{"id":3608,"date":"2013-01-08T22:21:25","date_gmt":"2013-01-08T22:21:25","guid":{"rendered":"http:\/\/pimedios.es\/?p=3608"},"modified":"2013-01-08T22:21:25","modified_gmt":"2013-01-08T22:21:25","slug":"matematicas-imposibles","status":"publish","type":"post","link":"https:\/\/pimedios.jesussoto.es\/?p=3608","title":{"rendered":"Matem\u00e1ticas imposibles"},"content":{"rendered":"<p>En la correcci\u00f3n de ejercicios es com\u00fan encontrar confusiones \u00a0y erratas. Por desgracia, \u00a0tambi\u00e9n equivocaciones que dan mucho donde pensar. Pongamos un ejemplo:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-830 aligncenter\" title=\"exm-1\" alt=\"\" src=\"http:\/\/jesussoto.es\/wp-content\/uploads\/2013\/01\/exm-1.png\" width=\"400\" height=\"161\" \/><\/p>\n<p>Est\u00e1 claro que el alumno se encontr\u00f3 con una gran dificultad al abordad $\\log(\\tan(px))$, decidi\u00e9ndose por comprender $\\tan(px)$ como un producto de $\\tan$ por $px$, de ah\u00ed que aplique la propiedad de los logaritmos par el producto:<br \/>\n$$\\log(\\tan(px))=\\log(\\tan)+\\log(px)$$<br \/>\nPero como $\\log(\\tan)$ le sonaba raro decide introducir la $x$ y as\u00ed dar sentido a la expresi\u00f3n<br \/>\n$$\\log(\\tan(px))=\\log(\\tan x)+\\log(px).$$<br \/>\nAhora parece hasta l\u00f3gica.<\/p>\n<p>Otro alumno opt\u00f3 por modificar $\\tan$ para que su significado fuese m\u00e1s claro:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-831 aligncenter\" title=\"exm-2\" alt=\"\" src=\"http:\/\/jesussoto.es\/wp-content\/uploads\/2013\/01\/exm-2.png\" width=\"400\" height=\"122\" \/><br \/>\nDe este modo la complejidad del $\\tan$ se solventa al sustituir $\\tan=\\frac{\\sin x}{\\cos x}$. Puesto a contar con esta obviedad, el resto conlleva otras m\u00e1s livianas, dentro de la premisa: si la primera es muy gorda y pasa, por el resto no hay que preocuparse.<\/p>\n<p>Como he dicho: mucho que pensar.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ejemplos de operaciones matem\u00e1ticas imposibles realizadas por los alumnos.<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[],"class_list":["post-3608","post","type-post","status-publish","format-standard","hentry","category-ocio","entry"],"_links":{"self":[{"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/3608","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3608"}],"version-history":[{"count":2,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/3608\/revisions"}],"predecessor-version":[{"id":3610,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/3608\/revisions\/3610"}],"wp:attachment":[{"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3608"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3608"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3608"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}