{"id":24485,"date":"2022-10-03T18:38:56","date_gmt":"2022-10-03T16:38:56","guid":{"rendered":"https:\/\/agora.xtec.cat\/iesroquetes\/?p=24485"},"modified":"2022-10-07T15:01:26","modified_gmt":"2022-10-07T13:01:26","slug":"la-proporcio-auria-en-diferents-contextos","status":"publish","type":"post","link":"https:\/\/agora.xtec.cat\/iesroquetes\/general\/la-proporcio-auria-en-diferents-contextos\/","title":{"rendered":"La proporci\u00f3 \u00e0uria en diferents contextos"},"content":{"rendered":"

Durant aquests dies els alumnes de 2n d’ESO a les classes de matem\u00e0tiques han estat estudiant la proporci\u00f3 \u00e0uria i on apareix en diferents contextos. Se’ls va fer l’enc\u00e0rrec de fer un article per a la p\u00e0gina web del centre i els seleccionats s\u00f3n els seg\u00fcents:<\/p>\n

5<\/strong> ESTUDIANTS DE 2n ESO C INVESTIGUEN LA RELACI\u00d3 ENTRE LA PROPORCI\u00d3 \u00c0URIA I LA PUBLICITAT <\/strong><\/p>\n

La proporci\u00f3 \u00e0uria o nombre d\u2019or, \u00e9s la proporci\u00f3 entre dos segments a i b, que compleixen la condici\u00f3 de que la proporci\u00f3 entre la suma dels dos segments, partit pel segment m\u00e9s gran, \u00e9s la mateixa proporci\u00f3 que hi ha entre el segment gran i el segment petit.\u00a0<\/span><\/p>\n

\"\"<\/a><\/p>\n

Es representada per la lletra Phi = 1.618033\u2026<\/span><\/p>\n

La proporci\u00f3 \u00e0uria s\u2019adopta al disseny, perqu\u00e8 \u00e9s una forma neta, f\u00e0cil i organitzada per als cartells, webs i diferents tipus de publicitat.<\/span><\/p>\n

Quina \u00e9s realment la relaci\u00f3 entre la proporci\u00f3 \u00e0uria i la publicitat? La proporci\u00f3 \u00e0uria s\u2019ha utilitzat durant segles en la fotografia, l\u2019art i l\u2019arquitectura.<\/span> Entre d’altres, i aquests elements inevitablement apareixen tamb\u00e9 en la publicitat.<\/b><\/p>\n

\"\"<\/a><\/p>\n

Aqu\u00ed podem observar la seva relaci\u00f3, la proporci\u00f3 \u00e0uria est\u00e0 dins dels anuncis publicitaris com el de “Coca-Cola” i tamb\u00e9 pot estar a les revistes. Si el rectangle \u00e9s auri, al treure el quadrat seguirem tenint un rectangle auri i aix\u00ed fins l’infinit.<\/span><\/p>\n

 <\/p>\n

Berta, J\u00falia, Maria, Miguel i Dani de 2n C<\/b><\/p>\n

QU\u00c8 HEM FET A CLASSE DE MATEM\u00c0TIQUES AQUESTS DIES?<\/strong><\/p>\n

A classe de matem\u00e0tiques hem investigat sobre la proporci\u00f3 \u00e0uria o el nombre d\u2019or, qu\u00e8 \u00e9s i on s\u2019aplica. El primer dia ens hem repartit en grups i cada grup ha escollit un tema per practicar la proporci\u00f3 \u00e0uria amb ell, nosaltres hem escollit els objectes quotidians, per aix\u00f2 el nostre treball tracta sobre la proporci\u00f3 \u00e0uria plasmada en els objectes quotidians. Hem provat si una targeta d\u2019autob\u00fas \u00e9s proporcionalment <\/span>\u00e0uria.<\/span><\/p>\n

\"\"<\/a><\/p>\n

 <\/p>\n

a=5,5 cm.\u00a0 b=3 cm.\u00a0 5,5 \/ 3 = 1,83333333. <\/span>Aquesta targeta \u00e9s aproximadament similar a <\/span>\u03a6. <\/span>Amb aquest exemple hem aconseguit comprovar si un objecte quotidi\u00e0, com \u00e9s una targeta d\u2019autob\u00fas \u00e9s proporcionalment \u00e0uria o no.<\/span><\/p>\n

 <\/p>\n

Roma, D\u00eddac, Eider i Jaume de 2n C.<\/strong><\/p>\n

LA PROPORCI\u00d3 \u00c0URIA EN LA PINTURA<\/strong><\/p>\n

La ra\u00f3 \u00e0uria, nombre auri, secci\u00f3 \u00e0uria o divina proporci\u00f3 \u00e9s la proporci\u00f3 entre dos segments a i b que compleixen la condici\u00f3 que la proporci\u00f3 entre la suma d’aquests dos segments i el segment m\u00e9s gran \u00e9s la mateixa que hi ha entre el segment m\u00e9s gran i el segment m\u00e9s petit<\/p>\n

Hi ha quadres que s\u00f3n m\u00e9s bonics que altres simplement perqu\u00e8 s\u00f3n m\u00e9s auris que altres.<\/strong><\/p>\n

\"\"<\/a>Com podem veure en aquest quadre, La Gioconda o Mona Lisa de Leonardo da Vinci, \u00e9s una pintura \u00e0uria. Ja que es pot dividir en diferents rectangles auris. Es compleix que a \/ b = a + b \/ a= 1,618033… Aquest nombre i el nombre que surt en el quadre \u00e9s el nombre d\u2019or.<\/span><\/p>\n

 <\/p>\n

\"\"<\/a><\/span>Aquest quadre \u00e9s el de Las Meninas<\/em> de Vel\u00e1zquez. Tots aquests rectangles que es formen s\u00f3n auris, per aquest motiu aquest quadre \u00e9s auri. Les corbes que es formen unint els v\u00e8rtex de la diagonal dels quadrats formen una corba anomenada, l\u2019espiral d’Arqu\u00edmedes. Podem anar fent m\u00e9s i m\u00e9s rectangles fins a l\u2019infinit, ja que aquesta \u00e9s una particularitat del rectangle auri.\u00a0<\/span><\/p>\n

\u00c0ngela, Jaione, Ainara i Cl\u00e0udia de 2n C.<\/strong><\/p>\n

LA PROPORCI\u00d3 \u00c0URIA EN OBJECTES QUOTIDIANS<\/strong><\/p>\n

A la mat\u00e8ria de matem\u00e0tiques estem estudiant les proporcions i m\u00e9s concretament la proporci\u00f3 \u00e0uria, tamb\u00e9 us explicarem on podem trobar-la en objectes quotidians.<\/span><\/p>\n

Qu\u00e8 \u00e9s la proporci\u00f3 \u00e0uria?<\/strong><\/p>\n

La ra\u00f3 \u00e0uria \u00e9s la proporci\u00f3 entre dos segments <\/span>a<\/span><\/i> i <\/span>b<\/span><\/i> (o per extensi\u00f3, entre dues quantitats <\/span>a<\/span><\/i> i <\/span>b<\/span><\/i>) que compleixen la condici\u00f3 que la proporci\u00f3 entre la suma d’aquests dos segments i el segment m\u00e9s gran \u00e9s la mateixa que hi ha entre el segment m\u00e9s gran i el segment m\u00e9s petit.\u00a0<\/span><\/p>\n

En qu\u00e8 consisteix la proporci\u00f3 \u00e0uria?<\/strong><\/p>\n

Suposem que tenim un segment i el volem dividir en dues parts. Aix\u00f2 s\u00ed, nosaltres el volem tallar de manera que el segment total entre el fragment gran sigui igual al gran entre el petit. Si resolem aquesta equaci\u00f3, obtenim una \u00fanica soluci\u00f3. <\/span>Aquest n\u00famero que hem obtingut \u00e9s l\u2019anomenat nombre phi (\u03a6=1,618033\u2026), anomenat aix\u00ed en honor a F\u00eddies, un dels arquitectes del Parten\u00f3 d\u2019Atenes. Ell mateix va fer servir aquesta proporci\u00f3 en tots i cadascun dels elements d\u2019aquest edifici. Si no t\u2019ho creus, agafa un regle i fes la prova. Divideix la seva amplada <\/span>entre la seva al\u00e7ada, l\u2019al\u00e7ada entre la mesura de la columna, etc. Obtindr\u00e0s sempre el mateix valor: el nombre phi.<\/span><\/p>\n

La proporci\u00f3 \u00e0uria en objectes quotidians:<\/strong><\/p>\n

L’exemple m\u00e9s proper i curi\u00f3s en qu\u00e8 trobarem la proporci\u00f3 \u00e0uria \u00e9s a les targetes de cr\u00e8dit. Si dividim l’amplada entre l’altura d’una targeta de cr\u00e8dit, aconseguirem el nombre auri: 1,618 .<\/span><\/p>\n

Aquesta proporci\u00f3 \u00e0uria continua viva als nostres dies, i \u00e9s precisament en el disseny de logotips on en trobem grans exemples.<\/span><\/p>\n

La proporci\u00f3 \u00e0uria ajudar\u00e0 a crear dissenys est\u00e8ticament m\u00e9s agradables, molt creatius per aix\u00f2 han optat per aplicar aquesta relaci\u00f3 a la construcci\u00f3 dels logotips.<\/span><\/p>\n

Quim F., Paula C., Marta i Izan de 2n B.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Durant aquests dies els alumnes de 2n d’ESO a les classes de matem\u00e0tiques han estat estudiant la proporci\u00f3 \u00e0uria i on apareix en diferents contextos.<\/p>\n","protected":false},"author":336,"featured_media":24486,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[680,3,5,14,15,16,98,1,29],"tags":[685,686,687,41,391],"class_list":["post-24485","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-curs22-23","category-eso","category-eso-2","category-eso-2a","category-eso-2b","category-eso-2c","category-eso-2e","category-general","category-portada","tag-investigacio","tag-nombre-auri","tag-proporcio-auria","tag-matematiques","tag-treball-cooperatiu"],"post_mailing_queue_ids":[],"_links":{"self":[{"href":"https:\/\/agora.xtec.cat\/iesroquetes\/wp-json\/wp\/v2\/posts\/24485","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/agora.xtec.cat\/iesroquetes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/agora.xtec.cat\/iesroquetes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/agora.xtec.cat\/iesroquetes\/wp-json\/wp\/v2\/users\/336"}],"replies":[{"embeddable":true,"href":"https:\/\/agora.xtec.cat\/iesroquetes\/wp-json\/wp\/v2\/comments?post=24485"}],"version-history":[{"count":3,"href":"https:\/\/agora.xtec.cat\/iesroquetes\/wp-json\/wp\/v2\/posts\/24485\/revisions"}],"predecessor-version":[{"id":24571,"href":"https:\/\/agora.xtec.cat\/iesroquetes\/wp-json\/wp\/v2\/posts\/24485\/revisions\/24571"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/agora.xtec.cat\/iesroquetes\/wp-json\/wp\/v2\/media\/24486"}],"wp:attachment":[{"href":"https:\/\/agora.xtec.cat\/iesroquetes\/wp-json\/wp\/v2\/media?parent=24485"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/agora.xtec.cat\/iesroquetes\/wp-json\/wp\/v2\/categories?post=24485"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/agora.xtec.cat\/iesroquetes\/wp-json\/wp\/v2\/tags?post=24485"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}