Rosoft" title="User talk:Mike Rosoft">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Mike_Rosoft-2010-06-09T11:45:00.000Z-Mike_Rosoft-2010-06-09T11:23:00.000Z" class="ext-discussiontools-init-timestamplink">11:45, 9 June 2010 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Mike_Rosoft-2010-06-09T11:45:00.000Z-Mike_Rosoft-2010-06-09T11:23:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Mike_Rosoft-2010-06-09T11:45:00.000Z-Mike_Rosoft-2010-06-09T11:23:00.000Z"></span> <ul><li><span data-mw-comment-start="" id="c-Sniffnoy-2010-06-09T16:38:00.000Z-Mike_Rosoft-2010-06-09T11:45:00.000Z"></span>Yeah, should the example really be removed? Assuming it's correct, which it seems to be offhand, it seems useful. I hadn't seen the concept of "path isometry" before. <a href="/w/index.php?title=User:Sniffnoy&action=edit&redlink=1" class="new" title="User:Sniffnoy (page does not exist)">Sniffnoy</a> (<a href="/wiki/User_talk:Sniffnoy" title="User talk:Sniffnoy">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Sniffnoy-2010-06-09T16:38:00.000Z-Mike_Rosoft-2010-06-09T11:45:00.000Z" class="ext-discussiontools-init-timestamplink">16:38, 9 June 2010 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Sniffnoy-2010-06-09T16:38:00.000Z-Mike_Rosoft-2010-06-09T11:45:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Sniffnoy-2010-06-09T16:38:00.000Z-Mike_Rosoft-2010-06-09T11:45:00.000Z"></span></li></ul></li> <li><span data-mw-comment-start="" id="c-Mike_Rosoft-2010-06-09T18:04:00.000Z-Mike_Rosoft-2010-06-09T11:23:00.000Z"></span>Well, the key question is: how, precisely, is path isometry defined? But x->abs(x) obviously isn't an isometry. (Can a function be a path isometry without being an isometry?) - <a href="/wiki/User:Mike_Rosoft" title="User:Mike Rosoft">Mike Rosoft</a> (<a href="/wiki/User_talk:Mike_Rosoft" title="User talk:Mike Rosoft">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Mike_Rosoft-2010-06-09T18:04:00.000Z-Mike_Rosoft-2010-06-09T11:23:00.000Z" class="ext-discussiontools-init-timestamplink">18:04, 9 June 2010 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Mike_Rosoft-2010-06-09T18:04:00.000Z-Mike_Rosoft-2010-06-09T11:23:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Mike_Rosoft-2010-06-09T18:04:00.000Z-Mike_Rosoft-2010-06-09T11:23:00.000Z"></span> <ul><li><span data-mw-comment-start="" id="c-Sniffnoy-2010-06-10T04:11:00.000Z-Mike_Rosoft-2010-06-09T18:04:00.000Z"></span>Evidently so - that's precisely what it was serving as an example of! Path isometry is pretty clearly defined in the article; it's a map that preserves lengths of paths. <a href="/w/index.php?title=User:Sniffnoy&action=edit&redlink=1" class="new" title="User:Sniffnoy (page does not exist)">Sniffnoy</a> (<a href="/wiki/User_talk:Sniffnoy" title="User talk:Sniffnoy">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Sniffnoy-2010-06-10T04:11:00.000Z-Mike_Rosoft-2010-06-09T18:04:00.000Z" class="ext-discussiontools-init-timestamplink">04:11, 10 June 2010 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Sniffnoy-2010-06-10T04:11:00.000Z-Mike_Rosoft-2010-06-09T18:04:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Sniffnoy-2010-06-10T04:11:00.000Z-Mike_Rosoft-2010-06-09T18:04:00.000Z"></span></li></ul></li></ul> <dl><dd><dl><dd><dl><dd><span data-mw-comment-start="" id="c-Patrick-2010-06-10T08:07:00.000Z-Sniffnoy-2010-06-10T04:11:00.000Z"></span>I have tried to clarify things with consistency between lead and definitions section, and restored the example in modified form.--<a href="/wiki/User:Patrick" title="User:Patrick">Patrick</a> (<a href="/wiki/User_talk:Patrick" title="User talk:Patrick">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Patrick-2010-06-10T08:07:00.000Z-Sniffnoy-2010-06-10T04:11:00.000Z" class="ext-discussiontools-init-timestamplink">08:07, 10 June 2010 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Patrick-2010-06-10T08:07:00.000Z-Sniffnoy-2010-06-10T04:11:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Patrick-2010-06-10T08:07:00.000Z-Sniffnoy-2010-06-10T04:11:00.000Z"></span></dd></dl></dd></dl></dd></dl> <p><span data-mw-comment-start="" id="c-Mike_Rosoft-2010-06-10T15:53:00.000Z-Huh?"></span>Further question: is path isometry defined on a general metric space, or just on R (or R^n)? Or, more to the point: how (if at all) do you define the length of a curve on a general metric space? - <a href="/wiki/User:Mike_Rosoft" title="User:Mike Rosoft">Mike Rosoft</a> (<a href="/wiki/User_talk:Mike_Rosoft" title="User talk:Mike Rosoft">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Mike_Rosoft-2010-06-10T15:53:00.000Z-Huh?" class="ext-discussiontools-init-timestamplink">15:53, 10 June 2010 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Mike_Rosoft-2010-06-10T15:53:00.000Z-Huh?"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Mike_Rosoft-2010-06-10T15:53:00.000Z-Huh?"></span> </p> <ul><li><span data-mw-comment-start="" id="c-Sniffnoy-2010-06-10T21:10:00.000Z-Mike_Rosoft-2010-06-10T15:53:00.000Z"></span>Yes, length of a curve is defined in general metric spaces. See <a href="/wiki/Arc_length#Definition" title="Arc length">Arc length#Definition</a> or <a href="/wiki/Curve#Lengths_of_curves" title="Curve">Curve#Lengths of curves</a>. <a href="/w/index.php?title=User:Sniffnoy&action=edit&redlink=1" class="new" title="User:Sniffnoy (page does not exist)">Sniffnoy</a> (<a href="/wiki/User_talk:Sniffnoy" title="User talk:Sniffnoy">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Sniffnoy-2010-06-10T21:10:00.000Z-Mike_Rosoft-2010-06-10T15:53:00.000Z" class="ext-discussiontools-init-timestamplink">21:10, 10 June 2010 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Sniffnoy-2010-06-10T21:10:00.000Z-Mike_Rosoft-2010-06-10T15:53:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Sniffnoy-2010-06-10T21:10:00.000Z-Mike_Rosoft-2010-06-10T15:53:00.000Z"></span></li></ul> <p><span data-mw-comment-start="" id="c-Jtabbsvt-2013-07-10T11:47:00.000Z-Huh?"></span>Okay, but the fact remains that earlier in the article, "isometry" is said to be automatically injective. The example is a valid path isometry, however it needs to be stated that not all path isometries are injective. The sequencing of the article makes it seem as though both global and path isometries are subsets of isometries, but the latter clearly isn't true; instead, we have that every isometry (global or not) is a path isometry, but not the converse.<a href="/w/index.php?title=User:Jtabbsvt&action=edit&redlink=1" class="new" title="User:Jtabbsvt (page does not exist)">Jtabbsvt</a> (<a href="/w/index.php?title=User_talk:Jtabbsvt&action=edit&redlink=1" class="new" title="User talk:Jtabbsvt (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Jtabbsvt-2013-07-10T11:47:00.000Z-Huh?" class="ext-discussiontools-init-timestamplink">11:47, 10 July 2013 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Jtabbsvt-2013-07-10T11:47:00.000Z-Huh?"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Jtabbsvt-2013-07-10T11:47:00.000Z-Huh?"></span> </p> <ul><li><span data-mw-comment-start="" id="c-Sniffnoy-2013-07-10T22:05:00.000Z-Jtabbsvt-2013-07-10T11:47:00.000Z"></span>I'm not seeing what the problem is here? The article does state -- twice -- that "path isometry" is a weaker notion than "isometry". If you still think this is misleading and it should explicitly state that path isometries need not be injective, well, go ahead and add that. I don't think it needs a whole resequencing. Perhaps I'll go and add that right after doing this. <a href="/w/index.php?title=User:Sniffnoy&action=edit&redlink=1" class="new" title="User:Sniffnoy (page does not exist)">Sniffnoy</a> (<a href="/wiki/User_talk:Sniffnoy" title="User talk:Sniffnoy">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Sniffnoy-2013-07-10T22:05:00.000Z-Jtabbsvt-2013-07-10T11:47:00.000Z" class="ext-discussiontools-init-timestamplink">22:05, 10 July 2013 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Sniffnoy-2013-07-10T22:05:00.000Z-Jtabbsvt-2013-07-10T11:47:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Sniffnoy-2013-07-10T22:05:00.000Z-Jtabbsvt-2013-07-10T11:47:00.000Z"></span></li></ul> <ul><li><ul><li><span data-mw-comment-start="" id="c-Jtabbsvt-2013-07-11T02:15:00.000Z-Sniffnoy-2013-07-10T22:05:00.000Z"></span>Understood, but the real problem is that in the beginning of the definitions, we're told that there are two varieties: global and path. Aren't there three: global, "plain ol'," and path? Or at the very least, two, with one being "plain ol'," of which global is a subset, and the other being path? Yes, path is weaker than global, but the missing distinction is that it is also weaker than "plain ol'." When I get to a laptop and not my phone, I'll edit. The rest of the problems spring from that. It wasn't until I came to the talk page that I fully understood what was meant, and that seems counterproductive. No offense to the author(s), who perhaps simply have a better intuition already in their minds. <a href="/w/index.php?title=User:Jtabbsvt&action=edit&redlink=1" class="new" title="User:Jtabbsvt (page does not exist)">Jtabbsvt</a> (<a href="/w/index.php?title=User_talk:Jtabbsvt&action=edit&redlink=1" class="new" title="User talk:Jtabbsvt (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Jtabbsvt-2013-07-11T02:15:00.000Z-Sniffnoy-2013-07-10T22:05:00.000Z" class="ext-discussiontools-init-timestamplink">02:15, 11 July 2013 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Jtabbsvt-2013-07-11T02:15:00.000Z-Sniffnoy-2013-07-10T22:05:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Jtabbsvt-2013-07-11T02:15:00.000Z-Sniffnoy-2013-07-10T22:05:00.000Z"></span></li></ul></li></ul> <ul><li><ul><li><ul><li><span data-mw-comment-start="" id="c-Sniffnoy-2013-07-12T06:39:00.000Z-Jtabbsvt-2013-07-11T02:15:00.000Z"></span>Oh, OK. I guess that makes sense then. <a href="/w/index.php?title=User:Sniffnoy&action=edit&redlink=1" class="new" title="User:Sniffnoy (page does not exist)">Sniffnoy</a> (<a href="/wiki/User_talk:Sniffnoy" title="User talk:Sniffnoy">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Sniffnoy-2013-07-12T06:39:00.000Z-Jtabbsvt-2013-07-11T02:15:00.000Z" class="ext-discussiontools-init-timestamplink">06:39, 12 July 2013 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Sniffnoy-2013-07-12T06:39:00.000Z-Jtabbsvt-2013-07-11T02:15:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Sniffnoy-2013-07-12T06:39:00.000Z-Jtabbsvt-2013-07-11T02:15:00.000Z"></span></li></ul></li></ul></li></ul> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Isometric_scaling_paragraph_in_lead" data-mw-thread-id="h-Isometric_scaling_paragraph_in_lead-2014-02-02T19:37:00.000Z"><span data-mw-comment-start="" id="h-Isometric_scaling_paragraph_in_lead-2014-02-02T19:37:00.000Z"></span>Isometric scaling paragraph in lead<span data-mw-comment-end="h-Isometric_scaling_paragraph_in_lead-2014-02-02T19:37:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Isometry&action=edit&section=6" title="Edit section: Isometric scaling paragraph in lead"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Quondum-2014-02-02T19:37:00.000Z-Isometric_scaling_paragraph_in_lead"></span>The addition of a paragraph in the lead to an unrelated topic (<a href="/wiki/Allometry" title="Allometry">Allometry</a>, aka isometric scaling) in response to an IP's insertion of a mention thereof seems strange and out-of-place to me. At most, a hatnote could be devoted to this. —<a href="/wiki/User_talk:Quondum" title="User talk:Quondum"><i>Quondum</i></a> <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Quondum-2014-02-02T19:37:00.000Z-Isometric_scaling_paragraph_in_lead" class="ext-discussiontools-init-timestamplink">19:37, 2 February 2014 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Quondum-2014-02-02T19:37:00.000Z-Isometric_scaling_paragraph_in_lead"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Quondum-2014-02-02T19:37:00.000Z-Isometric_scaling_paragraph_in_lead"></span> </p> <dl><dd><span data-mw-comment-start="" id="c-Wcherowi-2014-02-03T06:08:00.000Z-Quondum-2014-02-02T19:37:00.000Z"></span>You're right, it felt that way to me as well ... as I put it in. The hatnote was getting too crowded and I didn't want to just remove the statement, even though it was incorrect. I replaced it with a correct statement, but it really doesn't belong. Let's just put this down to too much late night editing. <a href="/wiki/User:Wcherowi" title="User:Wcherowi">Bill Cherowitzo </a> (<a href="/wiki/User_talk:Wcherowi" title="User talk:Wcherowi">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Wcherowi-2014-02-03T06:08:00.000Z-Quondum-2014-02-02T19:37:00.000Z" class="ext-discussiontools-init-timestamplink">06:08, 3 February 2014 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Wcherowi-2014-02-03T06:08:00.000Z-Quondum-2014-02-02T19:37:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Wcherowi-2014-02-03T06:08:00.000Z-Quondum-2014-02-02T19:37:00.000Z"></span> <dl><dd><span data-mw-comment-start="" id="c-Quondum-2014-02-03T17:24:00.000Z-Wcherowi-2014-02-03T06:08:00.000Z"></span>That still leaves the question of what to do with it. My inclination is towards an even more crowded hatnote, if "isometry" is used sufficiently in that context that interested readers may end up here; otherwise to simply remove it. A further (and not unreasonable) alternative is to move all the hatnotes to a disambiguation page, leaving a hatnote pointing to that page. —<a href="/wiki/User_talk:Quondum" title="User talk:Quondum"><i>Quondum</i></a> <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Quondum-2014-02-03T17:24:00.000Z-Wcherowi-2014-02-03T06:08:00.000Z" class="ext-discussiontools-init-timestamplink">17:24, 3 February 2014 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Quondum-2014-02-03T17:24:00.000Z-Wcherowi-2014-02-03T06:08:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Quondum-2014-02-03T17:24:00.000Z-Wcherowi-2014-02-03T06:08:00.000Z"></span></dd></dl></dd> <dd><span data-mw-comment-start="" id="c-Wcherowi-2014-02-03T18:24:00.000Z-Quondum-2014-02-02T19:37:00.000Z"></span><span class="nowrap"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/f/fb/Yes_check.svg/18px-Yes_check.svg.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/f/fb/Yes_check.svg/27px-Yes_check.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/fb/Yes_check.svg/36px-Yes_check.svg.png 2x" data-file-width="600" data-file-height="600" /></span></span><b> Done</b></span> but it was a little more complicated (more than one disambiguation page) and may require some adjustment. <a href="/wiki/User:Wcherowi" title="User:Wcherowi">Bill Cherowitzo </a> (<a href="/wiki/User_talk:Wcherowi" title="User talk:Wcherowi">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Wcherowi-2014-02-03T18:24:00.000Z-Quondum-2014-02-02T19:37:00.000Z" class="ext-discussiontools-init-timestamplink">18:24, 3 February 2014 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Wcherowi-2014-02-03T18:24:00.000Z-Quondum-2014-02-02T19:37:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Wcherowi-2014-02-03T18:24:00.000Z-Quondum-2014-02-02T19:37:00.000Z"></span> <dl><dd><span data-mw-comment-start="" id="c-Quondum-2014-02-04T03:57:00.000Z-Wcherowi-2014-02-03T18:24:00.000Z"></span>Wow, yes, I see that the disambiguation pages are a little confusing, but at least this page is essentially sorted now. —<a href="/wiki/User_talk:Quondum" title="User talk:Quondum"><i>Quondum</i></a> <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Quondum-2014-02-04T03:57:00.000Z-Wcherowi-2014-02-03T18:24:00.000Z" class="ext-discussiontools-init-timestamplink">03:57, 4 February 2014 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Quondum-2014-02-04T03:57:00.000Z-Wcherowi-2014-02-03T18:24:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Quondum-2014-02-04T03:57:00.000Z-Wcherowi-2014-02-03T18:24:00.000Z"></span></dd></dl></dd></dl> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="What_is_the_relationship_between_Isometric_and_"angle_and_distance_preserving"?" data-mw-thread-id="h-What_is_the_relationship_between_Isometric_and_"angle_and_distance_preserving"?-2015-05-28T13:59:00.000Z"><span id="What_is_the_relationship_between_Isometric_and_.22angle_and_distance_preserving.22.3F"></span><span data-mw-comment-start="" id="h-What_is_the_relationship_between_Isometric_and_"angle_and_distance_preserving"?-2015-05-28T13:59:00.000Z"></span>What is the relationship between Isometric and "angle and distance preserving"?<span data-mw-comment-end="h-What_is_the_relationship_between_Isometric_and_"angle_and_distance_preserving"?-2015-05-28T13:59:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Isometry&action=edit&section=7" title="Edit section: What is the relationship between Isometric and "angle and distance preserving"?"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-216.96.76.37-2015-05-28T13:59:00.000Z-What_is_the_relationship_between_Isometric_and_"angle_and_distance_preserving"?"></span>I've seen a lot in physics about "angle and distance preserving" transformations (when talking about metric spaces). It would be nice to see something explaining the relationship between concepts such as isometry and that.<a href="/wiki/Special:Contributions/216.96.76.37" title="Special:Contributions/216.96.76.37">216.96.76.37</a> (<a href="/w/index.php?title=User_talk:216.96.76.37&action=edit&redlink=1" class="new" title="User talk:216.96.76.37 (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-216.96.76.37-2015-05-28T13:59:00.000Z-What_is_the_relationship_between_Isometric_and_"angle_and_distance_preserving"?" class="ext-discussiontools-init-timestamplink">13:59, 28 May 2015 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-216.96.76.37-2015-05-28T13:59:00.000Z-What_is_the_relationship_between_Isometric_and_"angle_and_distance_preserving"?"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-216.96.76.37-2015-05-28T13:59:00.000Z-What_is_the_relationship_between_Isometric_and_"angle_and_distance_preserving"?"></span> </p> <dl><dd><span data-mw-comment-start="" id="c-JoergenB-2015-08-23T23:48:00.000Z-216.96.76.37-2015-05-28T13:59:00.000Z"></span>An isometry is precisely a distance-preserving function. On the other hand, it is not immediately clear how to define angles in a general metric space. (Angles between what entities?) <a href="/wiki/User:JoergenB" title="User:JoergenB">JoergenB</a> (<a href="/wiki/User_talk:JoergenB" title="User talk:JoergenB">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-JoergenB-2015-08-23T23:48:00.000Z-216.96.76.37-2015-05-28T13:59:00.000Z" class="ext-discussiontools-init-timestamplink">23:48, 23 August 2015 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-JoergenB-2015-08-23T23:48:00.000Z-216.96.76.37-2015-05-28T13:59:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-JoergenB-2015-08-23T23:48:00.000Z-216.96.76.37-2015-05-28T13:59:00.000Z"></span></dd></dl> <dl><dd><dl><dd><span data-mw-comment-start="" id="c-67.198.37.16-2020-11-10T02:34:00.000Z-JoergenB-2015-08-23T23:48:00.000Z"></span>The metric defines a dot-product between vectors in the <a href="/wiki/Tangent_manifold" class="mw-redirect" title="Tangent manifold">tangent manifold</a>. Whenever you got a dot product, you can write the angle as the arc-cosine of the dot product of two unit length vectors. And you know what unit length is, because the dot product tells you that. This article should be expanded to explain such things. <a href="/wiki/Special:Contributions/67.198.37.16" title="Special:Contributions/67.198.37.16">67.198.37.16</a> (<a href="/wiki/User_talk:67.198.37.16" title="User talk:67.198.37.16">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-67.198.37.16-2020-11-10T02:34:00.000Z-JoergenB-2015-08-23T23:48:00.000Z" class="ext-discussiontools-init-timestamplink">02:34, 10 November 2020 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-67.198.37.16-2020-11-10T02:34:00.000Z-JoergenB-2015-08-23T23:48:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-67.198.37.16-2020-11-10T02:34:00.000Z-JoergenB-2015-08-23T23:48:00.000Z"></span></dd></dl></dd></dl> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Citations" data-mw-thread-id="h-Citations-2016-02-10T14:30:00.000Z"><span data-mw-comment-start="" id="h-Citations-2016-02-10T14:30:00.000Z"></span>Citations<span data-mw-comment-end="h-Citations-2016-02-10T14:30:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Isometry&action=edit&section=8" title="Edit section: Citations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Schuddeboomw-2016-02-10T14:30:00.000Z-Citations"></span>Does this article really need sources? I think that most of it's pretty open source/common knowledge. <small><span class="autosigned">— Preceding <a href="/wiki/Wikipedia:Signatures" title="Wikipedia:Signatures">unsigned</a> comment added by <a href="/wiki/User:Schuddeboomw" title="User:Schuddeboomw">Schuddeboomw</a> (<a href="/wiki/User_talk:Schuddeboomw" title="User talk:Schuddeboomw">talk</a> • <a href="/wiki/Special:Contributions/Schuddeboomw" title="Special:Contributions/Schuddeboomw">contribs</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Schuddeboomw-2016-02-10T14:30:00.000Z-Citations" class="ext-discussiontools-init-timestamplink">14:30, 10 February 2016 (UTC)</a></span></small><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Schuddeboomw-2016-02-10T14:30:00.000Z-Citations"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Schuddeboomw-2016-02-10T14:30:00.000Z-Citations"></span> </p> <dl><dd><span data-mw-comment-start="" id="c-67.198.37.16-2020-11-10T02:36:00.000Z-Schuddeboomw-2016-02-10T14:30:00.000Z"></span>Yes, absolutely, it does. As the comment above immediately shows, what is "common knowledge" to you is totally opaque to others. Anyway, this article is sorely deficient in even the most basic details as to what isometries are. It needs to be expanded. <a href="/wiki/Special:Contributions/67.198.37.16" title="Special:Contributions/67.198.37.16">67.198.37.16</a> (<a href="/wiki/User_talk:67.198.37.16" title="User talk:67.198.37.16">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-67.198.37.16-2020-11-10T02:36:00.000Z-Schuddeboomw-2016-02-10T14:30:00.000Z" class="ext-discussiontools-init-timestamplink">02:36, 10 November 2020 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-67.198.37.16-2020-11-10T02:36:00.000Z-Schuddeboomw-2016-02-10T14:30:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-67.198.37.16-2020-11-10T02:36:00.000Z-Schuddeboomw-2016-02-10T14:30:00.000Z"></span></dd></dl> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Is_C^n_always_assumed_to_have_the_Euclidean_norm?" data-mw-thread-id="h-Is_C^n_always_assumed_to_have_the_Euclidean_norm?-2021-12-02T16:43:00.000Z"><span id="Is_C.5En_always_assumed_to_have_the_Euclidean_norm.3F"></span><span data-mw-comment-start="" id="h-Is_C^n_always_assumed_to_have_the_Euclidean_norm?-2021-12-02T16:43:00.000Z"></span>Is C^n always assumed to have the Euclidean norm?<span data-mw-comment-end="h-Is_C^n_always_assumed_to_have_the_Euclidean_norm?-2021-12-02T16:43:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Isometry&action=edit&section=9" title="Edit section: Is C^n always assumed to have the Euclidean norm?"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Vaughan_Pratt-2021-12-02T16:43:00.000Z-Is_C^n_always_assumed_to_have_the_Euclidean_norm?"></span>In the last example (maps on C^n), shouldn't C^n be "C^n with the Euclidean norm"? Or does Wikipedia say somewhere that C^n is always assumed to have that norm? <a href="/wiki/User:Vaughan_Pratt" title="User:Vaughan Pratt">Vaughan Pratt</a> (<a href="/wiki/User_talk:Vaughan_Pratt" title="User talk:Vaughan Pratt">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Vaughan_Pratt-2021-12-02T16:43:00.000Z-Is_C^n_always_assumed_to_have_the_Euclidean_norm?" class="ext-discussiontools-init-timestamplink">16:43, 2 December 2021 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Vaughan_Pratt-2021-12-02T16:43:00.000Z-Is_C^n_always_assumed_to_have_the_Euclidean_norm?"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Vaughan_Pratt-2021-12-02T16:43:00.000Z-Is_C^n_always_assumed_to_have_the_Euclidean_norm?"></span> </p> <dl><dd><span data-mw-comment-start="" id="c-D.Lazard-2021-12-02T19:10:00.000Z-Vaughan_Pratt-2021-12-02T16:43:00.000Z"></span>C^n is not always assumed to have any norm, but, when metric properties are considered, the norm defined by the dot product is generally implicitly implied, if not otherwise specified. On the other hand, I am not sure that the term "Euclidean norm" is common for complex vector spaces. Nevertheless, I have clarified the example. <a href="/wiki/User:D.Lazard" title="User:D.Lazard">D.Lazard</a> (<a href="/wiki/User_talk:D.Lazard" title="User talk:D.Lazard">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-D.Lazard-2021-12-02T19:10:00.000Z-Vaughan_Pratt-2021-12-02T16:43:00.000Z" class="ext-discussiontools-init-timestamplink">19:10, 2 December 2021 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-D.Lazard-2021-12-02T19:10:00.000Z-Vaughan_Pratt-2021-12-02T16:43:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-D.Lazard-2021-12-02T19:10:00.000Z-Vaughan_Pratt-2021-12-02T16:43:00.000Z"></span></dd></dl> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Isometry_in_Quantum_Unitarity_research." data-mw-thread-id="h-Isometry_in_Quantum_Unitarity_research.-20221219064800"><span data-mw-comment-start="" id="h-Isometry_in_Quantum_Unitarity_research.-20221219064800"></span>Isometry in Quantum Unitarity research.<span data-mw-comment-end="h-Isometry_in_Quantum_Unitarity_research.-20221219064800"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Isometry&action=edit&section=10" title="Edit section: Isometry in Quantum Unitarity research."><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-1.47.12.38-20221219064800-Isometry_in_Quantum_Unitarity_research."></span>Should add more ? <a href="/wiki/Special:Contributions/1.47.12.38" title="Special:Contributions/1.47.12.38">1.47.12.38</a> (<a href="/w/index.php?title=User_talk:1.47.12.38&action=edit&redlink=1" class="new" title="User talk:1.47.12.38 (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-1.47.12.38-20221219064800-Isometry_in_Quantum_Unitarity_research." class="ext-discussiontools-init-timestamplink">06:48, 19 December 2022 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-1.47.12.38-20221219064800-Isometry_in_Quantum_Unitarity_research."><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-1.47.12.38-20221219064800-Isometry_in_Quantum_Unitarity_research."></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Proposed_merge_of_Isometry_(disambiguation)_into_Isometry" data-mw-thread-id="h-Proposed_merge_of_Isometry_(disambiguation)_into_Isometry-20241110141700"><span id="Proposed_merge_of_Isometry_.28disambiguation.29_into_Isometry"></span><span data-mw-comment-start="" id="h-Proposed_merge_of_Isometry_(disambiguation)_into_Isometry-20241110141700"></span>Proposed merge of <a href="/wiki/Isometry_(disambiguation)" class="mw-disambig" title="Isometry (disambiguation)">Isometry (disambiguation)</a> into <a href="/wiki/Isometry" title="Isometry">Isometry</a><span data-mw-comment-end="h-Proposed_merge_of_Isometry_(disambiguation)_into_Isometry-20241110141700"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Isometry&action=edit&section=11" title="Edit section: Proposed merge of Isometry (disambiguation) into Isometry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Jay-20241110141700-Proposed_merge_of_Isometry_(disambiguation)_into_Isometry"></span>See <a href="/wiki/Wikipedia:Redirects_for_discussion/Log/2024_October_25#Isometry_(mathematics)" title="Wikipedia:Redirects for discussion/Log/2024 October 25">WP:Redirects for discussion/Log/2024 October 25#Isometry (mathematics)</a>. <span style="font-family:Segoe Script"><a href="/wiki/User:Jay" title="User:Jay"> Jay</a></span><span style="font-size:115%"><a href="/wiki/User_talk:Jay" title="User talk:Jay"> 💬</a></span> <a href="https://en.wikipedia.org/wiki/Talk:Isometry#c-Jay-20241110141700-Proposed_merge_of_Isometry_(disambiguation)_into_Isometry" class="ext-discussiontools-init-timestamplink">14:17, 10 November 2024 (UTC)</a><span 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