{"id":6039,"date":"2023-09-28T07:03:26","date_gmt":"2023-09-28T05:03:26","guid":{"rendered":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/?p=6039"},"modified":"2023-09-24T10:15:32","modified_gmt":"2023-09-24T08:15:32","slug":"deltoide-aureo-concavo-iii","status":"publish","type":"post","link":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/deltoide-aureo-concavo-iii\/","title":{"rendered":"Deltoide \u00e1ureo c\u00f3ncavo III"},"content":{"rendered":"<p style=\"text-align: justify\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\"><strong>C\u00e1lculo de las longitudes de los lados y medida de los \u00e1ngulos del deltoide en el que su eje de simetr\u00eda coincide con su diagonal menor<\/strong><\/span><\/p>\n<p style=\"text-align: justify\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Para calcular los lados del deltoide \u00e1ureo empezamos calculando la distancia x de la figura. Para ello se necesita calcular los lados l<sub>1<\/sub> y l<sub>2<\/sub> en funci\u00f3n de x y despu\u00e9s imponer la condici\u00f3n de que el cociente entre el lado mayor y el lado menor es el n\u00famero de oro.<\/span><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6041\" src=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_01.png\" alt=\"\" width=\"652\" height=\"230\" srcset=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_01.png 652w, https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_01-300x106.png 300w\" sizes=\"(max-width: 652px) 100vw, 652px\" \/><\/p>\n<p style=\"text-align: justify\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">&nbsp;Se debe verificar que:<\/span><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6042\" src=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_2.png\" alt=\"\" width=\"354\" height=\"143\" srcset=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_2.png 354w, https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_2-300x121.png 300w\" sizes=\"(max-width: 354px) 100vw, 354px\" \/><\/p>\n<p><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Se sustituye \u03a6<sup>2<\/sup> por \u03a6+1 y \u03a6<sup>4<\/sup> por (\u03a6+1)<sup>2<\/sup>=\u03a6<sup>2<\/sup>+2\u03a6+1=3\u03a6+2:<\/span><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6043\" src=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_3.png\" alt=\"\" width=\"341\" height=\"113\" srcset=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_3.png 341w, https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_3-300x99.png 300w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><\/p>\n<p><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Se resuelve la ecuaci\u00f3n de segundo grado:<\/span><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6046\" src=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_4.png\" alt=\"\" width=\"480\" height=\"141\" srcset=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_4.png 480w, https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_4-300x88.png 300w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><\/p>\n<p style=\"text-align: justify\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Se sustituye:<\/span><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6047\" src=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_5.png\" alt=\"\" width=\"312\" height=\"38\" srcset=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_5.png 312w, https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_5-300x37.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6048\" src=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_6.png\" alt=\"\" width=\"549\" height=\"65\" srcset=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_6.png 549w, https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_6-300x36.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p style=\"text-align: justify\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Se obtienen dos soluciones positivas, por tanto, hay dos deltoides con las proporciones buscadas:&nbsp;<\/span><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6049\" src=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_7.png\" alt=\"\" width=\"373\" height=\"152\" srcset=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_7.png 373w, https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_7-300x122.png 300w\" sizes=\"(max-width: 373px) 100vw, 373px\" \/><\/p>\n<p><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">\u2022 Longitudes de los lados y medida de los \u00e1ngulos de la primera soluci\u00f3n:<\/span><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6051\" src=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_8.png\" alt=\"\" width=\"664\" height=\"247\" srcset=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_8.png 664w, https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_8-300x112.png 300w\" sizes=\"(max-width: 664px) 100vw, 664px\" \/><\/p>\n<p><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">El per\u00edmetro y el \u00e1rea de este deltoide son, respectivamente:<\/span><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6052\" src=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_9.png\" alt=\"\" width=\"403\" height=\"40\" srcset=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_9.png 403w, https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_9-300x30.png 300w\" sizes=\"(max-width: 403px) 100vw, 403px\" \/><\/p>\n<p><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">\u2022 Longitudes de los lados y medida de los \u00e1ngulos de la segunda soluci\u00f3n:<\/span><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6054\" src=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_10.png\" alt=\"\" width=\"671\" height=\"249\" srcset=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_10.png 671w, https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_10-300x111.png 300w\" sizes=\"(max-width: 671px) 100vw, 671px\" \/><\/p>\n<p><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">El per\u00edmetro y el \u00e1rea de este deltoide son, respectivamente:<\/span><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6055\" src=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_11.png\" alt=\"\" width=\"411\" height=\"40\" srcset=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_11.png 411w, https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2023\/09\/deltoide10_11-300x29.png 300w\" sizes=\"(max-width: 411px) 100vw, 411px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>C\u00e1lculo de las longitudes de los lados y medida de los \u00e1ngulos del deltoide en el que su eje de simetr\u00eda coincide con su diagonal menor Para calcular los lados del deltoide \u00e1ureo empezamos&#46;&#46;&#46;<\/p>\n","protected":false},"author":7927,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[2075227],"tags":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/6039"}],"collection":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/users\/7927"}],"replies":[{"embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/comments?post=6039"}],"version-history":[{"count":6,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/6039\/revisions"}],"predecessor-version":[{"id":6056,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/6039\/revisions\/6056"}],"wp:attachment":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/media?parent=6039"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/categories?post=6039"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/tags?post=6039"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}