{"id":1277,"date":"2023-06-07T08:51:04","date_gmt":"2023-06-07T06:51:04","guid":{"rendered":"http:\/\/www.joanillo.org\/?p=1277"},"modified":"2023-06-07T09:05:18","modified_gmt":"2023-06-07T07:05:18","slug":"llesques-de-la-mateixa-altura-igual-superficie-de-crosta","status":"publish","type":"post","link":"https:\/\/www.joanillo.org\/?p=1277","title":{"rendered":"Llesques de la mateixa altura, igual superf\u00edcie de crosta"},"content":{"rendered":"<p><img class=\"alignright size-medium wp-image-2338\" title=\"Llesques\" src=\"http:\/\/www.joanillo.org\/wp-content\/uploads\/2023\/06\/llesques_problema_integracio.png\" alt=\"Llesques\" width=\"200\">Imaginem que tenim un pa rod\u00f3. Per\u00f2 rod\u00f3 rod\u00f3, esf\u00e8ric. Si el llesquem amb llesques de 1,5 cm (1 cm massa primes, 2 cm massa gruixudes), la crosta que obtenim de les diferents llesques t\u00e9 la mateixa superf\u00edcie.<br \/>\nTamb\u00e9 ho podem pensar en una taronja, que s\u00ed que \u00e9s esf\u00e8rica.<\/p>\n<p>La demostraci\u00f3 la vaig veure en aquest <a href=\"https:\/\/twitter.com\/fermatslibrary\/status\/1665326136702771200\" target=\"_blank\" rel=\"noopener noreferrer\">tweet<\/a>, tot i que l&#8217;explicaci\u00f3 i el dibuix no \u00e9s molt convincent. O sigui que l&#8217;he reprodu\u00eft a la meva manera.<\/p>\n<p>\u00c9s un exercici d&#8217;integraci\u00f3 i c\u00e0lcul de superf\u00edcie sobre una esfera, de nivell de primer de carrera. El resultat final \u00e9s que per b-a constants, que \u00e9s l&#8217;altura de la llesca, la superf\u00edcie \u00e9s la mateixa: A = 2*Pi*R*(b-a). Sempre s&#8217;aprenen coses noves.<\/p>\n<p>El pdf amb la meva soluci\u00f3:<\/p>\n<ul>\n<li><a href=\"http:\/\/www.joanillo.org\/wp-content\/uploads\/2023\/06\/llesques_problema_integracio.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">llesques_problema_integracio.pdf<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Imaginem que tenim un pa rod\u00f3. Per\u00f2 rod\u00f3 rod\u00f3, esf\u00e8ric. Si el llesquem amb llesques de 1,5 cm (1 cm massa primes, 2 cm massa gruixudes), la crosta que obtenim de les diferents llesques t\u00e9 la mateixa superf\u00edcie. Tamb\u00e9 ho podem pensar en una taronja, que s\u00ed que \u00e9s esf\u00e8rica. La demostraci\u00f3 la vaig veure [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1,16],"tags":[],"_links":{"self":[{"href":"https:\/\/www.joanillo.org\/index.php?rest_route=\/wp\/v2\/posts\/1277"}],"collection":[{"href":"https:\/\/www.joanillo.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.joanillo.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.joanillo.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.joanillo.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1277"}],"version-history":[{"count":5,"href":"https:\/\/www.joanillo.org\/index.php?rest_route=\/wp\/v2\/posts\/1277\/revisions"}],"predecessor-version":[{"id":1285,"href":"https:\/\/www.joanillo.org\/index.php?rest_route=\/wp\/v2\/posts\/1277\/revisions\/1285"}],"wp:attachment":[{"href":"https:\/\/www.joanillo.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1277"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.joanillo.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1277"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.joanillo.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1277"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}