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endpoint"> Sparql Endpoint </a> </li> </ul> </div> </div> </nav> <div style="margin-bottom: 60px"></div>   <section> <div class="container-xl"> <div class="row"> <div class="col"> <h1 id="title" class="display-6">About: <a href="http://dbpedia.org/resource/Laguerre_transformations">Laguerre transformations</a> </h1> </div> </div> <div class="row"> <div class="col"> <div class="text-muted"> An Entity of Type: <a href="http://www.w3.org/2002/07/owl#Thing">Thing</a>, from Named Graph: <a href="http://dbpedia.org">http://dbpedia.org</a>, within Data Space: <a href="http://dbpedia.org">dbpedia.org</a> </div> </div> </div> <div class="row pt-2"> <div class="col-xs-9 col-sm-10"> The Laguerre transformations or axial homographies are an analogue of M枚bius transformations over the dual numbers. When studying these transformations, the dual numbers are often interpreted as representing oriented lines on the plane. The Laguerre transformations map lines to lines, and include in particular all isometries of the plane. </div> <div class="col-xs-3 col-sm-2"> <a href="#" class="thumbnail"> <img src="http://commons.wikimedia.org/wiki/Special:FilePath/Opposite-circles-dilatating2.gif?width=300" alt="thumbnail" class="img-fluid" /> </a> </div> </div> </div> </section>   <section> <div class="container-xl"> <div class="row"> <div class="table-responsive"> <table class="table table-hover table-sm table-light"> <thead> <tr> <th class="col-xs-3 ">Property</th> <th class="col-xs-9 px-3">Value</th> </tr> </thead> <tbody> <tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/abstract">dbo:abstract</a> </td><td class="col-10 text-break"><ul> <li>The Laguerre transformations or axial homographies are an analogue of M枚bius transformations over the dual numbers. When studying these transformations, the dual numbers are often interpreted as representing oriented lines on the plane. The Laguerre transformations map lines to lines, and include in particular all isometries of the plane. Strictly speaking, these transformations act on the dual number projective line, which adjoins to the dual numbers a set of points at infinity. Topologically, this projective line is equivalent to a cylinder. Points on this cylinder are in a natural one-to-one correspondence with oriented lines on the plane. (en)</li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/thumbnail">dbo:thumbnail</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="dbo:thumbnail" resource="http://commons.wikimedia.org/wiki/Special:FilePath/Opposite-circles-dilatating2.gif?width=300" href="http://commons.wikimedia.org/wiki/Special:FilePath/Opposite-circles-dilatating2.gif?width=300">wiki-commons:Special:FilePath/Opposite-circles-dilatating2.gif?width=300</a></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageExternalLink">dbo:wikiPageExternalLink</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="dbo:wikiPageExternalLink nofollow" resource="https://www.youtube.com/watch%3Fv=QrXsRwop7C0&list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp&index=35" 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href="http://www.w3.org/2000/01/rdf-schema#comment">rdfs:comment</a> </td><td class="col-10 text-break"><ul> <li>The Laguerre transformations or axial homographies are an analogue of M枚bius transformations over the dual numbers. When studying these transformations, the dual numbers are often interpreted as representing oriented lines on the plane. The Laguerre transformations map lines to lines, and include in particular all isometries of the plane. (en)</li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#label">rdfs:label</a> </td><td class="col-10 text-break"><ul> <li>Laguerre transformations (en)</li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2002/07/owl#differentFrom">owl:differentFrom</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="owl:differentFrom" resource="http://dbpedia.org/resource/Laguerre_transform" href="http://dbpedia.org/resource/Laguerre_transform">dbr:Laguerre_transform</a></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2002/07/owl#sameAs">owl:sameAs</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="owl:sameAs" resource="http://www.wikidata.org/entity/Q97357520" href="http://www.wikidata.org/entity/Q97357520">wikidata:Laguerre transformations</a></li> <li><a class="uri" rel="owl:sameAs" 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