{"id":133698,"date":"2024-07-05T16:51:29","date_gmt":"2024-07-05T13:51:29","guid":{"rendered":"https:\/\/mathema.me\/?p=133698"},"modified":"2024-09-25T18:47:25","modified_gmt":"2024-09-25T15:47:25","slug":"wielosciany-i-bryly-obrotowe","status":"publish","type":"post","link":"https:\/\/mathema.me\/pl\/blog\/wielosciany-i-bryly-obrotowe\/","title":{"rendered":"Wielo\u015bciany i bry\u0142y obrotowe: graniastos\u0142up, ostros\u0142up, walec, sto\u017cek, kula"},"content":{"rendered":"\n<p>W tym artykule Mathema przedstawi wielo\u015bciany i bry\u0142y obrotowe, ich w\u0142a\u015bciwo\u015bci oraz g\u0142\u00f3wne r\u00f3\u017cnice mi\u0119dzy nimi.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Graniastos\u0142up <\/h2>\n\n\n\n<p>Rodzaj graniastos\u0142upa mo\u017cna okre\u015bli\u0107 na podstawie liczby kraw\u0119dzi podstawy. Dwie \u015bciany graniastos\u0142upa to r\u00f3wne wielok\u0105ty znajduj\u0105ce si\u0119 na r\u00f3wnoleg\u0142ych p\u0142aszczyznach. Nazywamy je podstawami graniastos\u0142upa. Pozosta\u0142e \u015bciany to r\u00f3wnoleg\u0142oboki. Ich liczba mo\u017ce by\u0107 r\u00f3\u017cna, w zale\u017cno\u015bci od rodzaju graniastos\u0142upa. Te \u015bciany nazywane s\u0105 \u015bcianami bocznymi.<\/p>\n\n\n\n<p>Je\u015bli kraw\u0119dzie graniastos\u0142upa s\u0105 prostopad\u0142e do podstawy, taki graniastos\u0142up nazywamy prostym. Je\u015bli podstawy tego graniastos\u0142upa s\u0105 foremne, nazywa si\u0119 go graniastos\u0142upem foremnym.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1920\" height=\"1080\" src=\"https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/pryzma.png?resize=1920%2C1080&#038;ssl=1\" alt=\"\" class=\"wp-image-122097\" srcset=\"https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/pryzma.png?w=1920&amp;ssl=1 1920w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/pryzma.png?resize=600%2C338&amp;ssl=1 600w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/pryzma.png?resize=300%2C169&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/pryzma.png?resize=1024%2C576&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/pryzma.png?resize=768%2C432&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/pryzma.png?resize=50%2C28&amp;ssl=1 50w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/pryzma.png?resize=1600%2C900&amp;ssl=1 1600w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/pryzma.png?resize=1536%2C864&amp;ssl=1 1536w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Graniastos\u0142up tr\u00f3jk\u0105tny <\/li>\n\n\n\n<li>Graniastos\u0142up czworok\u0105tny <\/li>\n\n\n\n<li>Graniastos\u0142up pi\u0119ciok\u0105tny <\/li>\n\n\n\n<li>Graniastos\u0142up foremny<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Ostros\u0142up <\/h2>\n\n\n\n<p>Ostros\u0142up mo\u017cna rozpozna\u0107 po jego \u015bcianach:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Jedna \u015bciana ostros\u0142upa to n-k\u0105t. <strong>Nazywa si\u0119 j\u0105 podstaw\u0105 ostros\u0142upa. <\/strong><\/li>\n\n\n\n<li>Pozosta\u0142e \u015bciany to tr\u00f3jk\u0105ty. <strong>Nazywa si\u0119 je \u015bcianami bocznymi ostros\u0142upa. <\/strong><\/li>\n<\/ul>\n\n\n\n<p>\u015aciany boczne maj\u0105 wsp\u00f3lny wierzcho\u0142ek, zwany wierzcho\u0142kiem ostros\u0142upa. Aby wyznaczy\u0107 wysoko\u015b\u0107 ostros\u0142upa, nale\u017cy poprowadzi\u0107 od wierzcho\u0142ka ostros\u0142upa prostopad\u0142\u0105 do jego podstawy.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1920\" height=\"1080\" src=\"https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/znimok-ekrana-2023-11-23-o-17.29.53-2.png?resize=1920%2C1080&#038;ssl=1\" alt=\"\" class=\"wp-image-128307\" srcset=\"https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/znimok-ekrana-2023-11-23-o-17.29.53-2.png?w=1920&amp;ssl=1 1920w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/znimok-ekrana-2023-11-23-o-17.29.53-2.png?resize=600%2C338&amp;ssl=1 600w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/znimok-ekrana-2023-11-23-o-17.29.53-2.png?resize=300%2C169&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/znimok-ekrana-2023-11-23-o-17.29.53-2.png?resize=1024%2C576&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/znimok-ekrana-2023-11-23-o-17.29.53-2.png?resize=768%2C432&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/znimok-ekrana-2023-11-23-o-17.29.53-2.png?resize=50%2C28&amp;ssl=1 50w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/znimok-ekrana-2023-11-23-o-17.29.53-2.png?resize=1600%2C900&amp;ssl=1 1600w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/znimok-ekrana-2023-11-23-o-17.29.53-2.png?resize=1536%2C864&amp;ssl=1 1536w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Walec <\/h2>\n\n\n\n<p>Walec to bry\u0142a geometryczna powsta\u0142a w wyniku obrotu prostok\u0105ta wok\u00f3\u0142 osi zawieraj\u0105cej jeden z jego bok\u00f3w. Przekr\u00f3j osiowy walca to przekr\u00f3j walca p\u0142aszczyzn\u0105, kt\u00f3ra przechodzi przez o\u015b walca. Ten przekr\u00f3j jest prostok\u0105tem.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1920\" height=\"1080\" src=\"https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/tsylindr-1.png?resize=1920%2C1080&#038;ssl=1\" alt=\"\" class=\"wp-image-128292\" srcset=\"https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/tsylindr-1.png?w=1920&amp;ssl=1 1920w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/tsylindr-1.png?resize=600%2C338&amp;ssl=1 600w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/tsylindr-1.png?resize=300%2C169&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/tsylindr-1.png?resize=1024%2C576&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/tsylindr-1.png?resize=768%2C432&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/tsylindr-1.png?resize=50%2C28&amp;ssl=1 50w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/tsylindr-1.png?resize=1600%2C900&amp;ssl=1 1600w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/tsylindr-1.png?resize=1536%2C864&amp;ssl=1 1536w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>O O1 \u2014 o\u015b walca <\/li>\n\n\n\n<li>A A1 \u2014 tworz\u0105ca walca <\/li>\n\n\n\n<li>O A \u2014 promie\u0144 walca<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Sto\u017cek <\/h2>\n\n\n\n<p>Sto\u017cek to bry\u0142a geometryczna powsta\u0142a w wyniku obrotu tr\u00f3jk\u0105ta prostok\u0105tnego wok\u00f3\u0142 osi zawieraj\u0105cej jedn\u0105 z jego przyprostok\u0105tnych. Sto\u017cek ma o\u015b, tworz\u0105c\u0105 i promie\u0144. Podstaw\u0105 sto\u017cka jest ko\u0142o.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1920\" height=\"1080\" src=\"https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/konus-1.png?resize=1920%2C1080&#038;ssl=1\" alt=\"\" class=\"wp-image-128322\" srcset=\"https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/konus-1.png?w=1920&amp;ssl=1 1920w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/konus-1.png?resize=600%2C338&amp;ssl=1 600w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/konus-1.png?resize=300%2C169&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/konus-1.png?resize=1024%2C576&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/konus-1.png?resize=768%2C432&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/konus-1.png?resize=50%2C28&amp;ssl=1 50w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/konus-1.png?resize=1600%2C900&amp;ssl=1 1600w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/konus-1.png?resize=1536%2C864&amp;ssl=1 1536w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>P \u2013 wierzcho\u0142ek sto\u017cka <\/li>\n\n\n\n<li>PO \u2013 o\u015b sto\u017cka <\/li>\n\n\n\n<li>PA \u2013 tworz\u0105ca sto\u017cka <\/li>\n\n\n\n<li>OA \u2013 promie\u0144 sto\u017cka<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Kula <\/h2>\n\n\n\n<p>Kula to bry\u0142a powsta\u0142a w wyniku obrotu ko\u0142a wok\u00f3\u0142 jego \u015brednicy. Promie\u0144 kuli to odcinek poprowadzony od \u015brodka kuli do dowolnego punktu na powierzchni kuli. Powierzchnia kuli nazywana jest sfer\u0105.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1920\" height=\"1080\" src=\"https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/kulia.png?resize=1920%2C1080&#038;ssl=1\" alt=\"\" class=\"wp-image-122112\" srcset=\"https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/kulia.png?w=1920&amp;ssl=1 1920w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/kulia.png?resize=600%2C338&amp;ssl=1 600w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/kulia.png?resize=300%2C169&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/kulia.png?resize=1024%2C576&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/kulia.png?resize=768%2C432&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/kulia.png?resize=50%2C28&amp;ssl=1 50w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/kulia.png?resize=1600%2C900&amp;ssl=1 1600w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/kulia.png?resize=1536%2C864&amp;ssl=1 1536w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<p>Potrzebujesz pomocy ze skomplikowanymi tematami szkolnymi z matematyki? <a href=\"https:\/\/mathema.me\/pl\/tutors\/\" data-type=\"link\" data-id=\"https:\/\/mathema.me\/pl\/tutors\/\">Korepetytorzy online Mathema<\/a> s\u0105 gotowi pom\u00f3c. Przejd\u017a do linku i zarezerwuj lekcj\u0119 diagnostyczn\u0105.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>W tym artykule Mathema przedstawi wielo\u015bciany i bry\u0142y obrotowe, ich w\u0142a\u015bciwo\u015bci oraz g\u0142\u00f3wne r\u00f3\u017cnice mi\u0119dzy nimi. Graniastos\u0142up Rodzaj graniastos\u0142upa mo\u017cna [&hellip;]<\/p>\n","protected":false},"author":15,"featured_media":61308,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_glsr_average":0,"_glsr_ranking":0,"_glsr_reviews":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[37,3383],"tags":[],"class_list":["post-133698","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-blog","category-liceum-pl"],"acf":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2024\/02\/post-cover-82.jpg?fit=1080%2C675&ssl=1","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/posts\/133698","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/users\/15"}],"replies":[{"embeddable":true,"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/comments?post=133698"}],"version-history":[{"count":1,"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/posts\/133698\/revisions"}],"predecessor-version":[{"id":178157,"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/posts\/133698\/revisions\/178157"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/media\/61308"}],"wp:attachment":[{"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/media?parent=133698"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/categories?post=133698"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/tags?post=133698"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}