{"id":65,"date":"2007-12-19T03:22:04","date_gmt":"2007-12-19T01:22:04","guid":{"rendered":"http:\/\/www.umitcanli.com\/school\/index.php\/2007\/12\/19\/klein-sisesi-1xmobius-seridi\/"},"modified":"2025-05-31T14:13:11","modified_gmt":"2025-05-31T12:13:11","slug":"klein-sisesi-1xmobius-seridi","status":"publish","type":"post","link":"http:\/\/www.umitcanli.com\/school\/index.php\/2007\/12\/19\/klein-sisesi-1xmobius-seridi\/","title":{"rendered":"Klein \u015ei\u015fesi -> 1x M\u00f6bius \u015eeridi"},"content":{"rendered":"<p>Klein \u015fi\u015fesi veya M\u00f6bius \u015feridi ile ilgili bir yaz\u0131 okudu\u011funuzda \u015fu bilgiye s\u0131k\u00e7a rastlan\u0131r : &#8220;Bir Klein \u015fi\u015fesi, kesildi\u011finde iki adet M\u00f6bius \u015feridine d\u00f6n\u00fc\u015f\u00fcr&#8221;. Buna ek olarak, Klein \u015ei\u015fesi yine kesilerek tek bir M\u00f6bius \u015feridine de d\u00f6n\u00fc\u015ft\u00fcr\u00fclebilir. Gayet do\u011fald\u0131r ki, bu iki geometrik nesneyi bilen biri i\u00e7in bile, bu d\u00f6n\u00fc\u015f\u00fcmlerin nas\u0131l ger\u00e7ekle\u015fti\u011fini g\u00f6z \u00f6n\u00fcne getirebilmek olduk\u00e7a g\u00fc\u00e7. A\u015fa\u011f\u0131daki video, bahsi ge\u00e7en d\u00f6n\u00fc\u015f\u00fcmlerden ikincisini, yani Klein \u015fi\u015fesinin tek bir M\u00f6bius \u015feridine d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fc g\u00f6steren g\u00fczel bir \u00e7al\u0131\u015fma. Videoda sunulan, bir dikd\u00f6rtgenin silindire, silindirin Klein \u015fi\u015fesine, ard\u0131ndan da boylamas\u0131na kesilerek Klein \u015fi\u015fesinin M\u00f6bius \u015feridine d\u00f6n\u00fc\u015f\u00fcm\u00fc. Bu iki geometrik nesne hakk\u0131nda fikir sahibi olmayanlar i\u00e7in <a href=\"http:\/\/mathworld.wolfram.com\/KleinBottle.html\" target=\"_blank\" rel=\"noopener noreferrer\">buradan<\/a> ve <a href=\"http:\/\/mathworld.wolfram.com\/MoebiusStrip.html\" target=\"_blank\" rel=\"noopener noreferrer\">\u015furadan<\/a> bilgi al\u0131nabilir. M\u00f6bius \u015feridi ile ilgili detayl\u0131 bir yaz\u0131, vakit bulabildi\u011fim en yak\u0131n zamanda burada olacak.<\/p>\n<p><iframe loading=\"lazy\" width=\"450\" height=\"255\" src=\"https:\/\/www.youtube.com\/embed\/E8rifKlq5hc\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"\"><\/iframe><\/p>\n<span id=\"post-ratings-65\" class=\"post-ratings\" data-nonce=\"3b913989ec\"><img decoding=\"async\" id=\"rating_65_1\" src=\"http:\/\/www.umitcanli.com\/school\/wp-content\/plugins\/wp-postratings\/images\/stars\/rating_on.gif\" alt=\"1 Y\u0131ld\u0131z\" title=\"1 Y\u0131ld\u0131z\" onmouseover=\"current_rating(65, 1, '1 Y\u0131ld\u0131z');\" onmouseout=\"ratings_off(4.9, 5, 0);\" onclick=\"rate_post();\" onkeypress=\"rate_post();\" style=\"cursor: pointer; border: 0px;\" \/><img decoding=\"async\" id=\"rating_65_2\" src=\"http:\/\/www.umitcanli.com\/school\/wp-content\/plugins\/wp-postratings\/images\/stars\/rating_on.gif\" alt=\"2 Y\u0131ld\u0131z\" title=\"2 Y\u0131ld\u0131z\" onmouseover=\"current_rating(65, 2, '2 Y\u0131ld\u0131z');\" onmouseout=\"ratings_off(4.9, 5, 0);\" onclick=\"rate_post();\" onkeypress=\"rate_post();\" style=\"cursor: pointer; border: 0px;\" \/><img decoding=\"async\" id=\"rating_65_3\" src=\"http:\/\/www.umitcanli.com\/school\/wp-content\/plugins\/wp-postratings\/images\/stars\/rating_on.gif\" alt=\"3 Y\u0131ld\u0131z\" title=\"3 Y\u0131ld\u0131z\" onmouseover=\"current_rating(65, 3, '3 Y\u0131ld\u0131z');\" onmouseout=\"ratings_off(4.9, 5, 0);\" onclick=\"rate_post();\" onkeypress=\"rate_post();\" style=\"cursor: pointer; border: 0px;\" \/><img decoding=\"async\" id=\"rating_65_4\" src=\"http:\/\/www.umitcanli.com\/school\/wp-content\/plugins\/wp-postratings\/images\/stars\/rating_on.gif\" alt=\"4 Y\u0131ld\u0131z\" title=\"4 Y\u0131ld\u0131z\" onmouseover=\"current_rating(65, 4, '4 Y\u0131ld\u0131z');\" onmouseout=\"ratings_off(4.9, 5, 0);\" onclick=\"rate_post();\" onkeypress=\"rate_post();\" style=\"cursor: pointer; border: 0px;\" \/><img decoding=\"async\" id=\"rating_65_5\" src=\"http:\/\/www.umitcanli.com\/school\/wp-content\/plugins\/wp-postratings\/images\/stars\/rating_half.gif\" alt=\"5 Y\u0131ld\u0131z\" title=\"5 Y\u0131ld\u0131z\" onmouseover=\"current_rating(65, 5, '5 Y\u0131ld\u0131z');\" onmouseout=\"ratings_off(4.9, 5, 0);\" onclick=\"rate_post();\" onkeypress=\"rate_post();\" style=\"cursor: pointer; border: 0px;\" \/> (<strong>8<\/strong> ki\u015finin oyu ile <strong>5<\/strong> \u00fczerinden ortalama <strong>4,88<\/strong> verilmi\u015f)<\/span><span id=\"post-ratings-65-loading\" class=\"post-ratings-loading\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/www.umitcanli.com\/school\/wp-content\/plugins\/wp-postratings\/images\/loading.gif\" width=\"16\" height=\"16\" class=\"post-ratings-image\" \/>Loading...<\/span>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_65\" class=\"pvc_stats all  \" data-element-id=\"65\" style=\"\"><i class=\"pvc-stats-icon medium\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"http:\/\/www.umitcanli.com\/school\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p>\n<div class=\"pvc_clear\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Klein \u015fi\u015fesi veya M\u00f6bius \u015feridi ile ilgili bir yaz\u0131 okudu\u011funuzda \u015fu bilgiye s\u0131k\u00e7a rastlan\u0131r : &#8220;Bir Klein \u015fi\u015fesi, kesildi\u011finde iki adet M\u00f6bius \u015feridine d\u00f6n\u00fc\u015f\u00fcr&#8221;. Buna ek olarak, Klein \u015ei\u015fesi yine kesilerek tek bir M\u00f6bius \u015feridine de d\u00f6n\u00fc\u015ft\u00fcr\u00fclebilir. Gayet do\u011fald\u0131r ki, &hellip; <a href=\"http:\/\/www.umitcanli.com\/school\/index.php\/2007\/12\/19\/klein-sisesi-1xmobius-seridi\/\">Okumaya devam et <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_65\" class=\"pvc_stats all  \" data-element-id=\"65\" style=\"\"><i class=\"pvc-stats-icon medium\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"http:\/\/www.umitcanli.com\/school\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p>\n<div class=\"pvc_clear\"><\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[8,10,3],"tags":[424,18,416,17,26],"class_list":["post-65","post","type-post","status-publish","format-standard","hentry","category-egitim","category-gorsel-tasarim","category-matematik","tag-geometri","tag-klein-sisesi","tag-matematik","tag-mobius-seridi","tag-topoloji"],"a3_pvc":{"activated":true,"total_views":6131,"today_views":0},"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/pc2dpV-13","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"http:\/\/www.umitcanli.com\/school\/index.php\/wp-json\/wp\/v2\/posts\/65","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.umitcanli.com\/school\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.umitcanli.com\/school\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.umitcanli.com\/school\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.umitcanli.com\/school\/index.php\/wp-json\/wp\/v2\/comments?post=65"}],"version-history":[{"count":5,"href":"http:\/\/www.umitcanli.com\/school\/index.php\/wp-json\/wp\/v2\/posts\/65\/revisions"}],"predecessor-version":[{"id":1454,"href":"http:\/\/www.umitcanli.com\/school\/index.php\/wp-json\/wp\/v2\/posts\/65\/revisions\/1454"}],"wp:attachment":[{"href":"http:\/\/www.umitcanli.com\/school\/index.php\/wp-json\/wp\/v2\/media?parent=65"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.umitcanli.com\/school\/index.php\/wp-json\/wp\/v2\/categories?post=65"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.umitcanli.com\/school\/index.php\/wp-json\/wp\/v2\/tags?post=65"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}