{"id":14599,"date":"2010-11-10T17:58:14","date_gmt":"2010-11-10T09:58:14","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=14599"},"modified":"2021-10-06T16:30:51","modified_gmt":"2021-10-06T08:30:51","slug":"%e5%86%b0%e6%b7%87%e6%b7%8b%e7%ad%92%e5%ae%9a%e7%90%86%ef%bc%88ice-cream-cone-theorem%ef%bc%89","status":"publish","type":"post","link":"http:\/\/localhost\/%e5%86%b0%e6%b7%87%e6%b7%8b%e7%ad%92%e5%ae%9a%e7%90%86%ef%bc%88ice-cream-cone-theorem%ef%bc%89\/","title":{"rendered":"\u51b0\u6dc7\u6dcb\u7b52\u5b9a\u7406\uff08Ice Cream Cone Theorem\uff09"},"content":{"rendered":"

\u51b0\u6dc7\u6dcb\u7b52\u5b9a\u7406\uff08Ice Cream Cone Theorem\uff09
\n<\/span>\u570b\u7acb\u81fa\u7063\u5927\u5b78\u6578\u5b78\u7cfb\u66f9\u4eae\u5409\u6559\u6388\/\u570b\u7acb\u81fa\u7063\u5927\u5b78\u6578\u5b78\u7cfb\u66f9\u4eae\u5409\u6559\u6388\u8cac\u4efb\u7de8\u8f2f<\/span><\/strong><\/p>\n

\u53e4\u5e0c\u81d8\u4eba\u7814\u7a76\u5713\u9310\u622a\u75d5\uff0c\u5f97\u5230\u5f88\u591a\u5e7e\u4f55\u6027\u8cea\uff0c\u5305\u62ec\u5169\uff08\u659c\uff09\u5750\u6a19\u9577\u5ea6\u4e4b\u9593\u7684\u95dc\u4fc2\uff0c\u9ede\u7126\u8ddd\u8207\u9ede\u6e96\u8ddd\u6210\u6b63\u6bd4\uff0c\u5207\u7dda\u6027\u8cea\uff0c\u4ee5\u53ca\u6709\u5fc3\u622a\u75d5\u5169\u9ede\u7126\u8ddd\u4e4b\u548c\uff08\u6216\u5dee\uff09\u70ba\u5b9a\u9577\u7b49\u3002\u4e0d\u904e\u5c0e\u51fa\u7684\u904e\u7a0b\u975e\u5e38\u8907\u96dc\uff0c\u5f88\u96e3\u8b93\u4eba\u611f\u53d7\u5230\u7d50\u679c\u4e4b\u5fc5\u7136\u3002\u518d\u8005\uff0c\u73fe\u4ee3\u4eba\u5b78\u5713\u9310\u66f2\u7dda\u7528\u7684\u662f\u5750\u6a19\u65b9\u6cd5\uff0c\u66f4\u96e3\u9818\u6703\u9019\u4e9b\u5e7e\u4f55\u6027\u8cea\u7684\u7f8e\u5999\u3002\u5341\u4e5d\u4e16\u7d00\u521d\uff0c\u5169\u4f4d\u6bd4\u5229\u6642\u6578\u5b78\u5bb6\uff0c\u63d0\u51fa\u51b0\u6dc7\u6dcb\u7b52\u5b9a\u7406\uff0c\u8aaa\u660e\u9ede\u7126\u8ddd\u8207\u9ede\u6e96\u8ddd\u6210\u6b63\u6bd4\uff0c\u4ee5\u53ca\u6709\u5fc3\u622a\u75d5\u5169\u9ede\u7126\u8ddd\u4e4b\u548c\uff08\u6216\u5dee\uff09\u70ba\u5b9a\u9577\u7684\u6027\u8cea\uff0c\u4e5f\u4e0d\u904e\u662f\u622a\u75d5\u5f88\u81ea\u7136\u7684\u5e7e\u4f55\u7d50\u679c\u3002<\/span><\/p>\n

\u5047\u8a2d\u5728\u4ee5 $${Q}$$ \u70ba\u9802\u9ede\u7684\u76f4\u5713\u9310\uff08\u51b0\u6dc7\u6dcb\u7b52\uff09\u5167\uff0c\u64fa\u9032\u4e00\u5713\u7403\uff08\u51b0\u6dc7\u6dcb\uff09\uff0c\u5247\u5713\u9310\u8207\u5713\u7403\u76f8\u5207\u65bc\u4e00\u5713 $${O}$$\u3002\u5047\u8a2d\u6709\u4e00\u5e73\u9762 $${\\pi}’$$\uff08\u9905\u4e7e\uff09\uff0c\u8207\u5713\u7403\u76f8\u5207\u65bc $${F}$$\uff0c\u4e14\u8207\u5713 $${O}$$ \u6240\u5728\u7684\u5e73\u9762 $$\\pi$$\uff0c\u76f8\u4ea4\u65bc\u4e00\u76f4\u7dda $${d}$$\u3002\u6211\u5011\u8981\u8b49\u660e\uff1a $${F}$$ \u8207 $${d}$$ \u70ba\u5e73\u9762 $${\\pi}’$$ \u8207\u5713\u9310\u76f8\u622a\u6240\u5f97\u622a\u75d5\u4e4b\u7126\u9ede\u8207\u6e96\u7dda\u3002<\/span><\/p>\n

\"\"<\/a><\/span><\/p>\n

\u5047\u8a2d $$P$$ \u70ba\u622a\u75d5\u4e0a\u4e00\u9ede\uff0c\u9023\u7dda $$PQ$$ \u4ea4\u5713 $$O$$ \u65bc $$E$$\u3002<\/p>\n

\u8a2d\u5e73\u9762 $$\\pi’$$ \u8207 $$\\pi$$ \u7684\u4ea4\u89d2\u70ba $$\\alpha$$\uff0c\u5713\u9310\u7684\u6bcd\u7dda\uff08\u5982 $$PQ$$\uff09\u8207\u5e73\u9762 $$\\pi$$ \u7684\u4ea4\u89d2\u70ba $$\\beta$$\u3002<\/p>\n

\u8a2d $$P$$ \u5230\u5e73\u9762 $$\\pi$$ \u7684\u5782\u8db3\u70ba $$H$$\uff0c$$H$$ \u5230\u76f4\u7dda $$d$$ \u7684\u5782\u8db3\u70ba $$R$$\uff0c<\/p>\n

\u5247 $$PR$$ \u70ba $$P$$ \u5230 $$d$$ \u7684\u5782\u7dda\uff08\u4e09\u5782\u7dda\u5b9a\u7406\uff09\uff0c\u800c $$\\angle PRH=\\alpha$$\u3002<\/p>\n

\u5247 $$PE=PF$$\uff0c\u56e0\u70ba\u5169\u8005\u540c\u70ba\u5713\u7403\u4e4b\u5207\u7dda\u3002\u5982\u6b64\u5247<\/p>\n

$$PR\\sin\\alpha = PH = PE\\sin\\beta =PF\\sin\\beta$$<\/p>\n

\u4ea6\u5373\uff0c$$\\displaystyle\\frac{PF}{PR}=\\frac{\\sin\\alpha}{\\sin\\beta}=\\epsilon$$\uff0c<\/p>\n

\u9019\u5c31\u662f\u9ede\u7126\u8ddd\u8207\u9ede\u6e96\u8ddd\u6709\u5b9a\u6bd4\u7684\u6027\u8cea\uff0c\u800c $$F$$ \u8207 $$d$$ \u81ea\u7136\u662f\u7126\u9ede\u8207\u6e96\u7dda\u3002<\/p>\n

$$\\alpha =\\beta$$ \u6642 $$(\\epsilon=1)$$\uff0c\u5e73\u9762 $$\\pi’$$ \u8207\u4e00\u6bcd\u7dda\u5e73\u884c\uff0c\u622a\u75d5\u70ba\u62cb\u7269\u7dda\u3002<\/p>\n

$$\\alpha<\\beta$$ \u6642 $$(1<\\epsilon)$$\uff0c\u5e73\u9762 $$\\pi’$$ \u6703\u8207\u6240\u6709\u6bcd\u7dda\u76f8\u4ea4\uff0c\u622a\u75d5\u70ba\u6a62\u5713\u3002<\/p>\n

$$\\alpha>\\beta$$ \u6642 $$(\\epsilon >1)$$\uff0c\u5e73\u9762 $$\\pi’$$ \u8f03\u9661\uff0c\u6703\u4ea4\u5230\u5713\u9310\u7684\u53e6\u4e00\u652f\uff0c\u622a\u75d5\u70ba\u96d9\u66f2\u7dda\u3002<\/p>\n

\"\"<\/a><\/p>\n

\u622a\u75d5\u70ba\u6a62\u5713\u6642\uff08\u5716\u4e09\uff09\uff0c\u5728\u5713\u9310\u5167\uff0c\u5e73\u9762 $$\\pi’$$ \u4e4b\u4e0a\uff0c\u53ef\u518d\u64fa\u9032\u4e00\u9069\u7576\u5927\u5c0f\u7684\u5713\u7403\uff0c\u4f7f\u4e4b\u8207\u5e73\u9762 $$\\pi’$$ \u76f8\u5207\u65bc\u4e00\u9ede $$F$$\uff0c\u4e26\u8207\u5713\u9310\u76f8\u5207\u65bc\u4e00\u5713 $$O’$$\u3002\u5047\u8a2d $$PQ$$ \u4ea4 $$O’$$ \u65bc $$E’$$\uff0c\u5247 $$PE’=PF’$$\uff0c\u56e0\u70ba\u5169\u8005\u90fd\u662f\u9019\u500b\u5713\u7403\u7684\u5207\u7dda\u3002\u65bc\u662f $$PF+PF’=PE+PE’=EE’$$ \u70ba\u5b9a\u9577\uff0c\u8207 $$P$$ \u9ede\u7121\u95dc\u3002\u9019\u5c31\u8b49\u660e\u4e86\u6a62\u5713\u7684\u5169\u9ede\u7126\u8ddd\u4e4b\u548c\u70ba\u5b9a\u9577\u3002<\/p>\n

\u96d9\u66f2\u7dda\u6642\uff0c\u5713\u7403\u8981\u64fa\u5728\u5e73\u9762 $$\\pi’$$ \u8207\u5713\u9310\u7684\u53e6\u4e00\u652f\u4e4b\u9593\uff0c\u5c31\u53ef\u4ee5\u8b49\u660e\u5169\u9ede\u7126\u8ddd\u4e4b\u5dee\u70ba\u5b9a\u9577\u3002<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

\u672c\u6587\u4ecb\u7d39\u51b0\u6dc7\u6dcb\u5b9a\u7406\u3002\u5b83\u4ee5\u5e7e\u4f55\u7684\u65b9\u6cd5\u5448\u73fe\u5713\u9310\u622a\u75d5\u7684\u9ede\u7126\u8ddd\u8207\u9ede\u6e96\u8ddd\u4e4b\u6bd4\uff0c\u4e26\u8aaa\u660e\u4e86\u6709\u5fc3\u622a\u75d5\u5169\u9ede\u7126\u8ddd\u4e4b\u548c\uff08\u6216\u5dee\uff09\u70ba\u5b9a\u9577\u7684\u6027\u8cea\u3002<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[226,224,111],"tags":[392,383,384,385,391,390,386],"class_list":["post-14599","post","type-post","status-publish","format-standard","hentry","category-math04-02","category-math04","category-mathematics00","tag-392","tag-383","tag-384","tag-385","tag-391","tag-390","tag-386","loop-entry","cat-226","cat-224","cat-111","no-thumbnail"],"views":5567,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/14599","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/comments?post=14599"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/14599\/revisions"}],"predecessor-version":[{"id":89360,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/14599\/revisions\/89360"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=14599"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=14599"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=14599"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}