{"id":255,"date":"2013-06-21T19:41:22","date_gmt":"2013-06-21T11:41:22","guid":{"rendered":"http:\/\/lttt.blog.ustc.edu.cn\/?p=255"},"modified":"2013-06-21T19:41:22","modified_gmt":"2013-06-21T11:41:22","slug":"%e4%b8%80%e4%b8%aa%e6%a0%bc%e7%82%b9%e9%97%ae%e9%a2%98","status":"publish","type":"post","link":"https:\/\/lttt.vanabel.cn\/?p=255","title":{"rendered":"\u4e00\u4e2a\u683c\u70b9\u95ee\u9898"},"content":{"rendered":"<p>\u6211\u89c9\u5f97\u4e0b\u9762\u7684\u95ee\u9898\u662f\u6709\u8da3\u7684:<br \/>\n\\begin{prob}<br \/>\n\u8bd5\u6c42\u6b27\u6c0f\u5e73\u9762\u4e0a\u4ee5\u539f\u70b9\u4e3a\u4e2d\u5fc3$R$\u4e3a\u534a\u5f84\u7684\u5f00\u5706\u76d8\u5185\u6709\u591a\u5c11\u4e2a\u5f62\u5982$(m,n)$\u7684\u6574\u6570\u70b9, \u5176\u4e2d$m,n$\u90fd\u662f\u6574\u6570?<br \/>\n\\end{prob}<br \/>\n\u6211\u7684\u60f3\u6cd5\u662f\u5229\u7528\u8ba1\u7b97\u673a\u6765\u5177\u4f53\u7684\u8ba1\u7b97\u6709\u591a\u5c11\u4e2a\u683c\u70b9.<br \/>\n\u9996\u5148, \u6211\u4eec\u53ef\u4ee5\u7528\u4e00\u4e2a\u51fd\u6570$F$\u6765\u5224\u65ad\u7ed9\u5b9a\u7684$(m,n)$\u662f\u5426\u662f\u6ee1\u8db3\u6761\u4ef6\u7684\u70b9, \u660e\u663e$F$\u53ef\u53d6\u4e3a<br \/>\n$$F(x,y,R)=x^2+y^2-R^2$$<br \/>\n\u5982\u679c, $F(m,n,R)&lt;0$\u5219$(m,n)$\u5c31\u662f\u6ee1\u8db3\u6761\u4ef6\u7684\u4e00\u4e2a\u70b9. \u6ce8\u610f\u5230$x,y$\u7684\u8303\u56f4\u4e3a:$-R&lt; x ,y&lt; R$, \u8fd9\u6837\u6211\u4eec\u5f88\u5bb9\u6613\u7528\u4e24\u4e2a\u5faa\u73af\u6765\u8ba1\u7b97\u7ed9\u5b9a$R$\u65f6, \u6ee1\u8db3\u8981\u6c42\u7684\u70b9\u6709\u591a\u5c11\u4e2a.<br \/>\n<!--more--><\/p>\n<h4 id=\"mathematica\">Mathematica\u4ee3\u7801<\/h4>\n<pre lang=\"matlab\">F[x_, y_, R_] := x^2 + y^2 - R^2\nNum[R_] := Length@DeleteDuplicates@Flatten[Table[\n If[F[i, j, R] &lt; 0, \n    {{i, j}, {-i, j}, {i, -j}, {-i, -j}, \n    {j, i}, {j, -i}, {-j, i}, {-j, -i}}, {{0, 0}}\n  ], {i, 0, Floor[R]}, {j, i, Floor[R]}], 2]<\/pre>\n<p>\u53ef\u4ee5\u8f7b\u6613\u7528\u5982\u4e0b\u4ee3\u7801\u4f5c\u51fa\u56fe\u5f62:<\/p>\n<pre lang=\"matlab\">Plot[Num[x], {x, 0, 5}]<\/pre>\n<p>\u8fd9\u8868\u793a\u57280\u52305\u4e4b\u95f4\u65f6, \u51fd\u6570\u7684\u56fe\u50cf.<\/p>\n<p><img decoding=\"async\" title=\"\" src=\"https:\/\/lttt.vanabel.cn\/wp-content\/uploads\/2013\/06\/num0_5.png\" alt=\"0\u52305\u4e4b\u95f4\u7684\u51fd\u6570\u56fe\u50cf\" \/><\/p>\n<p>\u7c7b\u4f3c\u53ef\u5f97:<\/p>\n<p><img decoding=\"async\" title=\"\" src=\"https:\/\/lttt.vanabel.cn\/wp-content\/uploads\/2013\/06\/num5_10.png\" alt=\"5\u523010\u4e4b\u95f4\u7684\u51fd\u6570\u56fe\u50cf\" \/><\/p>\n<p><img decoding=\"async\" title=\"\" src=\"https:\/\/lttt.vanabel.cn\/wp-content\/uploads\/2013\/06\/num100_101.png\" alt=\"100\u5230101\u4e4b\u95f4\u7684\u51fd\u6570\u56fe\u50cf\" \/><\/p>\n<h4>\u672a\u89e3\u51b3\u7684\u95ee\u9898<\/h4>\n<ol>\n<li>\u5982\u4f55\u627e\u5230\u56fe\u4e2d\u7684\u95f4\u65ad\u70b9?<\/li>\n<li>\u5982\u4f55\u4f18\u5316\u4ee3\u7801, \u5f53\u6570\u503c\u5f88\u5927\u65f6, \u8ba1\u7b97\u51e0\u4e4e\u4e0d\u80fd\u8fdb\u884c<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u6211\u89c9\u5f97\u4e0b\u9762\u7684\u95ee\u9898\u662f\u6709\u8da3\u7684: \\begin{prob} \u8bd5\u6c42\u6b27\u6c0f\u5e73\u9762\u4e0a\u4ee5\u539f\u70b9\u4e3a\u4e2d\u5fc3 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/lttt.vanabel.cn\/?p=255\"> <span class=\"screen-reader-text\">\u4e00\u4e2a\u683c\u70b9\u95ee\u9898<\/span> \u9605\u8bfb\u66f4\u591a &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[716],"class_list":["post-255","post","type-post","status-publish","format-standard","hentry","category-mathnotes","tag-716"],"_links":{"self":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/255","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=255"}],"version-history":[{"count":0,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/255\/revisions"}],"wp:attachment":[{"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=255"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=255"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lttt.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=255"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}