{"id":546,"date":"2017-12-14T02:41:49","date_gmt":"2017-12-14T02:41:49","guid":{"rendered":"https:\/\/blog.vanabel.cn\/?p=546"},"modified":"2017-12-14T02:57:16","modified_gmt":"2017-12-14T02:57:16","slug":"jixiaoqumiandelizi","status":"publish","type":"post","link":"https:\/\/blog.vanabel.cn\/?p=546","title":{"rendered":"\u6781\u5c0f\u66f2\u9762\u7684\u4f8b\u5b50"},"content":{"rendered":"

1. \u87ba\u65cb\u9762(Helicoid)<\/a><\/span>\n\n\u87ba\u65cb\u9762\u662f$\\RR^3$\u4e2d\u7684\u66f2\u9762, \u5176\u7684\u65b9\u7a0b\u662f
\n$$
\n\\set{(x,y,z)\\in\\RR^3:z=\\arctan(y\/x)}
\n$$
\n\u7528Mathematica\u4f5c\u56fe\u5f97\u5230<\/p>\n

\r\nr = 5;\r\nParametricPlot3D[{t Cos[s], t Sin[s], s}, {s, -r, r}, {t, -r, r}]\r\n<\/code><\/pre>\n
\"\"<\/a><\/p>\n
2. \u60ac\u94fe\u9762(Catenoid)<\/a><\/span>\n\n\u60ac\u94fe\u9762\u662f$\\RR^3$\u4e2d\u7684\u66f2\u9762, \u5176\u7684\u65b9\u7a0b\u662f
\n$$
\n\\set{(x,y,z)\\in\\RR^3:x^2+y^2=\\cosh^2 z}
\n$$
\n\u7528Mathematica\u4f5c\u56fe\u5f97\u5230<\/p>\n
\r\nr = 1.4;\r\nPlot3D[{ArcCosh[Sqrt[x^2 + y^2]], -ArcCosh[Sqrt[x^2 + y^2]], \r\n  PlotPoints -> 75}, {x, -r, r}, {y, -r, r}]\r\nRevolutionPlot3D[{{ArcCosh[x]}, {-ArcCosh[x]}}, {x, -r, r}]\r\n<\/code><\/pre>\n
\"\"<\/a><\/p>\n
\"\"<\/a>
\n3. Scherk\u53cc\u5468\u671f\u66f2\u9762(Scherk’s doubly-periodic surface)<\/a><\/span>\n\nScherk\u53cc\u5468\u671f\u66f2\u9762\u662f$\\RR^3$\u4e2d\u7684\u66f2\u9762, \u5176\u7684\u65b9\u7a0b\u662f
\n$$
\n\\set{(x,y,z)\\in\\RR^3:z=\\ln\\left(\\frac{\\cos y}{\\cos x}\\right)}
\n$$
\n\u7528Mathematica\u4f5c\u56fe\u5f97\u5230<\/p>\n
\r\nr = 3 Pi\/2;\r\nPlot3D[Log[Cos[y]\/Cos[x]], {x, -r, r}, {y, -r, r}, PlotRange -> Full]\r\n<\/code><\/pre>\n
\"\"<\/a>
\n4. Enneper\u66f2\u9762<\/a><\/span>\n\nEnneper\u662f$\\RR^3$\u4e2d\u7684\u66f2\u9762, \u5176\u7684\u65b9\u7a0b\u662f
\n$$
\n\\set{(x,y,z)\\in\\RR^3:x=-\\frac{s^3}{3}+s t^2+s,y=-s^2 t+\\frac{t^3}{3}-t,z=s^2-t^2}
\n$$
\n\u7528Mathematica\u4f5c\u56fe\u5f97\u5230<\/p>\n
\r\nr = 3;\r\nParametricPlot3D[{s - s^3\/3 + s t^2, -t - s^2 t + t^3\/3, \r\n  s^2 - t^2}, {s, -r, r}, {t, -r, r}]\r\n<\/code><\/pre>\n
\"\"<\/a><\/p>\n
\u5b8c\u6574\u7684MMA\u4ee3\u7801\u53ef\u4ee5\u8fd9\u91cc\u4e0b\u8f7d<\/a>\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
1. \u87ba\u65cb\u9762(Helicoid) \u87ba\u65cb\u9762\u662f$\\RR^3$\u4e2d\u7684\u66f2\u9762, \u5176\u7684\u65b9\u7a0b\u662f $$ \\set{… \u7ee7\u7eed\u9605\u8bfb\u6781\u5c0f\u66f2\u9762\u7684\u4f8b\u5b50<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[117,24,116],"class_list":["post-546","post","type-post","status-publish","format-standard","hentry","category-math","tag-mathematica","tag-24","tag-jixiaoqumian","entry"],"_links":{"self":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/546","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=546"}],"version-history":[{"count":8,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/546\/revisions"}],"predecessor-version":[{"id":563,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/546\/revisions\/563"}],"wp:attachment":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=546"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=546"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=546"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}