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href="mw-data:TemplateStyles:r1237879490"><table class="plainlinks imbox imbox-featured" role="presentation"><tbody><tr><td class="mbox-image"><span typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description" title="Mathematics icon"><img alt="Mathematics icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/24px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="24" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/36px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/48px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span></td><td class="mbox-text">This image was selected as <b><a href="/wiki/Portal:Mathematics/Featured_picture_archive" title="Portal:Mathematics/Featured picture archive">picture of the month</a></b> on the <a href="/wiki/Portal:Mathematics" title="Portal:Mathematics">Mathematics Portal</a> for November 2011.</td></tr></tbody></table>    </div></div><div id="shared-image-desc"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><meta property="mw:PageProp/toc"> <div class="mw-heading mw-heading2"><h2 id="Summary">Summary</h2></div> <div class="hproduct commons-file-information-table"> <table class="fileinfotpl-type-information vevent" dir="ltr"> <tbody><tr> <td id="fileinfotpl_desc" class="fileinfo-paramfield" lang="en">Description<span class="summary fn" style="display:none">Mug and Torus morph.gif</span></td> <td class="description"> <div class="description en" dir="ltr" lang="en"><span class="language en" title="English"><b>English: </b></span> A coffee <a href="https://en.wikipedia.org/wiki/mug" class="extiw" title="w:mug">mug</a> morphing into a <a href="https://en.wikipedia.org/wiki/torus" class="extiw" title="w:torus">torus</a>, a popular example in <a href="https://en.wikipedia.org/wiki/topology" class="extiw" title="w:topology">topology</a>.</div><div class="description tr" dir="ltr" lang="tr"><span class="language tr" title="Turkish"><b>Türkçe: </b></span> Bir kahve bardağının simide sürekli deformasyonunu gösteren bir homeomorfizma animasyonu.</div><div class="description ru" dir="ltr" lang="ru"><span class="language ru" title="Russian"><b>Русский: </b></span> Кофейная кружка, превращающаяся в тор, популярный пример в топологии..</div><div style="display:inline-block;width:;white-space:nowrap;vertical-align:middle;direction:ltr;float:left;line-height:22px;height:24px;font-size:.96em;margin:0px;padding:2px 4px 2px 6px;color:var(--color-base,#000);background:var(--background-color-neutral-subtle,#F8F9FA);border:1px solid #BAB;;"><span typeof="mw:File"><a href="//commons.wikimedia.org/wiki/File:Povray_logo_sphere.png" class="mw-file-description"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/62/Povray_logo_sphere.png/22px-Povray_logo_sphere.png" decoding="async" width="22" height="22" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/6/62/Povray_logo_sphere.png/33px-Povray_logo_sphere.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/6/62/Povray_logo_sphere.png/44px-Povray_logo_sphere.png 2x" data-file-width="2048" data-file-height="2048"></a></span> <div lang="en" dir="ltr" class="description en" style="display:inline;">This image was created with <a href="https://en.wikipedia.org/wiki/POV-Ray" class="extiw" title="w:POV-Ray">POV-Ray</a>.</div></div></td> </tr> <tr> <td id="fileinfotpl_src" class="fileinfo-paramfield" lang="en">Source</td> <td> <span class="int-own-work" lang="en">Own work</span></td> </tr> <tr> <td id="fileinfotpl_aut" class="fileinfo-paramfield" lang="en">Author</td> <td> <a href="//commons.wikimedia.org/wiki/User:LucasVB" title="User:LucasVB">Lucas Vieira</a></td> </tr> <tr> <td id="fileinfotpl_ver" class="fileinfo-paramfield" lang="en">Other versions</td> <td> <table style="background-color: var(--background-color-neutral-subtle, #f9f9f9); color: inherit;"> <tbody><tr> <td><span class="wpImageAnnotatorControl wpImageAnnotatorOff wpImageAnnotatorCaptionOff"><span typeof="mw:File"><a href="//commons.wikimedia.org/wiki/File:Mug_and_Torus_morph_frame.png" class="mw-file-description"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/05/Mug_and_Torus_morph_frame.png/120px-Mug_and_Torus_morph_frame.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/0/05/Mug_and_Torus_morph_frame.png/180px-Mug_and_Torus_morph_frame.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/0/05/Mug_and_Torus_morph_frame.png 2x" data-file-width="240" data-file-height="240"></a></span></span></td> <td valign="top"><a href="//commons.wikimedia.org/wiki/File:Mug_and_Torus_morph_frame.png" title="File:Mug and Torus morph frame.png">File:Mug and Torus morph frame.png</a> <br>single frame suitable for thumbnail purposes</td> </tr> </tbody></table></td> </tr> </tbody></table> </div> <div id="assessments" dir="ltr" lang="en"> <table cellspacing="0" cellpadding="0" style="margin:0.5em auto; width:100%"> <tbody><tr> <td> <table style="clear:both;margin:0em auto;width:100%; box-sizing: border-box; border:2px solid var(--border-color-warning,#e5d4a1);background-color:var(--background-color-warning-subtle,#FAF5E6); color: inherit;" dir="ltr"><tbody><tr><td> <table style="width:100%;"> <tbody><tr> <td style="width:40px;text-align:center;" rowspan="2"> </td> <td> </td> <td style="width:30px;text-align:center;" rowspan="2"> <p><span typeof="mw:File"><span title="Wikipedia"><img alt="Wikipedia" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/30px-Wikipedia-logo-v2.svg.png" decoding="async" width="30" height="27" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/45px-Wikipedia-logo-v2.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/60px-Wikipedia-logo-v2.svg.png 2x" data-file-width="103" data-file-height="94"></span></span> </p> </td></tr> <tr> <td><span typeof="mw:File"><span><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Cscr-featured.svg/20px-Cscr-featured.svg.png" decoding="async" width="20" height="19" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Cscr-featured.svg/30px-Cscr-featured.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Cscr-featured.svg/40px-Cscr-featured.svg.png 2x" data-file-width="466" data-file-height="443"></span></span> This is a <b>featured picture</b> on the English language Wikipedia (<a href="https://en.wikipedia.org/wiki/en:WP:Featured_pictures" class="extiw" title="w:en:WP:Featured pictures">Featured pictures</a>) and is considered one of the finest images. See its nomination <a href="https://en.wikipedia.org/wiki/en:WP:Featured_picture_candidates/Mug_and_Torus_morph.gif" class="extiw" title="w:en:WP:Featured picture candidates/Mug and Torus morph.gif">here</a>.<br><span typeof="mw:File"><span><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Cscr-featured.svg/20px-Cscr-featured.svg.png" decoding="async" width="20" height="19" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Cscr-featured.svg/30px-Cscr-featured.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Cscr-featured.svg/40px-Cscr-featured.svg.png 2x" data-file-width="466" data-file-height="443"></span></span> This is a <b>featured picture</b> on the Turkish language Wikipedia (<a href="https://en.wikipedia.org/wiki/tr:Vikipedi:Se%C3%A7kin_resimler" class="extiw" title="w:tr:Vikipedi:Seçkin resimler">Seçkin resimler</a>) and is considered one of the finest images. See its nomination <a href="https://en.wikipedia.org/wiki/tr:Vikipedi:Se%C3%A7kin_resim_adaylar%C4%B1/Mug_and_Torus_morph.gif" class="extiw" title="w:tr:Vikipedi:Seçkin resim adayları/Mug and Torus morph.gif">here</a>.<br> <hr> <p>If you think this file should be featured on Wikimedia Commons as well, feel free to <a href="//commons.wikimedia.org/wiki/Commons:Featured_picture_candidates" title="Commons:Featured picture candidates">nominate it</a>.<br> If you have an image of similar quality that can be published under a <a href="//commons.wikimedia.org/wiki/Commons:Licensing" title="Commons:Licensing">suitable copyright license</a>, be sure to <a href="//commons.wikimedia.org/wiki/Special:Upload" title="Special:Upload">upload</a> it, <a href="//commons.wikimedia.org/wiki/Commons:Copyright_tags" title="Commons:Copyright tags">tag</a> it, and <a href="//commons.wikimedia.org/wiki/Commons:Featured_picture_candidates" title="Commons:Featured picture candidates">nominate it</a>.<br> </p> </td></tr></tbody></table> </td></tr></tbody></table> </td></tr></tbody></table> </div> <div class="mw-heading mw-heading2"><h2 id="POV-Ray_source_code">POV-Ray source code</h2></div> <div style="border:1px solid #CCC;height:300px;overflow:auto;"><pre>/* Torus to mug morphing animation, by Lucas Vieira - January 17, 2007 - Coded in: POV-Ray 3.6 License: Public Domain Info ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ Author user page: http://en.wikipedia.org/wiki/User:LucasVB The final animation at Wikimedia Commons: [[:File:Mug_and_Torus_morph.gif]] Notes ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ Several modifications were done for each part of the animation and I didn't keep them all here. So if you wish to reproduce the animation, you'll have to play with this code quite a bit. :) */ background { color rgb 1 } global_settings { assumed_gamma 1.5 } camera { orthographic location <0,4,-5>*0.8 look_at <0,0,0> //rotate -45*y } #declare dist = 0.2; light_source { <0,0,0>, 1 //translate <-3,5,-5>*1 translate 5*y translate -5*z translate 2*x } #declare a = 1; // Cylinders for the mug shape #declare C_a = function { pow(x / a,2) + pow(z / a,2)-1.5 } #declare C_b = function { pow(x / a,2) + pow(z / a,2)-1.2 } #declare B_b = function { (y+1.3) } // Torus (handle and the morphing target) #declare R = 1; #declare r = 0.22; #declare T_a = function { pow(R - sqrt(pow(x,2) + pow(y,2)),2) + pow(z,2) - pow(r,2) } #declare R2 = 1; #declare r2 = 0.5; #declare T_b = function { pow(R2 - sqrt(pow(x,2) + pow(y,2)),2) + pow(z,2) - pow(r2,2) } // Hollow mug (concave) #declare Mug = function { min(min(max(C_a(x,y,z),B_b(x,y,z)),max(C_a(x,y,z),-C_b(x,y,z))),max(T_a(x-1,y,z),-C_a(x,y,z))) } // Solid mug (cylinder with handle, convex) #declare Mug2 = function { min(C_a(x,y,z),max(T_a(x-1,y,z),-C_a(x,y,z))) } #declare c = 0.5; // Linear to smooth interpolation #declare Int = pow(sin(clock*pi/2),2); // Functions for the mug parts, left as backups. // max(C_a(x,y,z),B_b(x,y,z)) bottom // max(C_a(x,y,z),-C_b(x,y,z)) sides // min(max(C_a(x,y,z),B_b(x,y,z)),max(C_a(x,y,z),-C_b(x,y,z))) bottom+sides // max(T_a(x-1,y,z),-C_a(x,y,z)) handle // min(min(max(C_a(x,y,z),B_b(x,y,z)),max(C_a(x,y,z),-C_b(x,y,z))),max(T_a(x-1,y,z),-C_a(x,y,z))) full mug // Render as isosurface or CSG. // Isosurface is used in the transitional states. #declare RenderIsosurface = 0; #if (RenderIsosurface) union { isosurface { function { // Add previously defined object functions using Int and (1-Int) as to generate the smooth transition //Mug2(x,y,z)*(1-Int) + Mug(x,y,z) //T_b(x-1,y,z)*Int } contained_by { box { -<3,1.5,3>, <3,1.5,3> } } accuracy 0.001 max_gradient 5 // 10 //rotate -90*x } cylinder { <0,-1.3+Int*2.8,0>, <0,-1.5,0>, sqrt(1.5) } pigment { color rgb <0.6,0.8,1> transmit 0.1 } finish { specular 0.5 roughness 0.01 ambient 0.2 } } #else union { difference { cylinder { -1.5*y, 1.5*y, sqrt(1.5) } cylinder { -2*y, 2*y, sqrt(1.2) } } difference { torus { R, r rotate 90*x translate x } cylinder { -1.5*y, 1.5*y, sqrt(1.5) } } cylinder { <0,0-0.25+Int*(1.5+0.25),0>, <0,-1.5,0>, sqrt(1.5) } pigment { color rgb <0.6,0.8,1> transmit 0.1 } finish { specular 0.5 roughness 0.01 ambient 0.2 } } #end /* END OF FILE */ </pre></div> <div class="mw-heading mw-heading2"><h2 id="Updated_January_12,_2007"><span id="Updated_January_12.2C_2007"></span>Updated January 12, 2007</h2></div> <ol><li>New colors: blue hue, brighter, softer shadows</li> <li>Changed light angle</li> <li>Non-linear interpolation: looks smoother and less boring</li> <li>Faster frame rate</li> <li>Cropped to relevant area</li> <li>Overall, smaller size for a better-looking image.</li></ol> <div class="mw-heading mw-heading2"><h2 id="Updated_January_20,_2007"><span id="Updated_January_20.2C_2007"></span>Updated January 20, 2007</h2></div> <ol><li>Removed dithering. Image now has visible color bands, but at least thumbnails won't look excessively grainy.</li></ol> <div class="mw-heading mw-heading2"><h2 id="Updated_March_1,_2007"><span id="Updated_March_1.2C_2007"></span>Updated March 1, 2007</h2></div> <ol><li>More saturation of colors</li></ol> <div class="mw-heading mw-heading2"><h2 id="Licensing">Licensing</h2></div> <table class="licensetpl" style="display:none"> <tbody><tr> <td><span class="licensetpl_short">Public domain</span><span class="licensetpl_long">Public domain</span><span class="licensetpl_link_req">false</span><span class="licensetpl_attr_req">false</span> </td></tr></tbody></table> <table style="width: 100%; clear: both; margin: 0.5em auto; background-color: var(--background-color-neutral-subtle, #f7f8ff); color: var(--color-base, #202122); border: var(--border-subtle, 2px solid #8888aa); border-spacing: 8px; padding: 0px;" dir="ltr" class="layouttemplate" lang="en"> <tbody><tr> <td><span typeof="mw:File"><span title="Public domain"><img alt="Public domain" src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/62/PD-icon.svg/64px-PD-icon.svg.png" decoding="async" width="64" height="64" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/6/62/PD-icon.svg/96px-PD-icon.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/6/62/PD-icon.svg/128px-PD-icon.svg.png 2x" data-file-width="196" data-file-height="196"></span></span> </td> <td>I, the copyright holder of this work, release this work into the <b><a href="https://en.wikipedia.org/wiki/en:public_domain" class="extiw" title="w:en:public domain">public domain</a></b>. This applies worldwide.<br><small>In some countries this may not be legally possible; if so:</small><br><i>I grant anyone the right to use this work <b>for any purpose</b>, without any conditions, unless such conditions are required by law.</i> </td></tr></tbody></table><h1 class="mw-slot-header"><mediainfoslotheader></mediainfoslotheader></h1><mediainfoview style="display: none"><mediainfoviewcaptions><div class="wbmi-entityview-captionsPanel oo-ui-layout oo-ui-panelLayout oo-ui-panelLayout-framed"><h3 class="wbmi-entityview-captions-header">Captions</h3><div class="wbmi-entityview-caption oo-ui-layout oo-ui-horizontalLayout"><label class="wbmi-language-label oo-ui-widget oo-ui-widget-enabled oo-ui-labelElement-label oo-ui-labelElement oo-ui-labelWidget">English</label><div lang="en" dir="ltr" class="wbmi-caption-value">A coffee mug turning into a torus, a popular example in topology.</div></div><div style="display:none;" class="wbmi-entityview-caption wbmi-entityview-hideable oo-ui-layout oo-ui-horizontalLayout"><label class="wbmi-language-label oo-ui-widget oo-ui-widget-enabled oo-ui-labelElement-label oo-ui-labelElement oo-ui-labelWidget">Russian</label><div lang="ru" dir="ltr" class="wbmi-caption-value">Кофейная кружка превращающаяся в тор, популярный пример в топологии.</div></div><div style="display:none;" class="wbmi-entityview-caption wbmi-entityview-hideable oo-ui-layout oo-ui-horizontalLayout"><label class="wbmi-language-label oo-ui-widget oo-ui-widget-enabled oo-ui-labelElement-label oo-ui-labelElement oo-ui-labelWidget">Turkish</label><div lang="tr" dir="ltr" class="wbmi-caption-value">Bir kahve bardağının simide sürekli deformasyonunu gösteren bir homeomorfizma animasyonu.</div></div></div></mediainfoviewcaptions><mediainfoviewstatements><div id="P180" data-property="P180" data-statements="[]" data-formatvalue="[]" class="wbmi-entityview-statementsGroup wbmi-entityview-statementsGroup-P180 oo-ui-layout oo-ui-panelLayout 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file</a></bdi></h4></div></div></div><div class="wbmi-content-items-group"><div class="wbmi-item wbmi-item-read"><div data-guid="M1236079$180F4C52-1EB9-45AA-AB8B-A2E7EB0AD521" class="wbmi-item-container"><div class="wbmi-entity-header"><div class="wbmi-entity-data"><div class="wbmi-entity-title"><h4 class="wbmi-entity-label"><bdi><a target="_blank" title="d:Special:EntityPage/Q66458942" href="https://www.wikidata.org/wiki/Special:EntityPage/Q66458942">original creation by uploader</a></bdi></h4></div></div></div></div></div></div></div></div></mediainfoviewstatements></mediainfoview>    </div></div> <h2 id="filehistory">File history</h2> <div id="mw-imagepage-section-filehistory"> <p>Click on a date/time to view the file as it appeared at that time. </p> <table class="wikitable filehistory"> <tr><th></th><th>Date/Time</th><th>Thumbnail</th><th>Dimensions</th><th>User</th><th>Comment</th></tr> <tr><td>current</td><td class="filehistory-selected" style="white-space: nowrap;"><a href="//upload.wikimedia.org/wikipedia/commons/2/26/Mug_and_Torus_morph.gif">00:56, 2 March 2007</a></td><td><a href="//upload.wikimedia.org/wikipedia/commons/2/26/Mug_and_Torus_morph.gif"><img alt="Thumbnail for version as of 00:56, 2 March 2007" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Mug_and_Torus_morph.gif/120px-Mug_and_Torus_morph.gif" decoding="async" loading="lazy" width="120" height="120" data-file-width="240" data-file-height="240" /></a></td><td>240 × 240 <span style="white-space: nowrap;">(497 KB)</span></td><td><a href="/wiki/User:LucasVB" class="mw-userlink" title="User:LucasVB"><bdi>LucasVB</bdi></a></td><td dir="ltr">back to old cropping - looks a lot better</td></tr> <tr><td></td><td style="white-space: nowrap;"><a href="//upload.wikimedia.org/wikipedia/commons/archive/2/26/20070302005604%21Mug_and_Torus_morph.gif">00:49, 2 March 2007</a></td><td><a href="//upload.wikimedia.org/wikipedia/commons/archive/2/26/20070302005604%21Mug_and_Torus_morph.gif"><img alt="Thumbnail for version as of 00:49, 2 March 2007" src="//upload.wikimedia.org/wikipedia/commons/thumb/archive/2/26/20070302005604%21Mug_and_Torus_morph.gif/94px-Mug_and_Torus_morph.gif" decoding="async" loading="lazy" width="94" height="120" data-file-width="189" data-file-height="240" /></a></td><td>189 × 240 <span style="white-space: nowrap;">(477 KB)</span></td><td><a href="/wiki/User:LucasVB" class="mw-userlink" title="User:LucasVB"><bdi>LucasVB</bdi></a></td><td dir="ltr">more saturation of colors</td></tr> <tr><td></td><td style="white-space: nowrap;"><a href="//upload.wikimedia.org/wikipedia/commons/archive/2/26/20070302004933%21Mug_and_Torus_morph.gif">08:30, 20 January 2007</a></td><td><a href="//upload.wikimedia.org/wikipedia/commons/archive/2/26/20070302004933%21Mug_and_Torus_morph.gif"><img alt="Thumbnail for version as of 08:30, 20 January 2007" src="//upload.wikimedia.org/wikipedia/commons/thumb/archive/2/26/20070302004933%21Mug_and_Torus_morph.gif/120px-Mug_and_Torus_morph.gif" decoding="async" loading="lazy" width="120" height="120" data-file-width="240" data-file-height="240" /></a></td><td>240 × 240 <span style="white-space: nowrap;">(465 KB)</span></td><td><a href="/wiki/User:LucasVB" class="mw-userlink" title="User:LucasVB"><bdi>LucasVB</bdi></a></td><td dir="ltr">Removed dithering since it was causing excessive grainy-ness in thumbnails. Image now has color bands, but at least thumbnails won't look bad.</td></tr> <tr><td></td><td style="white-space: nowrap;"><a href="//upload.wikimedia.org/wikipedia/commons/archive/2/26/20070120083001%21Mug_and_Torus_morph.gif">05:49, 12 January 2007</a></td><td><a href="//upload.wikimedia.org/wikipedia/commons/archive/2/26/20070120083001%21Mug_and_Torus_morph.gif"><img alt="Thumbnail for version as of 05:49, 12 January 2007" src="//upload.wikimedia.org/wikipedia/commons/thumb/archive/2/26/20070120083001%21Mug_and_Torus_morph.gif/120px-Mug_and_Torus_morph.gif" decoding="async" loading="lazy" width="120" height="120" data-file-width="240" data-file-height="240" /></a></td><td>240 × 240 <span style="white-space: nowrap;">(497 KB)</span></td><td><a href="/wiki/User:LucasVB" class="mw-userlink" title="User:LucasVB"><bdi>LucasVB</bdi></a></td><td dir="ltr">Better version -- bright color+softer shadows+color=blue instead of an ugly yellowish-brown --- non-linear interpolation (looks a lot smoother) --- cropped to relevant area -- all in all, looks better and the file is a hundred kilobytes smaller :)</td></tr> <tr><td></td><td style="white-space: nowrap;"><a href="//upload.wikimedia.org/wikipedia/commons/archive/2/26/20070112054937%21Mug_and_Torus_morph.gif">06:02, 2 October 2006</a></td><td><a href="//upload.wikimedia.org/wikipedia/commons/archive/2/26/20070112054937%21Mug_and_Torus_morph.gif"><img alt="Thumbnail for version as of 06:02, 2 October 2006" src="//upload.wikimedia.org/wikipedia/commons/thumb/archive/2/26/20070112054937%21Mug_and_Torus_morph.gif/120px-Mug_and_Torus_morph.gif" decoding="async" loading="lazy" width="120" height="90" data-file-width="320" data-file-height="240" /></a></td><td>320 × 240 <span style="white-space: nowrap;">(554 KB)</span></td><td><a href="/wiki/User:LucasVB" class="mw-userlink" title="User:LucasVB"><bdi>LucasVB</bdi></a></td><td dir="ltr">A coffee <a href="/wiki/Mug" title="Mug">w:mug</a> morphing into a <a href="/wiki/Torus" title="Torus">w:torus</a>.</td></tr> </table> </div> <h2 id="filelinks">File usage</h2> <div id='mw-imagepage-section-linkstoimage'> <p>The following 52 pages use this file: </p><ul class="mw-imagepage-linkstoimage"> <li class="mw-imagepage-linkstoimage-ns0"><a href="/wiki/Differential_topology" title="Differential topology">Differential topology</a></li> <li class="mw-imagepage-linkstoimage-ns0"><a href="/wiki/Emmy_Noether" title="Emmy Noether">Emmy Noether</a></li> <li class="mw-imagepage-linkstoimage-ns0"><a href="/wiki/Genus_(mathematics)" title="Genus (mathematics)">Genus (mathematics)</a></li> <li class="mw-imagepage-linkstoimage-ns0"><a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a></li> <li class="mw-imagepage-linkstoimage-ns0"><a href="/wiki/Hole" title="Hole">Hole</a></li> <li class="mw-imagepage-linkstoimage-ns0"><a href="/wiki/Homeomorphism" title="Homeomorphism">Homeomorphism</a></li> <li class="mw-imagepage-linkstoimage-ns0"><a href="/wiki/Homotopy" title="Homotopy">Homotopy</a></li> <li class="mw-imagepage-linkstoimage-ns0"><a href="/wiki/Homotopy_analysis_method" title="Homotopy analysis method">Homotopy analysis method</a></li> <li class="mw-imagepage-linkstoimage-ns0"><a href="/wiki/Mathematical_joke" title="Mathematical joke">Mathematical joke</a></li> <li class="mw-imagepage-linkstoimage-ns0"><a href="/wiki/Mug" title="Mug">Mug</a></li> <li class="mw-imagepage-linkstoimage-ns0"><a href="/wiki/Topology" title="Topology">Topology</a></li> <li class="mw-imagepage-linkstoimage-ns2"><a href="/wiki/User:Buster7/Totem" title="User:Buster7/Totem">User:Buster7/Totem</a></li> <li class="mw-imagepage-linkstoimage-ns2"><a href="/wiki/User:Farkle_Griffen/Draft_for_%22Mathematical_object%22" title="User:Farkle Griffen/Draft for "Mathematical object"">User:Farkle Griffen/Draft for "Mathematical object"</a></li> <li class="mw-imagepage-linkstoimage-ns2"><a href="/wiki/User:Ira_Leviton" title="User:Ira Leviton">User:Ira Leviton</a></li> <li class="mw-imagepage-linkstoimage-ns2"><a href="/wiki/User:Jkasd" title="User:Jkasd">User:Jkasd</a></li> <li class="mw-imagepage-linkstoimage-ns2"><a href="/wiki/User:Jkasd/Interests" title="User:Jkasd/Interests">User:Jkasd/Interests</a></li> <li class="mw-imagepage-linkstoimage-ns2"><a href="/wiki/User:Jonathunder/Doughnuts" title="User:Jonathunder/Doughnuts">User:Jonathunder/Doughnuts</a></li> <li class="mw-imagepage-linkstoimage-ns2"><a href="/wiki/User:Kelisi" title="User:Kelisi">User:Kelisi</a></li> <li class="mw-imagepage-linkstoimage-ns2"><a href="/wiki/User:Keomike/Neat_Animations" title="User:Keomike/Neat Animations">User:Keomike/Neat Animations</a></li> <li class="mw-imagepage-linkstoimage-ns2"><a href="/wiki/User:Locriani" title="User:Locriani">User:Locriani</a></li> <li class="mw-imagepage-linkstoimage-ns2"><a href="/wiki/User:LucasVB/Gallery" title="User:LucasVB/Gallery">User:LucasVB/Gallery</a></li> <li class="mw-imagepage-linkstoimage-ns2"><a href="/wiki/User:Palaeovia/Mathematics" title="User:Palaeovia/Mathematics">User:Palaeovia/Mathematics</a></li> <li class="mw-imagepage-linkstoimage-ns2"><a href="/wiki/User:Passargea/Favourite_pictures/Animations" title="User:Passargea/Favourite pictures/Animations">User:Passargea/Favourite pictures/Animations</a></li> <li class="mw-imagepage-linkstoimage-ns2"><a href="/wiki/User:PizzaKing13" title="User:PizzaKing13">User:PizzaKing13</a></li> <li class="mw-imagepage-linkstoimage-ns2"><a href="/wiki/User:RobertLovesPi" title="User:RobertLovesPi">User:RobertLovesPi</a></li> <li class="mw-imagepage-linkstoimage-ns2"><a href="/wiki/User:Rockower" title="User:Rockower">User:Rockower</a></li> <li class="mw-imagepage-linkstoimage-ns2"><a href="/wiki/User:Secret_Saturdays" title="User:Secret Saturdays">User:Secret Saturdays</a></li> <li class="mw-imagepage-linkstoimage-ns2"><a href="/wiki/User:VGrigas_(WMF)/Quality_Media" title="User:VGrigas (WMF)/Quality Media">User:VGrigas (WMF)/Quality Media</a></li> <li class="mw-imagepage-linkstoimage-ns2"><a href="/wiki/User:WillowW/Noether_notes" title="User:WillowW/Noether notes">User:WillowW/Noether notes</a></li> <li class="mw-imagepage-linkstoimage-ns3"><a href="/wiki/User_talk:LucasVB/Archive1" title="User talk:LucasVB/Archive1">User talk:LucasVB/Archive1</a></li> <li class="mw-imagepage-linkstoimage-ns3"><a href="/wiki/User_talk:TomStar81/Archive_2" title="User talk:TomStar81/Archive 2">User talk:TomStar81/Archive 2</a></li> <li class="mw-imagepage-linkstoimage-ns4"><a href="/wiki/Wikipedia:Did_you_know/Statistics/Monthly_DYK_pageview_leaders/2009" title="Wikipedia:Did you know/Statistics/Monthly DYK pageview leaders/2009">Wikipedia:Did you know/Statistics/Monthly DYK pageview leaders/2009</a></li> <li class="mw-imagepage-linkstoimage-ns4"><a href="/wiki/Wikipedia:Featured_picture_candidates/August-2007" title="Wikipedia:Featured picture candidates/August-2007">Wikipedia:Featured picture candidates/August-2007</a></li> <li class="mw-imagepage-linkstoimage-ns4"><a href="/wiki/Wikipedia:Featured_picture_candidates/March-2007" title="Wikipedia:Featured picture candidates/March-2007">Wikipedia:Featured picture candidates/March-2007</a></li> <li class="mw-imagepage-linkstoimage-ns4"><a href="/wiki/Wikipedia:Featured_picture_candidates/Mug_and_Torus_morph.gif" title="Wikipedia:Featured picture candidates/Mug and Torus morph.gif">Wikipedia:Featured picture candidates/Mug and Torus morph.gif</a></li> <li class="mw-imagepage-linkstoimage-ns4"><a href="/wiki/Wikipedia:Featured_picture_candidates/_Sarrus_linkage_Animation" title="Wikipedia:Featured picture candidates/ Sarrus linkage Animation">Wikipedia:Featured picture candidates/ Sarrus linkage Animation</a></li> <li class="mw-imagepage-linkstoimage-ns4"><a href="/wiki/Wikipedia:Featured_pictures/Sciences/Mathematics" title="Wikipedia:Featured pictures/Sciences/Mathematics">Wikipedia:Featured pictures/Sciences/Mathematics</a></li> <li class="mw-imagepage-linkstoimage-ns4"><a href="/wiki/Wikipedia:Featured_pictures_thumbs/06" title="Wikipedia:Featured pictures thumbs/06">Wikipedia:Featured pictures thumbs/06</a></li> <li class="mw-imagepage-linkstoimage-ns4"><a href="/wiki/Wikipedia:Recent_additions/2009/August" title="Wikipedia:Recent additions/2009/August">Wikipedia:Recent additions/2009/August</a></li> <li class="mw-imagepage-linkstoimage-ns4"><a href="/wiki/Wikipedia:Reference_desk/Archives/Mathematics/2006_October_7" title="Wikipedia:Reference desk/Archives/Mathematics/2006 October 7">Wikipedia:Reference desk/Archives/Mathematics/2006 October 7</a></li> <li class="mw-imagepage-linkstoimage-ns4"><a href="/wiki/Wikipedia:Today%27s_featured_picture_(animation)/July_18,_2007" title="Wikipedia:Today's featured picture (animation)/July 18, 2007">Wikipedia:Today's featured picture (animation)/July 18, 2007</a></li> <li class="mw-imagepage-linkstoimage-ns4"><a href="/wiki/Wikipedia:WikiProject_Mathematics/Graphics/Torus" title="Wikipedia:WikiProject Mathematics/Graphics/Torus">Wikipedia:WikiProject Mathematics/Graphics/Torus</a></li> <li class="mw-imagepage-linkstoimage-ns4"><a href="/wiki/Wikipedia:WikiProject_Mathematics/Recognized_content" title="Wikipedia:WikiProject Mathematics/Recognized content">Wikipedia:WikiProject Mathematics/Recognized content</a></li> <li class="mw-imagepage-linkstoimage-ns4"><a href="/wiki/Wikipedia:Wikipedia_Signpost/2007-03-20/Features_and_admins" title="Wikipedia:Wikipedia Signpost/2007-03-20/Features and admins">Wikipedia:Wikipedia Signpost/2007-03-20/Features and admins</a></li> <li class="mw-imagepage-linkstoimage-ns4"><a href="/wiki/Wikipedia:Wikipedia_Signpost/2007-03-20/SPV" title="Wikipedia:Wikipedia Signpost/2007-03-20/SPV">Wikipedia:Wikipedia Signpost/2007-03-20/SPV</a></li> <li class="mw-imagepage-linkstoimage-ns4"><a href="/wiki/Wikipedia:Wikipedia_Signpost/Single/2007-03-20" title="Wikipedia:Wikipedia Signpost/Single/2007-03-20">Wikipedia:Wikipedia Signpost/Single/2007-03-20</a></li> <li class="mw-imagepage-linkstoimage-ns5"><a href="/wiki/Wikipedia_talk:WikiProject_Userboxes/Ideas/Archive_8" title="Wikipedia talk:WikiProject Userboxes/Ideas/Archive 8">Wikipedia talk:WikiProject Userboxes/Ideas/Archive 8</a></li> <li class="mw-imagepage-linkstoimage-ns10"><a href="/wiki/Template:POTD/2007-07-18" title="Template:POTD/2007-07-18">Template:POTD/2007-07-18</a></li> <li class="mw-imagepage-linkstoimage-ns100"><a href="/wiki/Portal:Mathematics/Featured_picture/2007_05" title="Portal:Mathematics/Featured picture/2007 05">Portal:Mathematics/Featured picture/2007 05</a></li> <li class="mw-imagepage-linkstoimage-ns100"><a href="/wiki/Portal:Mathematics/Featured_picture/2011_11" title="Portal:Mathematics/Featured picture/2011 11">Portal:Mathematics/Featured picture/2011 11</a></li> <li class="mw-imagepage-linkstoimage-ns100"><a href="/wiki/Portal:Mathematics/Featured_picture_archive" title="Portal:Mathematics/Featured picture archive">Portal:Mathematics/Featured picture archive</a></li> <li class="mw-imagepage-linkstoimage-ns100"><a href="/wiki/Portal:Mathematics/Recognized_content" title="Portal:Mathematics/Recognized content">Portal:Mathematics/Recognized content</a></li> </ul> </div> <h2 id="globalusage">Global file usage</h2> <div id="mw-imagepage-section-globalusage"><p>The following other wikis use this file: </p><ul> <li class='mw-gu-onwiki-af_wikipedia_org'>Usage on af.wikipedia.org <ul> <li><a class="external" href="https://af.wikipedia.org/wiki/Gebruiker:MikeRumex%5CSandput">Gebruiker:MikeRumex\Sandput</a></li> <li><a class="external" href="https://af.wikipedia.org/wiki/Meetkunde">Meetkunde</a></li> <li><a class="external" href="https://af.wikipedia.org/wiki/Topologie">Topologie</a></li> </ul></li> <li class='mw-gu-onwiki-ar_wikipedia_org'>Usage on ar.wikipedia.org <ul> <li><a class="external" href="https://ar.wikipedia.org/wiki/%D8%B7%D9%88%D8%A8%D9%88%D9%84%D9%88%D8%AC%D9%8A%D8%A7">طوبولوجيا</a></li> <li><a class="external" href="https://ar.wikipedia.org/wiki/%D8%AA%D8%B5%D8%A7%D9%83%D9%84">تصاكل</a></li> <li><a class="external" href="https://ar.wikipedia.org/wiki/%D8%A8%D9%88%D8%A7%D8%A8%D8%A9:%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA/%D8%B5%D9%88%D8%B1%D8%A9_%D9%85%D8%AE%D8%AA%D8%A7%D8%B1%D8%A9/%D8%A3%D8%B1%D8%B4%D9%8A%D9%81">بوابة:رياضيات/صورة مختارة/أرشيف</a></li> <li><a class="external" href="https://ar.wikipedia.org/wiki/%D8%A8%D9%88%D8%A7%D8%A8%D8%A9:%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA/%D8%B5%D9%88%D8%B1%D8%A9_%D9%85%D8%AE%D8%AA%D8%A7%D8%B1%D8%A9/20">بوابة:رياضيات/صورة مختارة/20</a></li> <li><a class="external" href="https://ar.wikipedia.org/wiki/%D8%AA%D8%AD%D8%A7%D9%88%D9%84">تحاول</a></li> </ul></li> <li class='mw-gu-onwiki-ast_wikipedia_org'>Usage on ast.wikipedia.org <ul> <li><a class="external" href="https://ast.wikipedia.org/wiki/Emmy_Noether">Emmy Noether</a></li> </ul></li> <li class='mw-gu-onwiki-ba_wikipedia_org'>Usage on ba.wikipedia.org <ul> <li><a class="external" href="https://ba.wikipedia.org/wiki/%D0%A2%D0%BE%D0%BF%D0%BE%D0%BB%D0%BE%D0%B3%D0%B8%D1%8F">Топология</a></li> </ul></li> <li class='mw-gu-onwiki-be_wikipedia_org'>Usage on be.wikipedia.org <ul> <li><a class="external" href="https://be.wikipedia.org/wiki/%D0%A2%D0%B0%D0%BF%D0%B0%D0%BB%D0%BE%D0%B3%D1%96%D1%8F">Тапалогія</a></li> </ul></li> <li class='mw-gu-onwiki-bg_wikipedia_org'>Usage on bg.wikipedia.org <ul> <li><a class="external" href="https://bg.wikipedia.org/wiki/%D0%A5%D0%BE%D0%BC%D0%B5%D0%BE%D0%BC%D0%BE%D1%80%D1%84%D0%B8%D0%B7%D1%8A%D0%BC">Хомеоморфизъм</a></li> </ul></li> <li class='mw-gu-onwiki-bn_wikipedia_org'>Usage on bn.wikipedia.org <ul> <li><a class="external" href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A6%AE-%E0%A6%85%E0%A6%AC%E0%A6%BF%E0%A6%9A%E0%A7%8D%E0%A6%9B%E0%A6%BF%E0%A6%A8%E0%A7%8D%E0%A6%A8_%E0%A6%9A%E0%A6%BF%E0%A6%A4%E0%A7%8D%E0%A6%B0%E0%A6%A3">সম-অবিচ্ছিন্ন চিত্রণ</a></li> </ul></li> <li class='mw-gu-onwiki-bo_wikipedia_org'>Usage on bo.wikipedia.org <ul> <li><a class="external" href="https://bo.wikipedia.org/wiki/%E0%BD%90%E0%BD%BC%E0%BC%8B%E0%BD%95%E0%BD%B4%E0%BC%8B%E0%BD%A2%E0%BD%B2%E0%BD%82%E0%BC%8B%E0%BD%94%E0%BC%8D">ཐོ་ཕུ་རིག་པ།</a></li> </ul></li> <li class='mw-gu-onwiki-ca_wikipedia_org'>Usage on ca.wikipedia.org <ul> <li><a class="external" href="https://ca.wikipedia.org/wiki/Topologia">Topologia</a></li> <li><a class="external" href="https://ca.wikipedia.org/wiki/Homeomorfisme">Homeomorfisme</a></li> <li><a class="external" href="https://ca.wikipedia.org/wiki/Varietat_(matem%C3%A0tiques)">Varietat (matemàtiques)</a></li> </ul></li> <li class='mw-gu-onwiki-cbk-zam_wikipedia_org'>Usage on cbk-zam.wikipedia.org <ul> <li><a class="external" href="https://cbk-zam.wikipedia.org/wiki/Homeomorfismo">Homeomorfismo</a></li> </ul></li> <li class='mw-gu-onwiki-co_wikipedia_org'>Usage on co.wikipedia.org <ul> <li><a class="external" href="https://co.wikipedia.org/wiki/Omeumurfismu">Omeumurfismu</a></li> </ul></li> <li class='mw-gu-onwiki-cs_wikipedia_org'>Usage on cs.wikipedia.org <ul> <li><a class="external" href="https://cs.wikipedia.org/wiki/Geometrie">Geometrie</a></li> <li><a class="external" href="https://cs.wikipedia.org/wiki/Topologick%C3%BD_prostor">Topologický prostor</a></li> <li><a class="external" href="https://cs.wikipedia.org/wiki/Topologie">Topologie</a></li> <li><a class="external" href="https://cs.wikipedia.org/wiki/Wikipedie:Obr%C3%A1zek_t%C3%BDdne/2013">Wikipedie:Obrázek týdne/2013</a></li> <li><a class="external" href="https://cs.wikipedia.org/wiki/Wikipedie:Obr%C3%A1zek_t%C3%BDdne/2013/38">Wikipedie:Obrázek týdne/2013/38</a></li> </ul></li> <li class='mw-gu-onwiki-cv_wikipedia_org'>Usage on cv.wikipedia.org <ul> <li><a class="external" href="https://cv.wikipedia.org/wiki/%D0%93%D0%BE%D0%BC%D0%B5%D0%BE%D0%BC%D0%BE%D1%80%D1%84%D0%B8%D0%B7%D0%BC">Гомеоморфизм</a></li> </ul></li> <li class='mw-gu-onwiki-cy_wikipedia_org'>Usage on cy.wikipedia.org <ul> <li><a class="external" href="https://cy.wikipedia.org/wiki/Homeomorffedd">Homeomorffedd</a></li> </ul></li> <li class='mw-gu-onwiki-da_wikipedia_org'>Usage on da.wikipedia.org <ul> <li><a class="external" href="https://da.wikipedia.org/wiki/Homeomorfi">Homeomorfi</a></li> <li><a class="external" href="https://da.wikipedia.org/wiki/Topologi">Topologi</a></li> </ul></li> <li class='mw-gu-onwiki-de_wikipedia_org'>Usage on de.wikipedia.org <ul> <li><a class="external" href="https://de.wikipedia.org/wiki/Topologie_(Mathematik)">Topologie (Mathematik)</a></li> <li><a class="external" href="https://de.wikipedia.org/wiki/Homotopie">Homotopie</a></li> <li><a class="external" href="https://de.wikipedia.org/wiki/Holomorphe_Funktion">Holomorphe Funktion</a></li> <li><a class="external" href="https://de.wikipedia.org/wiki/Portal:Mathematik/Qualit%C3%A4tssicherung/Archiv/2011/November">Portal:Mathematik/Qualitätssicherung/Archiv/2011/November</a></li> <li><a class="external" href="https://de.wikipedia.org/wiki/Isomorphie_(Psychophysiologie)">Isomorphie (Psychophysiologie)</a></li> </ul></li> <li class='mw-gu-onwiki-de_wikibooks_org'>Usage on de.wikibooks.org <ul> <li><a class="external" href="https://de.wikibooks.org/wiki/Benutzer:J%C3%BCrgen-Michael_Glubrecht/Mathematik">Benutzer:Jürgen-Michael Glubrecht/Mathematik</a></li> </ul></li> <li class='mw-gu-onwiki-el_wikipedia_org'>Usage on el.wikipedia.org <ul> <li><a class="external" href="https://el.wikipedia.org/wiki/%CE%9F%CE%BC%CE%BF%CF%84%CE%BF%CF%80%CE%AF%CE%B1">Ομοτοπία</a></li> <li><a class="external" href="https://el.wikipedia.org/wiki/%CE%88%CE%BC%CE%B9_%CE%9D%CE%AD%CF%84%CE%B5%CF%81">Έμι Νέτερ</a></li> <li><a class="external" href="https://el.wikipedia.org/wiki/%CE%9F%CE%BC%CE%BF%CE%B9%CE%BF%CE%BC%CE%BF%CF%81%CF%86%CE%B9%CF%83%CE%BC%CF%8C%CF%82">Ομοιομορφισμός</a></li> <li><a class="external" href="https://el.wikipedia.org/wiki/%CE%93%CE%AD%CE%BD%CE%BF%CF%82_(%CE%BC%CE%B1%CE%B8%CE%B7%CE%BC%CE%B1%CF%84%CE%B9%CE%BA%CE%AC)">Γένος (μαθηματικά)</a></li> </ul></li> <li class='mw-gu-onwiki-el_wiktionary_org'>Usage on el.wiktionary.org <ul> <li><a class="external" href="https://el.wiktionary.org/wiki/%CF%84%CE%BF%CF%80%CE%BF%CE%BB%CE%BF%CE%B3%CE%AF%CE%B1">τοπολογία</a></li> </ul></li> <li class='mw-gu-onwiki-en_wikiquote_org'>Usage on en.wikiquote.org <ul> <li><a class="external" href="https://en.wikiquote.org/wiki/User:Kalki/%CE%B1">User:Kalki/α</a></li> </ul></li> <li class='mw-gu-onwiki-en_wikiversity_org'>Usage on en.wikiversity.org <ul> <li><a class="external" href="https://en.wikiversity.org/wiki/Basic_atomic_physics">Basic atomic physics</a></li> </ul></li> <li class='mw-gu-onwiki-es_wikipedia_org'>Usage on es.wikipedia.org <ul> <li><a class="external" href="https://es.wikipedia.org/wiki/Topolog%C3%ADa">Topología</a></li> <li><a class="external" href="https://es.wikipedia.org/wiki/Variedad_(matem%C3%A1ticas)">Variedad (matemáticas)</a></li> <li><a class="external" href="https://es.wikipedia.org/wiki/Homeomorfismo">Homeomorfismo</a></li> <li><a class="external" href="https://es.wikipedia.org/wiki/Homotop%C3%ADa">Homotopía</a></li> <li><a class="external" href="https://es.wikipedia.org/wiki/Efectos_visuales">Efectos visuales</a></li> <li><a class="external" href="https://es.wikipedia.org/wiki/Taza">Taza</a></li> <li><a class="external" href="https://es.wikipedia.org/wiki/Emmy_Noether">Emmy Noether</a></li> <li><a class="external" href="https://es.wikipedia.org/wiki/Portal:Matem%C3%A1tica/Buenos">Portal:Matemática/Buenos</a></li> <li><a class="external" href="https://es.wikipedia.org/wiki/Portal:Matem%C3%A1tica/Imagen_archivo_1-2008">Portal:Matemática/Imagen archivo 1-2008</a></li> </ul></li> </ul> <p>View <a href="/wiki/Special:GlobalUsage/Mug_and_Torus_morph.gif" title="Special:GlobalUsage/Mug and Torus morph.gif">more global usage</a> of this file. </p></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=File:Mug_and_Torus_morph.gif&oldid=458707673">https://en.wikipedia.org/w/index.php?title=File:Mug_and_Torus_morph.gif&oldid=458707673</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a 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