{"id":871,"date":"2025-09-04T21:11:42","date_gmt":"2025-09-05T03:11:42","guid":{"rendered":"https:\/\/portal.pronea.gt\/?p=871"},"modified":"2025-09-07T10:35:58","modified_gmt":"2025-09-07T16:35:58","slug":"temporary-title-790-2-2-2-2-2-2-2-2","status":"publish","type":"post","link":"https:\/\/portal.pronea.gt\/?p=871","title":{"rendered":"Funciones c\u00f3nicas: las curvas que dibujan las matem\u00e1ticas"},"content":{"rendered":"<div id=\"cmsmasters_row_0j6royqael\" class=\"cmsmasters_row cmsmasters_color_scheme_default cmsmasters_row_top_default cmsmasters_row_bot_default cmsmasters_row_fullwidth\">\n<div class=\"cmsmasters_row_outer_parent\">\n<div class=\"cmsmasters_row_outer\">\n<div class=\"cmsmasters_row_inner cmsmasters_row_fullwidth cmsmasters_row_no_margin\">\n<div class=\"cmsmasters_row_margin\">\n<div id=\"cmsmasters_column_69dy6p9ke\" class=\"cmsmasters_column one_first\">\n<div class=\"cmsmasters_column_inner\"><div class=\"cmsmasters_text\" data-animation=\"fadeInRight\" data-delay=\"0\">\n<p data-start=\"2226\" data-end=\"2556\">Las matem\u00e1ticas no solo se ocupan de n\u00fameros, tambi\u00e9n de formas que aparecen a nuestro alrededor. Entre ellas se encuentran las <strong data-start=\"2354\" data-end=\"2375\">funciones c\u00f3nicas<\/strong>, que incluyen al c\u00edrculo, la par\u00e1bola, la elipse y la hip\u00e9rbola. Estas figuras no son solo teor\u00eda: se encuentran en la vida diaria, en la naturaleza y en los avances cient\u00edficos.<\/p>\n<p data-start=\"2558\" data-end=\"2640\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f3a5.svg\" alt=\"\ud83c\udfa5\" \/> <strong data-start=\"2561\" data-end=\"2583\">Mira el video aqu\u00ed<\/strong><\/p>\n<iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/P_aKas8SPco?si=TfpedzVQmcbuaks8\" width=\"1120\" height=\"630\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe>\n<hr data-start=\"2642\" data-end=\"2645\" \/>\n<h2 data-start=\"2647\" data-end=\"2686\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f50e.svg\" alt=\"\ud83d\udd0e\" \/> \u00bfQu\u00e9 son las funciones c\u00f3nicas?<\/h2>\n<p data-start=\"2687\" data-end=\"2787\">Las <strong data-start=\"2691\" data-end=\"2702\">c\u00f3nicas<\/strong> se originan al cortar un cono con un plano. De este corte surgen distintas curvas:<\/p>\n<ul>\n<li data-start=\"2790\" data-end=\"2841\"><strong data-start=\"2790\" data-end=\"2802\">C\u00edrculo:<\/strong> distancia igual desde un punto fijo.<\/li>\n<li data-start=\"2844\" data-end=\"2901\"><strong data-start=\"2844\" data-end=\"2857\">Par\u00e1bola:<\/strong> forma de arco, muy com\u00fan en trayectorias.<\/li>\n<li data-start=\"2904\" data-end=\"2951\"><strong data-start=\"2904\" data-end=\"2915\">Elipse:<\/strong> una curva alargada con dos focos.<\/li>\n<li data-start=\"2954\" data-end=\"3036\"><strong data-start=\"2954\" data-end=\"2968\">Hip\u00e9rbola:<\/strong> dos ramas abiertas que aparecen en fen\u00f3menos como ondas de radio.<\/li>\n<\/ul>\n<hr data-start=\"3038\" data-end=\"3041\" \/>\n<h2 data-start=\"3043\" data-end=\"3076\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/270d.svg\" alt=\"\u270d\ufe0f\" \/> \u00bfPor qu\u00e9 son importantes?<\/h2>\n<p data-start=\"3077\" data-end=\"3101\">Estas curvas permiten:<\/p>\n<ul>\n<li data-start=\"3104\" data-end=\"3153\">Entender trayectorias de objetos en movimiento.<\/li>\n<li data-start=\"3156\" data-end=\"3197\">Dise\u00f1ar construcciones arquitect\u00f3nicas.<\/li>\n<li data-start=\"3200\" data-end=\"3243\">Estudiar \u00f3rbitas de planetas y sat\u00e9lites.<\/li>\n<li data-start=\"3246\" data-end=\"3287\">Modelar fen\u00f3menos en f\u00edsica y econom\u00eda.<\/li>\n<\/ul>\n<hr data-start=\"3289\" data-end=\"3292\" \/>\n<h2 data-start=\"3294\" data-end=\"3326\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f30d.svg\" alt=\"\ud83c\udf0d\" \/> Ejemplos en la vida real<\/h2>\n<ul>\n<li data-start=\"3329\" data-end=\"3404\">La <strong data-start=\"3332\" data-end=\"3344\">par\u00e1bola<\/strong> aparece en la trayectoria de una pelota al ser lanzada. <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/26bd.svg\" alt=\"\u26bd\" \/><\/li>\n<li data-start=\"3407\" data-end=\"3479\">La <strong data-start=\"3410\" data-end=\"3420\">elipse<\/strong> describe la \u00f3rbita de los planetas alrededor del Sol. <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/2600.svg\" alt=\"\u2600\ufe0f\" \/><\/li>\n<li data-start=\"3482\" data-end=\"3536\">Los <strong data-start=\"3486\" data-end=\"3498\">c\u00edrculos<\/strong> son la base de ruedas y engranajes.<\/li>\n<li data-start=\"3539\" data-end=\"3600\">La <strong data-start=\"3542\" data-end=\"3555\">hip\u00e9rbola<\/strong> se usa en antenas y telecomunicaciones. <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f4e1.svg\" alt=\"\ud83d\udce1\" \/><\/li>\n<\/ul>\n<hr data-start=\"3602\" data-end=\"3605\" \/>\n<h2 data-start=\"3607\" data-end=\"3634\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f393.svg\" alt=\"\ud83c\udf93\" \/> Aprender con PRONEA<\/h2>\n<p data-start=\"3635\" data-end=\"3883\">El <strong data-start=\"3638\" data-end=\"3693\">Programa Nacional de Educaci\u00f3n Alternativa \u2013PRONEA\u2013<\/strong> del Ministerio de Educaci\u00f3n de Guatemala te brinda la oportunidad de descubrir estas funciones de forma sencilla, comprendiendo no solo la teor\u00eda, sino tambi\u00e9n sus aplicaciones pr\u00e1cticas.<\/p>\n<hr data-start=\"3885\" data-end=\"3888\" \/>\n<h2 data-start=\"3890\" data-end=\"3907\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/2705.svg\" alt=\"\u2705\" \/> Conclusi\u00f3n<\/h2>\n<p data-start=\"3908\" data-end=\"4090\">Las <strong data-start=\"3912\" data-end=\"3933\">funciones c\u00f3nicas<\/strong> nos muestran que las matem\u00e1ticas est\u00e1n vivas en nuestro entorno. Aprenderlas es descubrir c\u00f3mo las curvas y las formas conectan la teor\u00eda con la realidad.<\/p>\n<p data-start=\"4092\" data-end=\"4143\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f449.svg\" alt=\"\ud83d\udc49\" \/> <strong data-start=\"4095\" data-end=\"4141\">PRONEA: La educaci\u00f3n que transforma vidas.<\/strong><\/p>\n<\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":874,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"image","meta":{"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false,"footnotes":""},"categories":[33,39],"tags":[],"class_list":["post-871","post","type-post","status-publish","format-image","has-post-thumbnail","hentry","category-matematicas","category-recursos","post_format-post-format-image"],"_links":{"self":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/871","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=871"}],"version-history":[{"count":3,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/871\/revisions"}],"predecessor-version":[{"id":875,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/871\/revisions\/875"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/media\/874"}],"wp:attachment":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=871"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=871"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=871"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}