{"id":1906,"date":"2020-09-27T06:38:53","date_gmt":"2020-09-27T04:38:53","guid":{"rendered":"http:\/\/mathe-lernen.net\/?p=1906"},"modified":"2021-11-20T10:18:43","modified_gmt":"2021-11-20T09:18:43","slug":"satz-des-pythagoras","status":"publish","type":"post","link":"https:\/\/mathe-lernen.net\/?p=1906","title":{"rendered":"Satz des Pythagoras"},"content":{"rendered":"\n<p class=\"has-light-gray-background-color has-background\">In einem rechtwinkligen Dreieck ist die <strong><span style=\"color:#ff0004\" class=\"has-inline-color\">Seite gegen\u00fcber dem rechten Winkel<\/span><\/strong> die l\u00e4ngste Seite des Dreiecks.<br>Sie wird<span style=\"color:#ff0004\" class=\"has-inline-color\"> <strong>Hypotenuse<\/strong><\/span> genannt. <br>Die beiden k\u00fcrzeren Seiten nennt man <strong><span class=\"has-inline-color has-primary-color\">Katheten<\/span><\/strong>, sie sind die <strong><span class=\"has-inline-color has-primary-color\">Schenkel des rechten Winkels<\/span><\/strong>.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_1.jpg\" alt=\"\" class=\"wp-image-1907\" width=\"526\" height=\"277\" srcset=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_1.jpg 1012w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_1-300x158.jpg 300w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_1-768x405.jpg 768w\" sizes=\"auto, (max-width: 526px) 100vw, 526px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-light-gray-background-color has-background\">Auch in den anderen Lagen bleibt diese Relation erhalten! Der rechte Winkel bestimmt die Funktion der Seiten!<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_3-1024x416.jpg\" alt=\"\" class=\"wp-image-1909\" width=\"811\" height=\"329\" srcset=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_3-1024x416.jpg 1024w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_3-300x122.jpg 300w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_3-768x312.jpg 768w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_3-1536x624.jpg 1536w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_3.jpg 1676w\" sizes=\"auto, (max-width: 811px) 100vw, 811px\" \/><\/figure><\/div>\n\n\n\n<p>Der griechische Mathematiker und Philosoph <a rel=\"noreferrer noopener\" href=\"https:\/\/de.wikipedia.org\/wiki\/Pythagoras\" target=\"_blank\">Pythagoras von Samos<\/a> entdeckte einen fundamentalen Zusammenhang zwischen Hypothenuse und den Katheten. Bis heute ist dies eine der wichtigsten Erkenntnisse der Mathematik!<\/p>\n\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Pythagorean theorem water demo\" width=\"860\" height=\"645\" src=\"https:\/\/www.youtube.com\/embed\/CAkMUdeB06o?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p class=\"has-text-align-center has-background\" style=\"background-color:#b8eaff\"><strong>Wir im obigen Video zu sehen ist, f\u00fcllen die beiden Quadrate der Katheten (a , b ) <br>zusammen das Quadrat der Hypotenuse (c) .<\/strong><\/p>\n\n\n\n<p>Man schreibt:<\/p>\n\n\n\n<p class=\"has-text-align-center has-white-color has-primary-background-color has-text-color has-background has-medium-font-size\"><strong>a\u00b2 + b \u00b2= c\u00b2 <\/strong><\/p>\n\n\n\n<p>Der ber\u00fchmte Satz des <a href=\"https:\/\/de.wikipedia.org\/wiki\/Pythagoras\" target=\"_blank\" rel=\"noreferrer noopener\">Pythagoras<\/a>!<\/p>\n\n\n\n<p class=\"has-text-align-center has-white-color has-primary-background-color has-text-color has-background\"><strong>Die Summe der Quadrate der Katheten ist gleich dem Quadrat der Hypotenuse!<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_2-842x1024.jpg\" alt=\"\" class=\"wp-image-1908\" width=\"622\" height=\"756\" srcset=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_2-842x1024.jpg 842w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_2-247x300.jpg 247w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_2-768x934.jpg 768w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_2.jpg 1050w\" sizes=\"auto, (max-width: 622px) 100vw, 622px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center has-background\" style=\"background-color:#ffb3b4\"><strong>Dieser Zusammenhang erm\u00f6glicht uns bei 2 bekannten Seiten <\/strong><br><strong>eines rechtwinkligen Dreiecks die Berechnung der 3. Seite!<\/strong><\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#eeffda\"><a href=\"https:\/\/youtu.be\/pVo6szYE13Y\" target=\"_blank\" rel=\"noreferrer noopener\">Beweis des Satzes des Pythagoras!<\/a><\/p>\n\n\n\n<p class=\"has-light-gray-background-color has-background\">Beispiel: <strong><span style=\"color:#ff0004\" class=\"has-inline-color\">Berechnung einer Hypotenuse!<\/span><\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_4a-1024x681.jpg\" alt=\"\" class=\"wp-image-1915\" width=\"641\" height=\"426\" srcset=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_4a-1024x681.jpg 1024w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_4a-300x200.jpg 300w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_4a-768x511.jpg 768w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_4a-90x60.jpg 90w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_4a.jpg 1210w\" sizes=\"auto, (max-width: 641px) 100vw, 641px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-light-gray-background-color has-background\">Beispiel: <strong><span class=\"has-inline-color has-primary-color\">Berechnung einer Kathete!<\/span><\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_5-1024x567.jpg\" alt=\"\" class=\"wp-image-1914\" width=\"653\" height=\"361\" srcset=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_5-1024x567.jpg 1024w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_5-300x166.jpg 300w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_5-768x425.jpg 768w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_5-1536x851.jpg 1536w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth_5.jpg 1683w\" sizes=\"auto, (max-width: 653px) 100vw, 653px\" \/><\/figure>\n\n\n\n<p><\/p>\n<div class=\"pvc_clear\"><\/div><p id=\"pvc_stats_1906\" class=\"pvc_stats all  \" data-element-id=\"1906\" style=\"\"><i class=\"pvc-stats-icon small\" 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=\"https:\/\/mathe-lernen.net\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p><div class=\"pvc_clear\"><\/div> ","protected":false},"excerpt":{"rendered":"<p>In einem rechtwinkligen Dreieck ist die Seite gegen\u00fcber dem rechten Winkel die l\u00e4ngste Seite des Dreiecks.Sie wird Hypotenuse genannt. Die beiden k\u00fcrzeren Seiten nennt man Katheten, sie sind die Schenkel des rechten Winkels. Auch in den anderen Lagen bleibt diese Relation erhalten! Der rechte Winkel bestimmt die Funktion der Seiten! Der griechische Mathematiker und Philosoph Pythagoras von Samos entdeckte einen<\/p>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_1906\" class=\"pvc_stats all  \" data-element-id=\"1906\" style=\"\"><i class=\"pvc-stats-icon small\" 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=\"https:\/\/mathe-lernen.net\/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":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[987,52,57,67],"tags":[124,157,158,159,160,161,162],"class_list":["post-1906","post","type-post","status-publish","format-standard","hentry","category-pythagoras","category-rechtwinklige-dreiecke","category-trigonometrie-dreiecke-und-vierecke","category-grundwissen","tag-dreieck","tag-hypotenuse","tag-kathete","tag-pythagoras","tag-satz","tag-rechter-winkel","tag-rechtwinklig"],"_links":{"self":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/1906","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1906"}],"version-history":[{"count":0,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/1906\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1906"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1906"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1906"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}