{"id":1416,"date":"2007-02-19T17:55:36","date_gmt":"2007-02-19T21:55:36","guid":{"rendered":"http:\/\/mjtsai.com\/blog\/2007\/02\/19\/proof-that-2-is-irrational\/"},"modified":"2007-02-19T17:55:36","modified_gmt":"2007-02-19T21:55:36","slug":"proof-that-2-is-irrational","status":"publish","type":"post","link":"https:\/\/mjtsai.com\/blog\/2007\/02\/19\/proof-that-2-is-irrational\/","title":{"rendered":"Proof That &radic;2 Is Irrational"},"content":{"rendered":"<p>\r\n<a href=\"http:\/\/blog.plover.com\/math\/sqrt-2-new.html\">Mark Dominus<\/a>:\r\n<\/p>\r\n<blockquote cite=\"http:\/\/blog.plover.com\/math\/sqrt-2-new.html\">\r\n<p>\r\nIn short, if &radic;2 were rational, we could construct an isosceles right triangle with integer sides. Given one such triangle, it is possible to construct another that is smaller. Repeating the construction, we could construct arbitrarily small integer triangles. But this is impossible since there is a lower limit on how small a triangle can be and still have integer sides. \r\n<\/p>\r\n<\/blockquote>\r\n","protected":false},"excerpt":{"rendered":"<p>Mark Dominus: In short, if &radic;2 were rational, we could construct an isosceles right triangle with integer sides. Given one such triangle, it is possible to construct another that is smaller. Repeating the construction, we could construct arbitrarily small integer triangles. But this is impossible since there is a lower limit on how small a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"apple_news_api_created_at":"","apple_news_api_id":"","apple_news_api_modified_at":"","apple_news_api_revision":"","apple_news_api_share_url":"","apple_news_coverimage":0,"apple_news_coverimage_caption":"","apple_news_is_hidden":false,"apple_news_is_paid":false,"apple_news_is_preview":false,"apple_news_is_sponsored":false,"apple_news_maturity_rating":"","apple_news_metadata":"\"\"","apple_news_pullquote":"","apple_news_pullquote_position":"","apple_news_slug":"","apple_news_sections":"\"\"","apple_news_suppress_video_url":false,"apple_news_use_image_component":false,"footnotes":""},"categories":[8],"tags":[],"class_list":["post-1416","post","type-post","status-publish","format-standard","hentry","category-science-category"],"apple_news_notices":[],"_links":{"self":[{"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/posts\/1416","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/comments?post=1416"}],"version-history":[{"count":0,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/posts\/1416\/revisions"}],"wp:attachment":[{"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/media?parent=1416"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/categories?post=1416"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/tags?post=1416"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}