{"id":1224,"date":"2020-06-21T17:39:08","date_gmt":"2020-06-21T17:39:08","guid":{"rendered":"http:\/\/mathe-lernen.net\/?p=1224"},"modified":"2024-07-15T06:10:19","modified_gmt":"2024-07-15T04:10:19","slug":"die-zentrische-streckung","status":"publish","type":"post","link":"https:\/\/mathe-lernen.net\/?p=1224","title":{"rendered":"Die zentrische Streckung"},"content":{"rendered":"\n<p><img loading=\"lazy\" decoding=\"async\" width=\"50\" height=\"50\" class=\"wp-image-7501\" style=\"width: 50px;\" src=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2024\/06\/award2.png\" alt=\"\" srcset=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2024\/06\/award2.png 100w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2024\/06\/award2-80x80.png 80w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2024\/06\/award2-50x50.png 50w\" sizes=\"auto, (max-width: 50px) 100vw, 50px\" \/><\/p>\n\n\n\n<p class=\"has-white-color has-primary-background-color has-text-color has-background\">Figuren lassen sich mit der zentrischen Streckung verkleinern und vergr\u00f6\u00dfern.<\/p>\n\n\n\n<p>Dabei f\u00fchrt von einem <strong>Streckungszentrum (Z)<\/strong> zu jedem Eckpunkt der Figur eine Gerade.  Der Abstand zwischen Zentrum(Z)  und dem jeweiligen Eckpunkt ist die Originalstrecke. Vervielfacht (ver-&#8222;k&#8220;-facht)  man diese, entsteht der Bildpunkt einer Vergr\u00f6\u00dferung.  Bei Teilung dieser Strecke entsteht eine Verkleinerung.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><iframe loading=\"lazy\" scrolling=\"no\" title=\"\" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/ZKVesKga\/width\/931\/height\/692\/border\/888888\/sfsb\/true\/smb\/false\/stb\/false\/stbh\/false\/ai\/false\/asb\/false\/sri\/false\/rc\/false\/ld\/false\/sdz\/false\/ctl\/false\" width=\"931px\" height=\"692px\" style=\"border:0px;\" allowfullscreen=\"\"> <\/iframe>\n\nGeotie, geogebra.org<\/pre>\n\n\n\n<p class=\"has-background\" style=\"background-color:#deffb4\">Die  Winkel  einer Figur bleiben bei der zentrischen  Streckung erhalten.<br>Seitenl\u00e4ngen der Figuren  ver-k-fachen sich. <br>Fl\u00e4chen werden auf das k\u00b2 &#8211; fache getreckt.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><iframe loading=\"lazy\" scrolling=\"no\" title=\"Properties of Dilations\" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/wrY5usTk\/width\/869\/height\/576\/border\/888888\/sfsb\/true\/smb\/true\/stb\/true\/stbh\/true\/ai\/false\/asb\/true\/sri\/true\/rc\/true\/ld\/true\/sdz\/true\/ctl\/false\" width=\"869px\" height=\"576px\" style=\"border:0px;\" allowfullscreen=\"\"> <\/iframe>\n\nAutor:\n<a href=\"https:\/\/www.geogebra.org\/u\/tbrzezinski\">Tim Brzezinski<\/a>, geogebra.org<\/pre>\n\n\n\n<p class=\"has-background\" style=\"background-color:#deffb4\">Bei K\u00f6rpern wird das Volumen auf das k\u00b3-fache Vergr\u00f6\u00dfert oder verkleinert.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><iframe loading=\"lazy\" scrolling=\"no\" title=\"\" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/DbbTKC3U\/width\/1920\/height\/866\/border\/888888\/sfsb\/true\/smb\/false\/stb\/false\/stbh\/false\/ai\/false\/asb\/false\/sri\/false\/rc\/false\/ld\/false\/sdz\/false\/ctl\/false\" width=\"1920px\" height=\"866px\" style=\"border:0px;\" allowfullscreen=\"\"> <\/iframe>\n\nHeining, geogebra.org<\/pre>\n\n\n\n<p class=\"has-white-color has-primary-background-color has-text-color has-background\">Die Funktionsweise eine Storchenschnabels (Pantograph)<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><iframe loading=\"lazy\" scrolling=\"no\" title=\"Storchenschnabel\" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/qXgyc9FD\/width\/1086\/height\/750\/border\/888888\/sfsb\/true\/smb\/false\/stb\/false\/stbh\/false\/ai\/false\/asb\/false\/sri\/false\/rc\/false\/ld\/false\/sdz\/false\/ctl\/false\" width=\"1086px\" height=\"750px\" style=\"border:0px;\" allowfullscreen=\"\"> <\/iframe><\/pre>\n<div class=\"pvc_clear\"><\/div><p id=\"pvc_stats_1224\" class=\"pvc_stats all  \" data-element-id=\"1224\" 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>Figuren lassen sich mit der zentrischen Streckung verkleinern und vergr\u00f6\u00dfern. Dabei f\u00fchrt von einem Streckungszentrum (Z) zu jedem Eckpunkt der Figur eine Gerade. Der Abstand zwischen Zentrum(Z) und dem jeweiligen Eckpunkt ist die Originalstrecke. Vervielfacht (ver-&#8222;k&#8220;-facht) man diese, entsteht der Bildpunkt einer Vergr\u00f6\u00dferung. Bei Teilung dieser Strecke entsteht eine Verkleinerung. Geotie, geogebra.org Die Winkel einer Figur bleiben bei der zentrischen<\/p>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_1224\" class=\"pvc_stats all  \" data-element-id=\"1224\" 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":[49],"tags":[184,186,187,302,303,304,305,1134,1135],"class_list":["post-1224","post","type-post","status-publish","format-standard","hentry","category-aehnlichkeit-klasse-8","tag-massstab","tag-vergroessern","tag-verkleinern","tag-zentrische-streckung","tag-strecken","tag-massstabsgetreu","tag-massstaeblich","tag-pantograf","tag-pantograph"],"a3_pvc":{"activated":true,"total_views":957,"today_views":4},"_links":{"self":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/1224","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=1224"}],"version-history":[{"count":1,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/1224\/revisions"}],"predecessor-version":[{"id":8332,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/1224\/revisions\/8332"}],"wp:attachment":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1224"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1224"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1224"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}