{"id":221,"date":"2009-07-21T14:35:43","date_gmt":"2009-07-21T12:35:43","guid":{"rendered":"http:\/\/formula.co.ua\/blog\/?p=221"},"modified":"2009-07-21T14:35:43","modified_gmt":"2009-07-21T12:35:43","slug":"alhorytm-evklida","status":"publish","type":"post","link":"https:\/\/formula.co.ua\/blog\/alhorytm-evklida\/","title":{"rendered":"\u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0415\u0432\u043a\u043b\u0456\u0434\u0430"},"content":{"rendered":"<p align=\"right\"><em>(\u041b. \u0412. \u041b\u043e\u0431\u0430\u043d\u043e\u0432\u0430, 1989)<\/em><\/p>\n<p>\u0429\u043e\u0431 \u0437\u043d\u0430\u0439\u0442\u0438 \u043d\u0430\u0439\u0431\u0456\u043b\u044c\u0448\u0438\u0439 \u0441\u043f\u0456\u043b\u044c\u043d\u0438\u0439 \u0434\u0456\u043b\u044c\u043d\u0438\u043a \u0434\u0432\u043e\u0445 \u0447\u0438\u0441\u0435\u043b, \u0454 \u0434\u0443\u0436\u0435 \u043f\u0440\u043e\u0441\u0442\u0438\u0439 \u0441\u043f\u043e\u0441\u0456\u0431, \u0432\u0456\u0434\u043e\u043c\u0438\u0439 \u043f\u0456\u0434 \u043d\u0430\u0437\u0432\u043e\u044e <strong>\u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0443 \u0415\u0432\u043a\u043b\u0456\u0434\u0430, <\/strong>\u0430\u0431\u043e <strong>\u0441\u043f\u043e\u0441\u043e\u0431\u0443 \u043f\u043e\u0441\u043b\u0456\u0434\u043e\u0432\u043d\u043e\u0433\u043e \u0434\u0456\u043b\u0435\u043d\u043d\u044f<\/strong>.<\/p>\n<p><!--more--><\/p>\n<p>\u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0415\u0432\u043a\u043b\u0456\u0434\u0430, \u0430\u0431\u043e \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u043f\u043e\u0441\u043b\u0456\u0434\u043e\u0432\u043d\u043e\u0433\u043e \u0434\u0456\u043b\u0435\u043d\u043d\u044f, \u043f\u043e\u043b\u044f\u0433\u0430\u0454 \u043e\u0441\u044c \u0443 \u0447\u043e\u043c\u0443. \u041d\u0435\u0445\u0430\u0439 \u0434\u0430\u043d\u043e \u043d\u0430\u0442\u0443\u0440\u0430\u043b\u044c\u043d\u0456 \u0447\u0438\u0441\u043b\u0430 <em>a<\/em> \u0456 <em>b<\/em>, <em>a<\/em> &gt; <em>b<\/em>.<\/p>\n<p>\u041f\u043e\u0434\u0456\u043b\u0438\u043c\u043e \u043f\u0435\u0440\u0448\u0435 \u0447\u0438\u0441\u043b\u043e \u043d\u0430 \u0434\u0440\u0443\u0433\u0435, \u0434\u0456\u0441\u0442\u0430\u043d\u0435\u043c\u043e \u043e\u0441\u0442\u0430\u0447\u0443 <em>r<\/em><em><sub>1<\/sub><\/em><em> <\/em>(<em>r<\/em><em><sub>1<\/sub><\/em> &lt; <em>b<\/em><em>). <\/em>\u0422\u0435\u043f\u0435\u0440 <em>b<\/em><em> <\/em>\u043f\u043e\u0434\u0456\u043b\u0438\u043c\u043e \u043d\u0430 <em>r<\/em><em><sub>1<\/sub><\/em>,<em> <\/em>\u0434\u0456\u0441\u0442\u0430\u043d\u0435\u043c\u043e \u043e\u0441\u0442\u0430\u0447\u0443 <em>r<\/em><em><sub>2<\/sub><\/em> (<em>r<\/em><em><sub>2<\/sub><\/em> &lt; <em>r<\/em><em><sub>1<\/sub><\/em>), \u0434\u0430\u043b\u0456 \u043f\u043e\u0434\u0456\u043b\u0438\u043c\u043e <em>r<\/em><em><sub>1<\/sub><\/em><strong> <\/strong>\u043d\u0430 <em>r<\/em><em><sub>2<\/sub><\/em> \u0456 \u0442. \u0434.<\/p>\n<p>\u041e\u0441\u043a\u0456\u043b\u044c\u043a\u0438 \u043f\u0456\u0441\u043b\u044f \u043a\u043e\u0436\u043d\u043e\u0433\u043e \u043d\u0430\u0441\u0442\u0443\u043f\u043d\u043e\u0433\u043e \u043a\u0440\u043e\u043a\u0443 \u0443\u0442\u0432\u043e\u0440\u044e\u0454\u0442\u044c\u0441\u044f \u043e\u0441\u0442\u0430\u0447\u0430, \u043c\u0435\u043d\u0448\u0430 \u0432\u0456\u0434 \u043f\u043e\u043f\u0435\u0440\u0435\u0434\u043d\u044c\u043e\u0457, \u0442\u043e \u0447\u0435\u0440\u0435\u0437 \u0441\u043a\u0456\u043d\u0447\u0435\u043d\u043d\u0443 \u043a\u0456\u043b\u044c\u043a\u0456\u0441\u0442\u044c \u043a\u0440\u043e\u043a\u0456\u0432 \u0434\u0456\u0441\u0442\u0430\u043d\u0435\u043c\u043e \u043e\u0441\u0442\u0430\u0447\u0443, \u044f\u043a\u0430 \u0434\u043e\u0440\u0456\u0432\u043d\u044e\u0454 \u043d\u0443\u043b\u044e: \u0434\u0456\u043b\u0435\u043d\u043d\u044f \u0432\u0456\u0434\u0431\u0443\u0434\u0435\u0442\u044c\u0441\u044f \u043d\u0430\u0446\u0456\u043b\u043e \u0456 \u043f\u0440\u043e\u0446\u0435\u0441 \u043f\u0440\u0438\u043f\u0438\u043d\u0438\u0442\u044c\u0441\u044f.<\/p>\n<p>\u041e\u0441\u0442\u0430\u043d\u043d\u044f \u0432\u0456\u0434\u043c\u0456\u043d\u043d\u0430 \u0432\u0456\u0434 \u043d\u0443\u043b\u044f \u043e\u0441\u0442\u0430\u0447\u0430 <em>r<sub>k<\/sub><\/em>,<em> <\/em>\u043d\u0430 \u044f\u043a\u0443 \u043d\u0430\u0446\u0456\u043b\u043e \u0434\u0456\u043b\u0438\u0442\u044c\u0441\u044f \u043e\u0441\u0442\u0430\u0447\u0430 <em>r<sub>k<\/sub><\/em><em><sub>-1<\/sub><\/em>, \u0431\u0443\u0434\u0435 \u043d\u0430\u0439\u0431\u0456\u043b\u044c\u0448\u0438\u043c \u0441\u043f\u0456\u043b\u044c\u043d\u0438\u043c \u0434\u0456\u043b\u044c\u043d\u0438\u043a\u043e\u043c \u0447\u0438\u0441\u0435\u043b <em>a<\/em><em> <\/em>\u0456 <em>b<\/em><em>.<\/em><em><\/em><\/p>\n<p>\u0421\u043f\u0440\u0430\u0432\u0434\u0456, \u0437\u0430\u043f\u0438\u0448\u0435\u043c\u043e \u0441\u043a\u0430\u0437\u0430\u043d\u0435 \u044f\u043a \u043b\u0430\u043d\u0446\u044e\u0436\u043e\u043a \u0440\u0456\u0432\u043d\u043e\u0441\u0442\u0435\u0439:<\/p>\n<p style=\"font-size:16px\" align=\"center\"><em>a<\/em> = <em>bq<\/em> +<em> r<sub>1<\/sub><\/em>,<\/p>\n<p style=\"font-size:16px\" align=\"center\"><em>b<\/em> = <em>r<sub>1<\/sub>q<sub>1<\/sub><\/em> +<em> r<sub>2<\/sub><\/em>,<\/p>\n<p style=\"font-size:16px\" align=\"center\"><em>r<sub>1<\/sub><\/em> = <em>r<sub>2<\/sub>q<sub>2<\/sub><\/em> +<em> r<sub>3<\/sub><\/em>,<\/p>\n<p style=\"font-size:16px\" align=\"center\">...<\/p>\n<p style=\"font-size:16px\" align=\"center\"><em>r<sub>k-2<\/sub><\/em> = <em>r<sub>k-1<\/sub>q<sub>k-1<\/sub><\/em> +<em> r<sub>k<\/sub><\/em>,<\/p>\n<p style=\"font-size:16px\" align=\"center\"><em>r<sub>k-1<\/sub><\/em> = <em>r<sub>k<\/sub>q<sub>k<\/sub><\/em>.<\/p>\n<p>\u0417<strong> <\/strong>\u043e\u0441\u0442\u0430\u043d\u043d\u044c\u043e\u0457 \u0440\u0456\u0432\u043d\u043e\u0441\u0442\u0456 \u0432\u0438\u043f\u043b\u0438\u0432\u0430\u0454, \u0449\u043e <em>r<sub>k<\/sub><\/em> \u0454 \u0434\u0456\u043b\u044c\u043d\u0438\u043a\u043e\u043c <em>r<sub>k-1<\/sub><\/em>,<em> <\/em><em>r<sub>k<\/sub><\/em><em> <\/em>= (<em>r<sub>k<\/sub><\/em>;<em> r<sub>k-1<\/sub><\/em>). \u0427\u0435\u0440\u0435\u0437 (<em>n<\/em>;<em> \u0442<\/em>)<em> <\/em>\u043f\u043e\u0437\u043d\u0430\u0447\u0435\u043d\u043e \u043d\u0430\u0439\u0431\u0456\u043b\u044c\u0448\u0438\u0439 \u0441\u043f\u0456\u043b\u044c\u043d\u0438\u0439 \u0434\u0456\u043b\u044c\u043d\u0438\u043a \u0447\u0438\u0441\u0435\u043b <em>n<\/em><em> <\/em><em> <\/em>\u0456<em> <\/em><em>m<\/em><em>. <\/em>\u0417<em> <\/em>\u043f\u0435\u0440\u0435\u0434\u043e\u0441\u0442\u0430\u043d\u043d\u044c\u043e\u0457 \u0440\u0456\u0432\u043d\u043e\u0441\u0442\u0456 \u0432\u0438\u043f\u043b\u0438\u0432\u0430\u0454, \u0449\u043e <em>r<sub>k<\/sub><\/em> \u0434\u0456\u043b\u0438\u0442\u044c \u0442\u0430\u043a\u043e\u0436 <em>r<sub>k<\/sub><\/em><em><sub>-2<\/sub><\/em> \u0456 <em>r<sub>k<\/sub><\/em> <em> = <\/em>(<em>r<sub>k<\/sub><\/em><em><sub>-1<\/sub><\/em>;<em> <\/em><em>r<sub>k<\/sub><\/em><em><sub>-2<\/sub><\/em>).<\/p>\n<p>\u0422\u0430\u043a, \u043f\u043e\u0441\u043b\u0456\u0434\u043e\u0432\u043d\u043e \u043f\u0456\u0434\u043d\u0456\u043c\u0430\u044e\u0447\u0438\u0441\u044c \u043a\u0440\u043e\u043a\u0430\u043c\u0438 \u0432\u0433\u043e\u0440\u0443, \u0434\u0456\u0441\u0442\u0430\u043d\u0435\u043c\u043e, \u0449\u043e <em>r<sub>k<\/sub><\/em> = (<em>a<\/em>;<em> <\/em><em>b<\/em>).<\/p>\n<p><strong>\u041f\u0440\u0438\u043a\u043b\u0430\u0434. <\/strong>\u0417\u043d\u0430\u0439\u0442\u0438 \u041d\u0421\u0414 \u0447\u0438\u0441\u0435\u043b 9765 \u0456 6944.<\/p>\n<p><strong>\u0420\u043e\u0437\u0432'\u044f\u0437\u0430\u043d\u043d\u044f.<\/strong><strong><\/strong><\/p>\n<p style=\"text-align: center;\">9765 = 6944 \u00b7 1 + 2821,<\/p>\n<p style=\"text-align: center;\">6944 = 2821 \u00b7 2 + 1302,<\/p>\n<p style=\"text-align: center;\">2821 = 1302 \u00b7 2 + 217,<\/p>\n<p style=\"text-align: center;\">1302 = 217 \u00b7 6.<\/p>\n<p><strong>\u0412\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u044c.<\/strong> 217.<\/p>\n<p align=\"right\"><em>\u0414\u0436\u0435\u0440\u0435\u043b\u043e:<\/em> \u0423 \u0441\u0432\u0456\u0442\u0456 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438. \u0412\u0438\u043f\u0443\u0441\u043a 19. \u0417\u0430 \u0440\u0435\u0434\u0430\u043a\u0446\u0456\u0454\u044e \u041c. \u0419. \u042f\u0434\u0440\u0435\u043d\u043a\u0430. \u041a\u0438\u0457\u0432 1989.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>(\u041b. \u0412. \u041b\u043e\u0431\u0430\u043d\u043e\u0432\u0430, 1989) \u0429\u043e\u0431 \u0437\u043d\u0430\u0439\u0442\u0438 \u043d\u0430\u0439\u0431\u0456\u043b\u044c\u0448\u0438\u0439 \u0441\u043f\u0456\u043b\u044c\u043d\u0438\u0439 \u0434\u0456\u043b\u044c\u043d\u0438\u043a \u0434\u0432\u043e\u0445 \u0447\u0438\u0441\u0435\u043b, \u0454 \u0434\u0443\u0436\u0435 \u043f\u0440\u043e\u0441\u0442\u0438\u0439 \u0441\u043f\u043e\u0441\u0456\u0431, \u0432\u0456\u0434\u043e\u043c\u0438\u0439 \u043f\u0456\u0434 \u043d\u0430\u0437\u0432\u043e\u044e \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0443 \u0415\u0432\u043a\u043b\u0456\u0434\u0430, \u0430\u0431\u043e \u0441\u043f\u043e\u0441\u043e\u0431\u0443 \u043f\u043e\u0441\u043b\u0456\u0434\u043e\u0432\u043d\u043e\u0433\u043e \u0434\u0456\u043b\u0435\u043d\u043d\u044f.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[11,4],"tags":[40],"_links":{"self":[{"href":"https:\/\/formula.co.ua\/blog\/wp-json\/wp\/v2\/posts\/221"}],"collection":[{"href":"https:\/\/formula.co.ua\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/formula.co.ua\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/formula.co.ua\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/formula.co.ua\/blog\/wp-json\/wp\/v2\/comments?post=221"}],"version-history":[{"count":0,"href":"https:\/\/formula.co.ua\/blog\/wp-json\/wp\/v2\/posts\/221\/revisions"}],"wp:attachment":[{"href":"https:\/\/formula.co.ua\/blog\/wp-json\/wp\/v2\/media?parent=221"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/formula.co.ua\/blog\/wp-json\/wp\/v2\/categories?post=221"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/formula.co.ua\/blog\/wp-json\/wp\/v2\/tags?post=221"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}