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	<title>Escher archivos | iNSiGHTS</title>
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	<title>Escher archivos | iNSiGHTS</title>
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		<title>Les matemàtiques darrere els quadres</title>
		<link>https://www.insights.cat/2021/08/12/les-matematiques-darrere-els-quadres/</link>
					<comments>https://www.insights.cat/2021/08/12/les-matematiques-darrere-els-quadres/#respond</comments>
		
		<dc:creator><![CDATA[Mateu Sabala Jarque]]></dc:creator>
		<pubDate>Thu, 12 Aug 2021 07:44:00 +0000</pubDate>
				<category><![CDATA[Destacada]]></category>
		<category><![CDATA[Exposicions]]></category>
		<category><![CDATA[Propostes]]></category>
		<category><![CDATA[Art]]></category>
		<category><![CDATA[Escher]]></category>
		<category><![CDATA[Exposició]]></category>
		<category><![CDATA[Mateu Sabala Jarque]]></category>
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					<description><![CDATA[<p>Un recorregut per les obres impossibles de Maurits Cornelis Escher al Museu Marítim de Barcelona</p>
<p>La entrada <a href="https://www.insights.cat/2021/08/12/les-matematiques-darrere-els-quadres/">Les matemàtiques darrere els quadres</a> se publicó primero en <a href="https://www.insights.cat">iNSiGHTS</a>.</p>
]]></description>
										<content:encoded><![CDATA[
<p class="wp-block-paragraph"><strong>Una proposta de Mateu Sabala Jarque.</strong> </p>



<p class="wp-block-paragraph">Maurits Cornelis Escher (Països Baixos, 1898-1972) fou un gran artista i, inconscientment, un gran matemàtic. Amb més de 200 obres originals, l’exposició, <em><a href="https://www.mmb.cat/exposicio-escher-a-la-sala-gran-de-les-drassanes/">Escher</a></em>, que es pot veure al Museu Marítim de Barcelona, ofereix una retrospectiva dels enigmàtics i paradoxals dissenys de l’artista. Excel·lents obres d’art, que a mesura que t’hi fixes més, te n&#8217;adones de la seva complexitat. L’artista dissenyava obres amb un rerefons que fascinava als grans matemàtics de l’època. Mitjançant la <a href="https://ca.wikipedia.org/wiki/Xilografia">xilografia</a> i la <a href="https://ca.wikipedia.org/wiki/Litografia">litografia</a> amb tessel·lacions, figures geomètriques, blancs i negres, aconseguí representar figures impossibles, fins i tot l’infinit. Una barreja d’art i ciència, que segueix fascinant i provocant mals de cap arreu del món.</p>



<h2 class="kt-adv-heading_2a9599-0f wp-block-kadence-advancedheading" data-kb-block="kb-adv-heading_2a9599-0f"><strong>Els inicis d’Escher</strong></h2>



<p class="wp-block-paragraph">Escher estudiava a l’escola d’Art i Arquitectura de Harlem, on Samuel Jesserun de Mesquita fou el seu professor i responsable de l’amor de Maurits Escher per l’art, concretament per l’<em>Art Noveau</em>, corrent artístic en el qual tot es pot decorar principalment amb formes de la naturalesa. Així que Mesquita va ser el culpable també de què Escher deixés els estudis, però amb un gran domini de la xilografia. La presència de molts edificis en les seves obres, és producte d’aquesta etapa de l’autor.</p>



<p class="wp-block-paragraph">Amb una gúbia i un burí, Escher fa els seus primers gravats a la fusta.</p>



<figure class="wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-1 is-layout-flex wp-block-gallery-is-layout-flex">
<figure class="wp-block-image size-large"><img fetchpriority="high" decoding="async" width="768" height="1024" data-id="7220" src="https://www.insights.cat/wp-content/uploads/2021/07/2-768x1024.jpeg" alt="" class="wp-image-7220" srcset="https://www.insights.cat/wp-content/uploads/2021/07/2-768x1024.jpeg 768w, https://www.insights.cat/wp-content/uploads/2021/07/2-225x300.jpeg 225w, https://www.insights.cat/wp-content/uploads/2021/07/2-1152x1536.jpeg 1152w, https://www.insights.cat/wp-content/uploads/2021/07/2-550x733.jpeg 550w, https://www.insights.cat/wp-content/uploads/2021/07/2.jpeg 1536w" sizes="(max-width: 768px) 100vw, 768px" /></figure>



<figure class="wp-block-image size-large"><img decoding="async" width="768" height="1024" data-id="7218" src="https://www.insights.cat/wp-content/uploads/2021/07/3-768x1024.jpeg" alt="" class="wp-image-7218" srcset="https://www.insights.cat/wp-content/uploads/2021/07/3-768x1024.jpeg 768w, https://www.insights.cat/wp-content/uploads/2021/07/3-225x300.jpeg 225w, https://www.insights.cat/wp-content/uploads/2021/07/3-1152x1536.jpeg 1152w, https://www.insights.cat/wp-content/uploads/2021/07/3-550x733.jpeg 550w, https://www.insights.cat/wp-content/uploads/2021/07/3.jpeg 1536w" sizes="(max-width: 768px) 100vw, 768px" /></figure>



<figure class="wp-block-image size-large"><img decoding="async" width="1024" height="768" data-id="7216" src="https://www.insights.cat/wp-content/uploads/2021/07/4-1024x768.jpeg" alt="" class="wp-image-7216" srcset="https://www.insights.cat/wp-content/uploads/2021/07/4-1024x768.jpeg 1024w, https://www.insights.cat/wp-content/uploads/2021/07/4-300x225.jpeg 300w, https://www.insights.cat/wp-content/uploads/2021/07/4-768x576.jpeg 768w, https://www.insights.cat/wp-content/uploads/2021/07/4-1536x1152.jpeg 1536w, https://www.insights.cat/wp-content/uploads/2021/07/4-550x413.jpeg 550w, https://www.insights.cat/wp-content/uploads/2021/07/4.jpeg 2048w" sizes="(max-width: 1024px) 100vw, 1024px" /></figure>
</figure>



<p class="wp-block-paragraph">Els exlibris i segells de correus van ser del primers encàrrecs que va rebre Escher. A <em>La Torre de Babel</em> podem veure com comença a jugar amb figures geomètriques, blancs i negres o la flor de pasqua, representant així, en aquest quadre, que no hi ha relació entre classes. A les <em>emblemata</em> ja s’hi observen més detalls, tonalitats amb més profunditat i volum. </p>



<p class="wp-block-paragraph">Després de l’etapa universitària, Escher viatjà a Itàlia. Una època en la que dibuixa molts paisatges naturals i sobretot edificis, producte també del seu pas pel món de l’arquitectura.</p>



<figure class="wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-2 is-layout-flex wp-block-gallery-is-layout-flex">
<figure class="wp-block-image size-large"><img loading="lazy" decoding="async" width="768" height="1024" data-id="7226" src="https://www.insights.cat/wp-content/uploads/2021/07/5-768x1024.jpeg" alt="" class="wp-image-7226" srcset="https://www.insights.cat/wp-content/uploads/2021/07/5-768x1024.jpeg 768w, https://www.insights.cat/wp-content/uploads/2021/07/5-225x300.jpeg 225w, https://www.insights.cat/wp-content/uploads/2021/07/5-1152x1536.jpeg 1152w, https://www.insights.cat/wp-content/uploads/2021/07/5-550x733.jpeg 550w, https://www.insights.cat/wp-content/uploads/2021/07/5.jpeg 1536w" sizes="auto, (max-width: 768px) 100vw, 768px" /></figure>



<figure class="wp-block-image size-large"><img loading="lazy" decoding="async" width="768" height="1024" data-id="7224" src="https://www.insights.cat/wp-content/uploads/2021/07/6-768x1024.jpeg" alt="" class="wp-image-7224" srcset="https://www.insights.cat/wp-content/uploads/2021/07/6-768x1024.jpeg 768w, https://www.insights.cat/wp-content/uploads/2021/07/6-225x300.jpeg 225w, https://www.insights.cat/wp-content/uploads/2021/07/6-1152x1536.jpeg 1152w, https://www.insights.cat/wp-content/uploads/2021/07/6-550x733.jpeg 550w, https://www.insights.cat/wp-content/uploads/2021/07/6.jpeg 1536w" sizes="auto, (max-width: 768px) 100vw, 768px" /></figure>
</figure>



<p class="wp-block-paragraph"><em>Olivera a Carisca</em>: Escher comença a fer ús de la litografia; i <em>Pentedattilo</em>: Un dels molts pobles italians retratats per Escher. Li agradava retratar-los a la nit per les llums que hi havia.</p>



<h2 class="kt-adv-heading_2ea3b5-03 wp-block-kadence-advancedheading" data-kb-block="kb-adv-heading_2ea3b5-03"><strong>Escher i la tessel·lació</strong></h2>



<p class="wp-block-paragraph">En un viatge a Espanya amb la seva dona, Jetta Umiker, l’artista s’enamora dels mosaics nassarites de l’Alhambra de Granada i els comença a dibuixar conjuntament amb Umiker. És en aquest moment, quan, inconscientment, entren les matemàtiques en les obres d’Escher. L’artista només juga amb polígons regulars i la profunditat.</p>



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<figure class="wp-block-image size-large"><img loading="lazy" decoding="async" width="768" height="1024" data-id="7230" src="https://www.insights.cat/wp-content/uploads/2021/07/11-768x1024.jpeg" alt="" class="wp-image-7230" srcset="https://www.insights.cat/wp-content/uploads/2021/07/11-768x1024.jpeg 768w, https://www.insights.cat/wp-content/uploads/2021/07/11-225x300.jpeg 225w, https://www.insights.cat/wp-content/uploads/2021/07/11-1152x1536.jpeg 1152w, https://www.insights.cat/wp-content/uploads/2021/07/11-550x733.jpeg 550w, https://www.insights.cat/wp-content/uploads/2021/07/11.jpeg 1536w" sizes="auto, (max-width: 768px) 100vw, 768px" /></figure>



<figure class="wp-block-image size-large"><img loading="lazy" decoding="async" width="768" height="1024" data-id="7232" src="https://www.insights.cat/wp-content/uploads/2021/07/10-768x1024.jpeg" alt="" class="wp-image-7232" srcset="https://www.insights.cat/wp-content/uploads/2021/07/10-768x1024.jpeg 768w, https://www.insights.cat/wp-content/uploads/2021/07/10-225x300.jpeg 225w, https://www.insights.cat/wp-content/uploads/2021/07/10-1152x1536.jpeg 1152w, https://www.insights.cat/wp-content/uploads/2021/07/10-550x733.jpeg 550w, https://www.insights.cat/wp-content/uploads/2021/07/10.jpeg 1536w" sizes="auto, (max-width: 768px) 100vw, 768px" /></figure>



<figure class="wp-block-image size-large"><img loading="lazy" decoding="async" width="768" height="1024" data-id="7234" src="https://www.insights.cat/wp-content/uploads/2021/07/9-768x1024.jpeg" alt="" class="wp-image-7234" srcset="https://www.insights.cat/wp-content/uploads/2021/07/9-768x1024.jpeg 768w, https://www.insights.cat/wp-content/uploads/2021/07/9-225x300.jpeg 225w, https://www.insights.cat/wp-content/uploads/2021/07/9-1152x1536.jpeg 1152w, https://www.insights.cat/wp-content/uploads/2021/07/9-550x733.jpeg 550w, https://www.insights.cat/wp-content/uploads/2021/07/9.jpeg 1536w" sizes="auto, (max-width: 768px) 100vw, 768px" /></figure>



<figure class="wp-block-image size-large"><img loading="lazy" decoding="async" width="768" height="1024" data-id="7236" src="https://www.insights.cat/wp-content/uploads/2021/07/8-1-768x1024.jpeg" alt="" class="wp-image-7236" srcset="https://www.insights.cat/wp-content/uploads/2021/07/8-1-768x1024.jpeg 768w, https://www.insights.cat/wp-content/uploads/2021/07/8-1-225x300.jpeg 225w, https://www.insights.cat/wp-content/uploads/2021/07/8-1-1152x1536.jpeg 1152w, https://www.insights.cat/wp-content/uploads/2021/07/8-1-550x733.jpeg 550w, https://www.insights.cat/wp-content/uploads/2021/07/8-1.jpeg 1536w" sizes="auto, (max-width: 768px) 100vw, 768px" /></figure>
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<blockquote class="wp-block-quote is-layout-flow wp-block-quote-is-layout-flow">
<p class="wp-block-paragraph">&#8220;Per mi segueix no estant clar en absolut si el joc de les figures blanques i negres pertany al món de les matemàtiques o a l’art&#8221;, deia Escher</p>
</blockquote>



<h2 class="kt-adv-heading_ca2adc-c0 wp-block-kadence-advancedheading" data-kb-block="kb-adv-heading_ca2adc-c0"><strong>Escher i la metamorfosis</strong></h2>



<p class="wp-block-paragraph">En el món d’Escher, els peixos es poden transformar en ocells. Un món ple de transformacions i metamorfosis com el dia i la nit. Tot, amb complexes tessel·lacions i matemàtiques.</p>



<figure class="wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-4 is-layout-flex wp-block-gallery-is-layout-flex">
<figure class="wp-block-image size-large"><img loading="lazy" decoding="async" width="768" height="1024" data-id="7246" src="https://www.insights.cat/wp-content/uploads/2021/07/13-768x1024.jpeg" alt="" class="wp-image-7246" srcset="https://www.insights.cat/wp-content/uploads/2021/07/13-768x1024.jpeg 768w, https://www.insights.cat/wp-content/uploads/2021/07/13-225x300.jpeg 225w, https://www.insights.cat/wp-content/uploads/2021/07/13-1152x1536.jpeg 1152w, https://www.insights.cat/wp-content/uploads/2021/07/13-550x733.jpeg 550w, https://www.insights.cat/wp-content/uploads/2021/07/13.jpeg 1536w" sizes="auto, (max-width: 768px) 100vw, 768px" /></figure>



<figure class="wp-block-image size-large"><img loading="lazy" decoding="async" width="1024" height="768" data-id="7242" src="https://www.insights.cat/wp-content/uploads/2021/07/15-1024x768.jpeg" alt="" class="wp-image-7242" srcset="https://www.insights.cat/wp-content/uploads/2021/07/15-1024x768.jpeg 1024w, https://www.insights.cat/wp-content/uploads/2021/07/15-300x225.jpeg 300w, https://www.insights.cat/wp-content/uploads/2021/07/15-768x576.jpeg 768w, https://www.insights.cat/wp-content/uploads/2021/07/15-1536x1152.jpeg 1536w, https://www.insights.cat/wp-content/uploads/2021/07/15-550x413.jpeg 550w, https://www.insights.cat/wp-content/uploads/2021/07/15.jpeg 2048w" sizes="auto, (max-width: 1024px) 100vw, 1024px" /></figure>



<figure class="wp-block-image size-large"><img loading="lazy" decoding="async" width="1024" height="768" data-id="7244" src="https://www.insights.cat/wp-content/uploads/2021/07/14-1024x768.jpeg" alt="" class="wp-image-7244" srcset="https://www.insights.cat/wp-content/uploads/2021/07/14-1024x768.jpeg 1024w, https://www.insights.cat/wp-content/uploads/2021/07/14-300x225.jpeg 300w, https://www.insights.cat/wp-content/uploads/2021/07/14-768x576.jpeg 768w, https://www.insights.cat/wp-content/uploads/2021/07/14-1536x1152.jpeg 1536w, https://www.insights.cat/wp-content/uploads/2021/07/14-550x413.jpeg 550w, https://www.insights.cat/wp-content/uploads/2021/07/14.jpeg 2048w" sizes="auto, (max-width: 1024px) 100vw, 1024px" /></figure>



<figure class="wp-block-image size-large"><img loading="lazy" decoding="async" width="768" height="1024" data-id="7240" src="https://www.insights.cat/wp-content/uploads/2021/07/16-768x1024.jpeg" alt="" class="wp-image-7240" srcset="https://www.insights.cat/wp-content/uploads/2021/07/16-768x1024.jpeg 768w, https://www.insights.cat/wp-content/uploads/2021/07/16-225x300.jpeg 225w, https://www.insights.cat/wp-content/uploads/2021/07/16-1152x1536.jpeg 1152w, https://www.insights.cat/wp-content/uploads/2021/07/16-550x733.jpeg 550w, https://www.insights.cat/wp-content/uploads/2021/07/16.jpeg 1536w" sizes="auto, (max-width: 768px) 100vw, 768px" /></figure>
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<h2 class="kt-adv-heading_ce7508-47 wp-block-kadence-advancedheading" data-kb-block="kb-adv-heading_ce7508-47"><strong>Escher i l’estructura de l’espai</strong></h2>



<p class="wp-block-paragraph">Des de què va marxar d’Itàlia, Escher no va deixar mai l’espai intacte. En un sol gravat s’ajuntaven diferents representacions amb una gran lògica, com si veiéssim els gravats a través d’una superfície reflectant.</p>



<figure class="wp-block-image size-large"><img loading="lazy" decoding="async" width="768" height="1024" src="https://www.insights.cat/wp-content/uploads/2021/07/17-1-768x1024.jpeg" alt="" class="wp-image-7277" srcset="https://www.insights.cat/wp-content/uploads/2021/07/17-1-768x1024.jpeg 768w, https://www.insights.cat/wp-content/uploads/2021/07/17-1-225x300.jpeg 225w, https://www.insights.cat/wp-content/uploads/2021/07/17-1-1152x1536.jpeg 1152w, https://www.insights.cat/wp-content/uploads/2021/07/17-1-550x733.jpeg 550w, https://www.insights.cat/wp-content/uploads/2021/07/17-1.jpeg 1536w" sizes="auto, (max-width: 768px) 100vw, 768px" /></figure>



<p class="wp-block-paragraph">Escher representa una estructura purament matemàtica, la cinta de Moebius. L’artista va tenir una gran admiració per les superfícies topològiques. En la cinta de Moebius, si vas seguint les formigues, no saps si van per dintre o van per fora. Escher també va admirar les formes de cristall, de tal manera que les seves obres s’observessin com si fossin vistes des de superfícies reflectants.</p>



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<figure class="wp-block-image size-large"><img loading="lazy" decoding="async" width="1024" height="768" data-id="7258" src="https://www.insights.cat/wp-content/uploads/2021/07/18-1024x768.jpeg" alt="" class="wp-image-7258" srcset="https://www.insights.cat/wp-content/uploads/2021/07/18-1024x768.jpeg 1024w, https://www.insights.cat/wp-content/uploads/2021/07/18-300x225.jpeg 300w, https://www.insights.cat/wp-content/uploads/2021/07/18-768x576.jpeg 768w, https://www.insights.cat/wp-content/uploads/2021/07/18-1536x1152.jpeg 1536w, https://www.insights.cat/wp-content/uploads/2021/07/18-550x413.jpeg 550w, https://www.insights.cat/wp-content/uploads/2021/07/18.jpeg 2048w" sizes="auto, (max-width: 1024px) 100vw, 1024px" /></figure>



<figure class="wp-block-image size-large"><img loading="lazy" decoding="async" width="768" height="1024" data-id="7256" src="https://www.insights.cat/wp-content/uploads/2021/07/19-1-768x1024.jpeg" alt="" class="wp-image-7256" srcset="https://www.insights.cat/wp-content/uploads/2021/07/19-1-768x1024.jpeg 768w, https://www.insights.cat/wp-content/uploads/2021/07/19-1-225x300.jpeg 225w, https://www.insights.cat/wp-content/uploads/2021/07/19-1-1152x1536.jpeg 1152w, https://www.insights.cat/wp-content/uploads/2021/07/19-1-550x733.jpeg 550w, https://www.insights.cat/wp-content/uploads/2021/07/19-1.jpeg 1536w" sizes="auto, (max-width: 768px) 100vw, 768px" /></figure>



<figure class="wp-block-image size-large"><img loading="lazy" decoding="async" width="768" height="1024" data-id="7254" src="https://www.insights.cat/wp-content/uploads/2021/07/20-768x1024.jpeg" alt="" class="wp-image-7254" srcset="https://www.insights.cat/wp-content/uploads/2021/07/20-768x1024.jpeg 768w, https://www.insights.cat/wp-content/uploads/2021/07/20-225x300.jpeg 225w, https://www.insights.cat/wp-content/uploads/2021/07/20-1152x1536.jpeg 1152w, https://www.insights.cat/wp-content/uploads/2021/07/20-550x733.jpeg 550w, https://www.insights.cat/wp-content/uploads/2021/07/20.jpeg 1536w" sizes="auto, (max-width: 768px) 100vw, 768px" /></figure>
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<h2 class="kt-adv-heading_0d9ded-3a wp-block-kadence-advancedheading" data-kb-block="kb-adv-heading_0d9ded-3a"><strong>Escher i les paradoxes geomètriques</strong></h2>



<p class="wp-block-paragraph">Durant la seva trajectòria, Escher va interactuar amb matemàtics i científics i això el va inspirar en la investigació sobre construccions impossibles, il·lusions òptiques i representacions de l’infinit. </p>



<p class="wp-block-paragraph">Veient les imatges, ens preguntem: Quantes plantes hi ha? Les escales pugen o baixen? <em>Belvedere</em>, la figura impossible. L’escala va per dintre o per fora? La representació impossible dels arcs ens impedeix respondre la pregunta. En el quadre també observem una persona asseguda al banc, analitzant la matemàtica de la representació. Què és a dalt i què és a baix? Una altra representació impossible de M.C Escher. Escala de <em>Penrose</em>, puja o baixa? Veiem l’impossible recorregut de l’aigua.</p>



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<h2 class="kt-adv-heading_86da27-e0 wp-block-kadence-advancedheading" data-kb-block="kb-adv-heading_86da27-e0"><strong>De les matemàtiques al terreny artístic</strong></h2>



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<p class="wp-block-paragraph">L’obra de Maurits Cornelis Escher ha incidit en tots els àmbits creatius amb una gran influència a la cultura contemporània. Amb les seves representacions impossibles, l’artista s’ha convertit en una font d’inspiració en el món dels dibuixos animats com els Simpson, anuncis publicitaris com els d’Audi, films com <em>Origen</em>, protagonitzat per Leonardo Di Caprio, dissenyadors de moda com Chanel, grups musicals com Pink Floyd, i fins i tot, en l’estètica hippy.</p>
<p>La entrada <a href="https://www.insights.cat/2021/08/12/les-matematiques-darrere-els-quadres/">Les matemàtiques darrere els quadres</a> se publicó primero en <a href="https://www.insights.cat">iNSiGHTS</a>.</p>
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