{"id":4007,"date":"2024-06-29T12:00:17","date_gmt":"2024-06-29T16:00:17","guid":{"rendered":"https:\/\/josmfs.net\/?p=4007"},"modified":"2024-06-29T12:00:17","modified_gmt":"2024-06-29T16:00:17","slug":"horses-to-qi","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2024\/06\/29\/horses-to-qi\/","title":{"rendered":"Horses to Qi"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-4004\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/06\/Horses-to-Qi-Fig2.jpg\" alt=\"\" width=\"200\" height=\"206\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/06\/Horses-to-Qi-Fig2.jpg 400w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/06\/Horses-to-Qi-Fig2-291x300.jpg 291w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>This is a challenging problem from the c.100AD Chinese mathematical work, <em>Ji\u01d4 zh\u0101ng su\u00e0n sh\u00f9<\/em> (<em>The Nine Chapters on the Mathematical Art<\/em>) found at the MAA Convergence website.<\/p>\n<p>\u201cNow a good horse and an inferior horse set out from Chang\u2019an to Qi.\u00a0 Qi is 3000<em> li <\/em>from Chang\u2019an.\u00a0 The good horse travels 193 <em>li<\/em> on the first day and daily increases by 13 <em>li<\/em>; the inferior horse travels 97 <em>li<\/em> on the first day and daily decreases by\u00a0\u00bd <em>li<\/em>.\u00a0 The good horse reaches Qi first and turns back to meet the inferior horse.\u00a0 Tell: how many days until they meet and how far has each traveled?\u201d<\/p>\n<p>The solution involves common fractions, which the Chinese were already adept at <a href=\"https:\/\/josmfs.net\/2024\/06\/22\/making-arrows\/\">using<\/a> by 100 BC.<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/06\/Horses-to-Qi-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/06\/Horses-to-Qi-240622.pdf\">Horses to Qi<\/a> for a solution.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is a challenging problem from the c.100AD Chinese mathematical work, Ji\u01d4 zh\u0101ng su\u00e0n sh\u00f9 (The Nine Chapters on the Mathematical Art) found at the MAA Convergence website. \u201cNow a good horse and an inferior horse set out from Chang\u2019an to Qi.\u00a0 Qi is 3000 li from Chang\u2019an.\u00a0 The good horse travels 193 li on [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[7,81],"class_list":["post-4007","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-math-history","tag-travel-puzzles"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4007","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=4007"}],"version-history":[{"count":1,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4007\/revisions"}],"predecessor-version":[{"id":4008,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4007\/revisions\/4008"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=4007"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=4007"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=4007"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}