{"id":1655,"date":"2025-12-20T07:59:43","date_gmt":"2025-12-20T06:59:43","guid":{"rendered":"https:\/\/control-advent.com\/?p=1655"},"modified":"2025-12-20T07:59:44","modified_gmt":"2025-12-20T06:59:44","slug":"20-wie-erschafft-man-ein-riesiges-susigkeit-dreieck","status":"publish","type":"post","link":"https:\/\/control-advent.com\/?p=1655&lang=de","title":{"rendered":"20 &#8211; Wie erschafft man ein riesiges S\u00fc\u00dfigkeit-Dreieck?"},"content":{"rendered":"\n<p>Santa testet die\u00a0<strong>S\u00fc\u00dfigkeits-Regeldynamik<\/strong>\u00a0seiner magischen Hei\u00dfkakaomaschine. Um ihr Verhalten zu beobachten, lassen die Wichtel einen langen, verzauberten\u00a0<strong>S\u00fc\u00dfigkeits-Teststreifen<\/strong>\u00a0laufen: Die Maschine schiebt einen Papierstreifen mit konstanter Geschwindigkeit heraus und zeichnet darauf den jeweils erzeugten S\u00fc\u00dfigkeitsgrad auf, sodass die S\u00fc\u00dfigkeitsdynamik als Form auf dem Streifen erscheint, wobei\u00a0<strong>1 cm Breite dem S\u00fc\u00dfigkeitsgrad einer Sekunde entspricht<\/strong>.<\/p>\n\n\n\n<p>F\u00fcr den ersten Test zieht der Wichtel Bushy den braunen Hebel\u00a0<strong>genau 1 Minute lang<\/strong>\u00a0mit voller Kraft. Die Maschine:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>beginnt sofort zu s\u00fc\u00dfen,<\/li>\n\n\n\n<li>f\u00e4hrt langsam hoch,<\/li>\n\n\n\n<li>erreicht ihren H\u00f6hepunkt genau in dem Moment, in dem Bushy den Hebel losl\u00e4sst,<\/li>\n\n\n\n<li>und f\u00e4hrt dann sanft wieder herunter.<\/li>\n<\/ul>\n\n\n\n<p>Auf dem Streifen erscheint dies als ein perfektes&nbsp;<strong>gleichschenkliges Dreieck<\/strong>,&nbsp;<strong>120 Sekunden breit<\/strong>&nbsp;und&nbsp;<strong>120 S\u00fc\u00dfigkeitseinheiten hoch<\/strong>.<\/p>\n\n\n\n<p>Santa strahlt: \u201eHo-ho-ho! Ein Dreieck der S\u00fc\u00dfigkeit! Jetzt machen wir es doppelt so breit in der Zeit und doppelt so hoch in der S\u00fc\u00dfe!\u201c<\/p>\n\n\n\n<p>F\u00fcr den zweiten Test ziehen zwei Wichtel \u2014 Bushy und seine Schwester Shinny \u2014 den Hebel\u00a0<strong>gemeinsam<\/strong>\u00a0und mit voller Kraft\u00a0<strong>2 Minuten lang<\/strong>.<\/p>\n\n\n\n<p>Die Maschine ist daf\u00fcr bekannt, sich auf magische, aber ingenieurfreundliche Weise zu verhalten, und zwar:<\/p>\n\n\n\n<p><strong>Linear<\/strong>: zwei Wichtel \u2192 doppelte S\u00fc\u00dfe.<\/p>\n\n\n\n<p><strong>Zeitinvariant<\/strong>: sp\u00e4ter ausf\u00fchren \u2192 gleiche Form, nur sp\u00e4ter.<\/p>\n\n\n\n<p>Mit diesem Wissen und da Bushy und Shinny einen solchen Test durchf\u00fchren, bekommt Santa das riesige, doppelt so breite und doppelt so hohe Dreieck, das er sich vorstellt?<\/p>\n\n\n\n<p>a. \ud83c\udf6b\ud83d\udccf Nicht ganz \u2026 Er bekommt etwas, das nur&nbsp;<strong>120 Sekunden breit<\/strong>, aber fast&nbsp;<strong>500 S\u00fc\u00dfigkeitseinheiten hoch<\/strong>&nbsp;ist \u2014 die zus\u00e4tzliche S\u00fc\u00dfe stapelt sich vertikal!<br>b. \u2615\u27a1\ufe0f\u2b05\ufe0f Ebenfalls nein \u2026 Es wird fast&nbsp;<strong>500 Sekunden breit<\/strong>, aber nur&nbsp;<strong>100 S\u00fc\u00dfigkeitseinheiten hoch<\/strong>, weil sich die S\u00fc\u00dfe \u00fcber die Zeit verteilt.<br>c. \ud83c\udf84\ud83d\udcd0 Ja! Ein perfektes&nbsp;<strong>gleichschenkliges Dreieck mit 240 Sekunden \u00d7 240 S\u00fc\u00dfigkeitseinheiten<\/strong>&nbsp;\u2014 exakt verdoppelt.<br>d. \u2b50\ud83c\udfd4\ufe0f Nein \u2014 er bekommt ein&nbsp;<strong>Trapez<\/strong>! Die \u00fcberlappenden dreieckigen Antworten erzeugen eine flache Spitze.<br>e. \ud83c\udf46 Das ist mir egal, ich trinke nur unges\u00fc\u00dften Auberginensaft.<\/p>\n\n\n<div class='bootstrap-yop yop-poll-mc'>\n\t\t\t\t\t\t\t<div class=\"basic-yop-poll-container\" style=\"background-color:#b70004; border:0px; border-style:solid; border-color:#b70004; border-radius:0px; padding:10px 10px;\" data-id=\"57\" data-temp=\"basic\" data-skin=\"minimal\" data-cscheme=\"black\" data-cap=\"0\" data-access=\"wordpress\" data-tid=\"\" data-uid=\"99f17a7dedd54bbf8514fc895f5aa8e0\" data-pid=\"1655\" data-resdet=\"percentages\" data-show-results-to=\"\" data-show-results-moment=\"never\" data-show-results-only=\"false\" data-show-message=\"true\" data-show-results-as=\"bar\" data-sort-results-by=\"as-defined\" data-sort-results-rule=\"asc\"data-is-ended=\"0\" data-gdpr=\"no\" data-gdpr-sol=\"consent\" data-css=\".basic-yop-poll-container[data-uid] .basic-vote { text-align: center; }\" data-counter=\"0\" data-load-with=\"1\" data-notification-section=\"top\"><div class=\"row\"><div class=\"col-md-12\"><div class=\"basic-inner\"><div class=\"basic-message hide\" style=\"border-left: 10px solid #008000; padding: 0px 10px;\" data-error=\"#ff0000\" data-success=\"#008000\"><p class=\"basic-message-text\" style=\"color:#000000; font-size:14px; font-weight:normal;\"><\/p><\/div><div class=\"basic-overlay hide\"><div class=\"basic-vote-options\"><\/div><div class=\"basic-preloader\"><div class=\"basic-windows8\"><div class=\"basic-wBall basic-wBall_1\"><div class=\"basic-wInnerBall\"><\/div><\/div><div class=\"basic-wBall basic-wBall_2\"><div class=\"basic-wInnerBall\"><\/div><\/div><div class=\"basic-wBall basic-wBall_3\"><div class=\"basic-wInnerBall\"><\/div><\/div><div class=\"basic-wBall basic-wBall_4\"><div class=\"basic-wInnerBall\"><\/div><\/div><div class=\"basic-wBall basic-wBall_5\"><div class=\"basic-wInnerBall\"><\/div><\/div><\/div><\/div><\/div><form class=\"basic-form\"><input type=\"hidden\" name=\"_token\" value=\"ae68b26c6e\" autocomplete=\"off\"><div class=\"basic-elements\"><div class=\"basic-element basic-question basic-question-text-horizontal\" data-id=\"57\" data-uid=\"ca9109499a28fcf50dccec70f41805f0\" data-type=\"question\" data-question-type=\"text\" data-allow-multiple=\"no\" data-min=\"1\" data-max=\"1\" data-display=\"horizontal\" data-colnum=\"\" data-display-others=\"no\" data-others-color=\"\" data-others=\"\"><div role=\"heading\" aria-level=\"5\" class=\"basic-question-title\" style=\"color:#ffffff; font-size:14px; font-weight:normal; text-align:center;\">Choose an option:<\/div><ul class=\"basic-answers basic-h-answers\"><li class=\"basic-answer col-xs-6 col-sm-6 col-md-2\" style=\"padding:0px 0px;\" data-id=\"596\" data-type=\"text\" data-vn=\"3\" data-color=\"#000000\" data-make-link=\"no\" data-link=\"\"><div class=\"basic-answer-content basic-text-horizontal\"><label for=\"answer[596]\" class=\"basic-answer-label\"><input type=\"radio\" id=\"answer[596]\" name=\"answer[57]\" value=\"596\" autocomplete=\"off\"><span class=\"basic-text\" style=\"color: #ffffff; font-size: 14px; font-weight: normal;\" tabindex=\"0\">a<\/span><\/label><\/div><\/li><li class=\"basic-answer col-xs-6 col-sm-6 col-md-2\" style=\"padding:0px 0px;\" data-id=\"597\" data-type=\"text\" data-vn=\"0\" data-color=\"#000000\" data-make-link=\"no\" data-link=\"\"><div class=\"basic-answer-content basic-text-horizontal\"><label for=\"answer[597]\" class=\"basic-answer-label\"><input type=\"radio\" id=\"answer[597]\" name=\"answer[57]\" value=\"597\" autocomplete=\"off\"><span class=\"basic-text\" style=\"color: #ffffff; font-size: 14px; font-weight: normal;\" tabindex=\"0\">b<\/span><\/label><\/div><\/li><li class=\"basic-answer col-xs-6 col-sm-6 col-md-2\" style=\"padding:0px 0px;\" data-id=\"598\" data-type=\"text\" data-vn=\"9\" data-color=\"#000000\" data-make-link=\"no\" data-link=\"\"><div class=\"basic-answer-content basic-text-horizontal\"><label for=\"answer[598]\" class=\"basic-answer-label\"><input type=\"radio\" id=\"answer[598]\" name=\"answer[57]\" value=\"598\" autocomplete=\"off\"><span class=\"basic-text\" style=\"color: #ffffff; font-size: 14px; font-weight: normal;\" tabindex=\"0\">c<\/span><\/label><\/div><\/li><li class=\"basic-answer col-xs-6 col-sm-6 col-md-2\" style=\"padding:0px 0px;\" data-id=\"602\" data-type=\"text\" data-vn=\"15\" data-color=\"#000000\" data-make-link=\"no\" data-link=\"\"><div class=\"basic-answer-content basic-text-horizontal\"><label for=\"answer[602]\" class=\"basic-answer-label\"><input type=\"radio\" id=\"answer[602]\" name=\"answer[57]\" value=\"602\" autocomplete=\"off\"><span class=\"basic-text\" style=\"color: #ffffff; font-size: 14px; font-weight: normal;\" tabindex=\"0\">d<\/span><\/label><\/div><\/li><li class=\"basic-answer col-xs-6 col-sm-6 col-md-2\" style=\"padding:0px 0px;\" data-id=\"613\" data-type=\"text\" data-vn=\"0\" data-color=\"#000000\" data-make-link=\"no\" data-link=\"\"><div class=\"basic-answer-content basic-text-horizontal\"><label for=\"answer[613]\" class=\"basic-answer-label\"><input type=\"radio\" id=\"answer[613]\" name=\"answer[57]\" value=\"613\" autocomplete=\"off\"><span class=\"basic-text\" style=\"color: #ffffff; font-size: 14px; font-weight: normal;\" tabindex=\"0\">e<\/span><\/label><\/div><\/li><li class=\"basic-answer col-xs-6 col-sm-6 col-md-2\" style=\"padding:0px 0px;\" data-id=\"614\" data-type=\"text\" data-vn=\"0\" data-color=\"#000000\" data-make-link=\"no\" data-link=\"\"><div class=\"basic-answer-content basic-text-horizontal\"><label for=\"answer[614]\" class=\"basic-answer-label\"><input type=\"radio\" id=\"answer[614]\" name=\"answer[57]\" value=\"614\" autocomplete=\"off\"><span class=\"basic-text\" style=\"color: #ffffff; font-size: 14px; font-weight: normal;\" tabindex=\"0\">e<\/span><\/label><\/div><\/li><\/ul><\/div><div class=\"clearfix\"><\/div><\/div><div class=\"basic-vote\"><a href=\"#\" class=\"button basic-vote-button\" role=\"button\" style=\"background:#ffffff; border:1px; border-style: solid; border-color:#000000; border-radius:0px; padding:5px 10px; color:#000000; font-size:14px; font-weight:normal;\">&gt;&gt;&gt;<\/a><\/div><\/form><div class=\"yop-poll-modal\"><div class=\"yop-poll-modal-content\"><div class=\"yop-poll-modal-header\"><span class=\"yop-poll-modal-close\">&times;<\/span><\/div><div class=\"yop-poll-modal-body\"><div class=\"yop-poll-form-group\"><label class=\"yop-poll-user-or-email-label\">Username or Email Address<\/label><input type=\"text\" class=\"yop-poll-user-or-email-input\" autocomplete=\"off\"><\/div><div class=\"yop-poll-form-group\"><label class=\"yop-poll-password-label\">Password<\/label><input type=\"password\" class=\"yop-poll-password-input\" autocomplete=\"off\"><\/div><div class=\"yop-poll-form-group submit\"><button class=\"button button-primary button-large yop-poll-login-button\">Log In<\/button><\/div><div class=\"yop-poll-form-group yop-poll-section-login-options\"><p><a href=\"https:\/\/control-advent.com\/wp-login.php?action=register\" target=\"_blank\">No account? Register here<\/a><\/p><p><a href=\"https:\/\/control-advent.com\/wp-login.php?action=lostpassword\" target=\"_blank\">Forgot password<\/a><\/p><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div>\n\t\t\t\t\t\t<\/div>\n\n\n\n<p><strong>Verwandtes Regelungstechnikthema: lineare, zeitinvariante Systeme<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Santa testet die\u00a0S\u00fc\u00dfigkeits-Regeldynamik\u00a0seiner magischen Hei\u00dfkakaomaschine. Um ihr Verhalten zu beobachten, lassen die Wichtel einen langen, verzauberten\u00a0S\u00fc\u00dfigkeits-Teststreifen\u00a0laufen: Die Maschine schiebt einen Papierstreifen mit konstanter Geschwindigkeit heraus und zeichnet darauf den jeweils erzeugten S\u00fc\u00dfigkeitsgrad auf, sodass die S\u00fc\u00dfigkeitsdynamik als Form auf dem &hellip; <span class=\"more-link\"><a href=\"https:\/\/control-advent.com\/?p=1655&#038;lang=de\" class=\"readmore\">Continue reading<span class=\"screen-reader-text\">20 &#8211; Wie erschafft man ein riesiges S\u00fc\u00dfigkeit-Dreieck?<\/span><\/a><\/span><\/p>\n","protected":false},"author":1,"featured_media":1657,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[17],"tags":[107],"class_list":["post-1655","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-deutsch","tag-107"],"_links":{"self":[{"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/posts\/1655","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/control-advent.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1655"}],"version-history":[{"count":2,"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/posts\/1655\/revisions"}],"predecessor-version":[{"id":1658,"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/posts\/1655\/revisions\/1658"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/media\/1657"}],"wp:attachment":[{"href":"https:\/\/control-advent.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1655"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/control-advent.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1655"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/control-advent.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1655"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}