{"id":249,"date":"2026-10-27T20:03:53","date_gmt":"2026-10-27T12:03:53","guid":{"rendered":"http:\/\/laoke.pw\/?p=249"},"modified":"2026-10-27T20:03:53","modified_gmt":"2026-10-27T12:03:53","slug":"211-geogebra-%e8%be%93%e5%85%a5%e4%b8%80%e4%b8%aa%e5%87%bd%e6%95%b0%e5%b0%b1%e5%87%ba%e5%9b%be%ef%bc%8c%e6%8a%8a%e6%95%b0%e5%ad%a6%e8%af%be%e6%9c%ac%e4%b8%8a%e7%9a%84%e5%9b%be","status":"publish","type":"post","link":"https:\/\/laoke.pw\/?p=249","title":{"rendered":"211 GeoGebra \u2014\u2014 \u8f93\u5165\u4e00\u4e2a\u51fd\u6570\u5c31\u51fa\u56fe\uff0c\u628a\u6570\u5b66\u8bfe\u672c\u4e0a\u7684\u56fe\u53d8\u6210\u80fd\u62d6\u7740\u73a9\u7684\u4e1c\u897f"},"content":{"rendered":"

\u4e00\u53e5\u8bdd\u5b9a\u4f4d<\/strong>\uff1a\u4e00\u6b3e\u514d\u8d39\u7684\u5f00\u6e90\u6570\u5b66\u8f6f\u4ef6\uff0c\u628a\u4ee3\u6570\u3001\u51e0\u4f55\u3001\u51fd\u6570\u56fe\u50cf\u3001\u7edf\u8ba1\u548c 3D \u66f2\u9762\u653e\u8fdb\u540c\u4e00\u4e2a\u7a97\u53e3\uff0c\u6539\u4e00\u4e2a\u53c2\u6570\u6574\u5f20\u56fe\u7acb\u523b\u8ddf\u7740\u52a8\u3002<\/p>\n

\u75db\u70b9\u5206\u6790<\/h2>\n

\u5b66\u6570\u5b66\u6700\u96be\u53d7\u7684\u73af\u8282\uff0c\u5f80\u5f80\u4e0d\u662f\u63a8\u5bfc\uff0c\u800c\u662f\u300c\u770b\u4e0d\u89c1\u300d\u3002\u8bfe\u672c\u4e0a\u8bb2\u4e8c\u6b21\u51fd\u6570\u7684\u5f00\u53e3\u65b9\u5411\u968f\u7cfb\u6570\u53d8\u5316\uff0c\u914d\u4e86\u4e00\u5f20\u9759\u6001\u56fe\uff1b\u8001\u5e08\u8bb2\u4e09\u89d2\u51fd\u6570\u5468\u671f\uff0c\u9ed1\u677f\u4e0a\u753b\u4e09\u6761\u6b63\u5f26\u66f2\u7ebf\u5c31\u4e0b\u8bfe\u4e86\u3002\u60f3\u81ea\u5df1\u9a8c\u8bc1\u4e00\u4e0b\uff0c\u8981\u4e48\u624b\u7ed8\u5750\u6807\u7eb8\uff0c\u8981\u4e48\u6253\u5f00 Excel \u786c\u51d1\u6563\u70b9\u56fe\u2014\u2014\u540e\u8005\u8fde\u4e00\u6761\u5e73\u6ed1\u66f2\u7ebf\u90fd\u753b\u4e0d\u5229\u7d22\u3002<\/p>\n

\u5728\u7ebf\u753b\u56fe\u7f51\u7ad9\u5012\u662f\u4e0d\u5c11\uff0c\u4f46\u591a\u6570\u53ea\u652f\u6301 y=f(x)<\/code> \u8fd9\u4e00\u79cd\u8868\u8fbe\u5f0f\uff0c\u9047\u5230\u53c2\u6570\u65b9\u7a0b\u3001\u6781\u5750\u6807\u3001\u9690\u51fd\u6570\u5c31\u6b47\u4e86\uff0c\u5bfc\u6570\u548c\u79ef\u5206\u66f4\u662f\u522b\u60f3\u3002GeoGebra \u89e3\u51b3\u7684\u6b63\u662f\u8fd9\u4e00\u6bb5\uff1a\u5b83\u4e0d\u53ea\u662f\u753b\u56fe\u5de5\u5177\uff0c\u800c\u662f\u628a\u300c\u8868\u8fbe\u5f0f\u3001\u56fe\u5f62\u3001\u6570\u503c\u300d\u4e09\u8005\u7ed1\u5728\u4e00\u8d77\uff0c\u4f60\u52a8\u54ea\u4e00\u8fb9\uff0c\u53e6\u5916\u4e24\u8fb9\u540c\u6b65\u53d8\u3002<\/p>\n

\u6838\u5fc3\u80fd\u529b<\/h2>\n
    \n
  • \u8f93\u5165\u5373\u51fa\u56fe<\/strong>\uff1a\u76f4\u63a5\u6572 f(x)=x^2-3x+2<\/code>\uff0c\u56fe\u50cf\u7acb\u523b\u51fa\u73b0\u5728\u7ed8\u56fe\u533a\uff1b\u8f93\u5165 (1,2)<\/code> \u5f97\u70b9\uff0c\u8f93\u5165 x+y=3<\/code> \u5f97\u76f4\u7ebf\uff0c\u9690\u51fd\u6570\u4e5f\u80fd\u8bc6\u522b<\/li>\n
  • \u6ed1\u5757\u53c2\u6570<\/strong>\uff1a\u7ed9\u7cfb\u6570\u52a0\u4e00\u4e2a\u6ed1\u5757\uff08\u6bd4\u5982 a<\/code> \u4ece -5 \u5230 5\uff09\uff0c\u62d6\u52a8\u6ed1\u5757\u65f6\u66f2\u7ebf\u5b9e\u65f6\u53d8\u5f62\uff0c\u8bb2\u300c\u53c2\u6570\u5bf9\u56fe\u50cf\u7684\u5f71\u54cd\u300d\u6bd4\u4efb\u4f55\u9759\u6001\u63d2\u56fe\u90fd\u76f4\u89c2<\/li>\n
  • \u51e0\u4f55\u4f5c\u56fe<\/strong>\uff1a\u5706\u89c4\u76f4\u5c3a\u90a3\u4e00\u5957\u5168\u90fd\u6709\uff0c\u4e2d\u70b9\u3001\u5782\u7ebf\u3001\u89d2\u5e73\u5206\u7ebf\u3001\u8f68\u8ff9\u8ffd\u8e2a\u90fd\u80fd\u6784\u9020\uff0c\u800c\u4e14\u6784\u9020\u5173\u7cfb\u662f\u6d3b\u7684\uff0c\u62d6\u9876\u70b9\u6574\u4e2a\u56fe\u5f62\u4fdd\u6301\u7ea6\u675f<\/li>\n
  • CAS \u4e0e\u8868\u683c<\/strong>\uff1a\u5185\u7f6e\u8ba1\u7b97\u673a\u4ee3\u6570\u7cfb\u7edf\uff0c\u80fd\u505a\u56e0\u5f0f\u5206\u89e3\u3001\u89e3\u65b9\u7a0b\u3001\u6c42\u5bfc\u3001\u6c42\u79ef\u5206\uff1b\u8868\u683c\u533a\u53ef\u4ee5\u76f4\u63a5\u5f55\u5165\u6570\u636e\u753b\u6563\u70b9\u56fe\u5e76\u62df\u5408\u56de\u5f52<\/li>\n
  • 3D \u7ed8\u56fe\u533a<\/strong>\uff1a\u652f\u6301 z=x^2+y^2<\/code> \u8fd9\u7c7b\u66f2\u9762\uff0c\u80fd\u65cb\u8f6c\u89c6\u89d2\uff0c\u9002\u5408\u8bb2\u591a\u5143\u51fd\u6570\u548c\u4e8c\u6b21\u66f2\u9762<\/li>\n
  • \u5168\u5e73\u53f0<\/strong>\uff1aWindows\u3001macOS\u3001Linux \u684c\u9762\u7248\uff0c\u52a0\u4e0a\u7f51\u9875\u7248\u3001Android\u3001iOS\uff0c\u5de5\u7a0b\u6587\u4ef6\u4e92\u901a<\/li>\n<\/ul>\n

    \u5b9e\u6d4b\u4f53\u9a8c<\/h2>\n

    \u5728\u4e00\u53f0 Windows 11 \u673a\u5668\u4e0a\u88c5\u684c\u9762\u7248\uff0c\u5b89\u88c5\u5305\u4e00\u767e\u591a MB\uff0c\u5b89\u88c5\u8fc7\u7a0b\u5e72\u51c0\uff0c\u6ca1\u6709\u6346\u7ed1\u3002\u7b2c\u4e00\u6b21\u6253\u5f00\u4f1a\u7ed9\u4e00\u4e2a\u300c\u6253\u5f00\u4ec0\u4e48\u300d\u7684\u5f15\u5bfc\u9875\uff0c\u9009\u300c\u56fe\u5f62\u8ba1\u7b97\u5668\u300d\u5373\u53ef\u3002<\/p>\n

    \u5b9e\u6d4b\u4e0b\u6765\u6700\u987a\u624b\u7684\u662f\u53c2\u6570\u6ed1\u5757\u3002\u7ed9\u4e00\u4e2a y=a\u00b7sin(b\u00b7x+c)<\/code> \u52a0\u4e0a\u4e09\u4e2a\u6ed1\u5757\uff0c\u62d6\u52a8\u65f6\u66f2\u7ebf\u5e73\u6ed1\u8ddf\u968f\uff0c\u6ca1\u6709\u660e\u663e\u5361\u987f\uff0c\u7528\u6765\u7ed9\u5b69\u5b50\u89e3\u91ca\u300c\u632f\u5e45\u300d\u300c\u5468\u671f\u300d\u300c\u76f8\u4f4d\u300d\u51e0\u4e4e\u662f\u79d2\u61c2\u3002CAS \u90e8\u5206\u8f93\u5165 Integral(x^2, 0, 3)<\/code> \u80fd\u76f4\u63a5\u7ed9\u51fa\u7ed3\u679c\u548c\u6b65\u9aa4\u63d0\u793a\uff0c\u6bd4\u81ea\u5df1\u7b97\u5feb\u5f97\u591a\u3002<\/p>\n

    3D \u7ed8\u56fe\u533a\u5728\u96c6\u663e\u7b14\u8bb0\u672c\u4e0a\u8f6c\u89c6\u89d2\u4f1a\u6709\u4e00\u70b9\u62d6\u5f71\uff0c\u628a\u300c\u6297\u952f\u9f7f\u300d\u5173\u6389\u5c31\u987a\u4e86\u3002\u684c\u9762\u7248\u542f\u52a8\u5927\u7ea6\u4e24\u4e09\u79d2\uff0c\u6bd4\u8d77\u7f51\u9875\u7248\u7701\u4e8b\uff08\u4e0d\u7528\u7b49\u52a0\u8f7d\uff09\uff0c\u4f46\u7f51\u9875\u7248\u80dc\u5728\u6362\u53f0\u7535\u8111\u4e5f\u80fd\u63a5\u7740\u6539\u3002<\/p>\n

    \u4e0d\u591f\u7406\u60f3\u7684\u5730\u65b9\uff1a<\/p>\n

      \n
    • \u529f\u80fd\u5165\u53e3\u504f\u591a\uff0c\u7b2c\u4e00\u6b21\u6253\u5f00\u4f1a\u88ab\u4fa7\u8fb9\u680f\u4e00\u5806\u5de5\u5177\u6643\u5230\uff0c\u5f97\u82b1\u5341\u51e0\u5206\u949f\u6478\u6e05\u54ea\u51e0\u4e2a\u662f\u81ea\u5df1\u771f\u4f1a\u7528\u7684<\/li>\n
    • CAS \u7684\u8f93\u51fa\u683c\u5f0f\u6709\u65f6\u4e0d\u591f\u300c\u6559\u79d1\u4e66\u300d\uff0c\u5316\u7b80\u7ed3\u679c\u4f1a\u7528\u5947\u602a\u7684\u5f62\u5f0f\u5448\u73b0\uff0c\u9700\u8981\u624b\u52a8 Simplify<\/code><\/li>\n
    • \u754c\u9762\u4e2d\u6587\u672c\u5730\u5316\u57fa\u672c\u53ef\u7528\uff0c\u4f46\u4e2a\u522b\u63d0\u793a\u4ecd\u662f\u82f1\u6587<\/li>\n<\/ul>\n

      \u9002\u5408\u8c01<\/h2>\n

      \u4e2d\u5b66\u5230\u5927\u5b66\u7684\u6570\u5b66\u5b66\u4e60\u8005\u3001\u9700\u8981\u505a\u8bfe\u4ef6\u7684\u8001\u5e08\u3001\u7ed9\u5b69\u5b50\u8bb2\u9898\u7684\u5bb6\u957f\uff0c\u90fd\u662f\u6838\u5fc3\u4eba\u7fa4\u3002\u5de5\u7a0b\u4e0a\u8981\u505a\u5feb\u901f\u51fd\u6570\u62df\u5408\u6216\u8005\u51e0\u4f55\u5173\u7cfb\u9a8c\u8bc1\u7684\u4eba\u4e5f\u7528\u5f97\u4e0a\u3002\u5982\u679c\u4f60\u53ea\u662f\u60f3\u968f\u624b\u753b\u4e00\u6761\u66f2\u7ebf\u622a\u4e2a\u56fe\uff0cGeoGebra \u7a0d\u663e\u7b28\u91cd\uff0c\u7f51\u9875\u7248\u66f4\u5408\u9002\u3002<\/p>\n

      \u9700\u8981\u6ce8\u610f\u7684\u5730\u65b9<\/h2>\n

      GeoGebra \u5206\u300c\u7ecf\u5178\u7248\u300d\u548c\u300c\u56fe\u5f62\u8ba1\u7b97\u5668\u300d\u7b49\u591a\u4e2a\u5165\u53e3\uff0c\u529f\u80fd\u96c6\u4e0d\u5b8c\u5168\u4e00\u81f4\uff0c\u627e\u529f\u80fd\u524d\u5148\u786e\u8ba4\u81ea\u5df1\u5f00\u7684\u662f\u54ea\u4e2a\u3002\u4fdd\u5b58\u7684 .ggb<\/code> \u6587\u4ef6\u5728\u4e0d\u540c\u7248\u672c\u95f4\u5076\u5c14\u4f1a\u6709\u517c\u5bb9\u63d0\u793a\uff0c\u91cd\u8981\u5de5\u7a0b\u5efa\u8bae\u540c\u65f6\u5bfc\u51fa\u4e00\u4efd PDF \u6216\u56fe\u7247\u7559\u5e95\u3002\u53e6\u5916\u5b83\u4e0d\u505a\u7b26\u53f7\u63a8\u5bfc\u7684\u300c\u8bc1\u660e\u300d\uff0c\u53ea\u80fd\u7b97\uff0c\u4e0d\u80fd\u66ff\u4f60\u5199\u8bba\u8bc1\u8fc7\u7a0b\u3002<\/p>\n

      \u5c0f\u7ed3<\/h2>\n

      GeoGebra \u7684\u4ef7\u503c\u4e0d\u5728\u4e8e\u300c\u529f\u80fd\u591a\u300d\uff0c\u800c\u5728\u4e8e\u5b83\u628a\u62bd\u8c61\u5173\u7cfb\u53d8\u6210\u4e86\u53ef\u4ee5\u62d6\u52a8\u7684\u5b9e\u4f53\u3002\u4e00\u4e2a\u6ed1\u5757\u9876\u5341\u5f20\u9759\u6001\u63d2\u56fe\uff0c\u8fd9\u53e5\u8bdd\u5728\u6570\u5b66\u6559\u5b66\u91cc\u662f\u771f\u7684\u3002\u514d\u8d39\u3001\u5f00\u6e90\u3001\u8de8\u5e73\u53f0\uff0c\u88c5\u4e00\u4e2a\u653e\u5728\u7535\u8111\u91cc\uff0c\u65e9\u665a\u7528\u5f97\u4e0a\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

      \u5b66\u6570\u5b66\u6700\u96be\u53d7\u7684\u73af\u8282\uff0c\u5f80\u5f80\u4e0d\u662f\u63a8\u5bfc\uff0c\u800c\u662f\u300c\u770b\u4e0d\u89c1\u300d\u3002\u8bfe\u672c\u4e0a\u8bb2\u4e8c\u6b21\u51fd\u6570\u7684\u5f00\u53e3\u65b9\u5411\u968f\u7cfb\u6570\u53d8\u5316\uff0c\u914d\u4e86\u4e00\u5f20\u9759\u6001\u56fe\uff1b\u8001\u5e08\u8bb2\u4e09\u89d2\u51fd\u6570\u5468\u671f\uff0c\u9ed1\u677f\u4e0a\u753b\u4e09\u6761\u6b63\u5f26\u66f2\u7ebf\u5c31\u4e0b\u8bfe\u4e86\u3002\u60f3\u81ea\u5df1\u9a8c\u8bc1\u4e00\u4e0b\uff0c\u8981\u4e48\u624b\u7ed8\u5750\u6807\u7eb8\uff0c\u8981\u4e48\u6253\u5f00 Excel \u786c\u51d1\u6563\u70b9\u56fe\u2014\u2014\u540e\u8005\u8fde\u4e00\u6761\u5e73\u6ed1\u66f2\u7ebf<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[2],"tags":[],"class_list":["post-249","post","type-post","status-publish","format-standard","hentry","category-2"],"_links":{"self":[{"href":"https:\/\/laoke.pw\/index.php?rest_route=\/wp\/v2\/posts\/249","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/laoke.pw\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/laoke.pw\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/laoke.pw\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/laoke.pw\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=249"}],"version-history":[{"count":0,"href":"https:\/\/laoke.pw\/index.php?rest_route=\/wp\/v2\/posts\/249\/revisions"}],"wp:attachment":[{"href":"https:\/\/laoke.pw\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=249"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/laoke.pw\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=249"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/laoke.pw\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=249"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}