跳到内容
当前位置：首页>课件>AI课件/交互式课件制作边界:三看三不

AI课件/交互式课件制作边界:三看三不

  • 2026-09-18 20:35:50
AI课件/交互式课件制作边界:三看三不
滚一滚 · 实验室
换一个形状，中心点的轨迹会变吗？

选择一个形状，或直接拖动"边数"滑块，观察中心点（红色轨迹）的起伏变化。

三角形正方形五边形六边形十边形圆（0颠簸）
4 条边
▶ 开始滚动重置轨迹
当前边数4
车轮"半径"（角到中心）55 px
贴地时中心到地面39 px
颠簸幅度（R − 贴地高度）16 px
再想一想
边数越多，颠簸越小——那圆是不是"唯一"答案？

当边数从 3 慢慢滑到 60，你会看到颠簸幅度不断逼近 0——这正是"圆可以看作边数无限多的正多边形"的道理，也是"距离处处相等"这一本质的体现。

但课例结尾留了一个反例：三角形车轮配上有规律凹槽的三角形轨道，一样可以平稳滚动。

想一想：车轮"必须"是圆的吗？还是说——圆只是"平地上、任意方向都要平稳"这个条件下的最优解？如果轨道本身可以配合车轮的形状设计，答案还会一样吗？
本文来自网友投稿或网络内容，如有侵犯您的权益请联系我们删除，联系邮箱：wyl860211@qq.com 。

100多个赛课/公开课课件一次性获取,省市级获奖者助力磨课,AI课程随时学,星光教研等你加入

基本 文件 流程 错误 SQL 调试
  1. 请求信息 : 2026-09-20 23:01:13 HTTP/1.1 GET : http://a.sjds.net/a/519005.html
  2. 运行时间 : 0.074396s [ 吞吐率：13.44req/s ] 内存消耗：4,291.40kb 文件加载：140
  3. 缓存信息 : 0 reads,0 writes
  4. 会话信息 : SESSION_ID=e8b91b8d7f737e839a9ccf51630369d4
  1. /www/wwwroot/a.sjds.net/public/index.php ( 0.79 KB )
  2. /www/wwwroot/a.sjds.net/vendor/autoload.php ( 0.17 KB )
  3. /www/wwwroot/a.sjds.net/vendor/composer/autoload_real.php ( 2.49 KB )
  4. /www/wwwroot/a.sjds.net/vendor/composer/platform_check.php ( 0.90 KB )
  5. /www/wwwroot/a.sjds.net/vendor/composer/ClassLoader.php ( 14.03 KB )
  6. /www/wwwroot/a.sjds.net/vendor/composer/autoload_static.php ( 4.90 KB )
  7. /www/wwwroot/a.sjds.net/vendor/topthink/think-helper/src/helper.php ( 8.34 KB )
  8. /www/wwwroot/a.sjds.net/vendor/topthink/think-validate/src/helper.php ( 2.19 KB )
  9. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/helper.php ( 1.47 KB )
  10. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/stubs/load_stubs.php ( 0.16 KB )
  11. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/Exception.php ( 1.69 KB )
  12. /www/wwwroot/a.sjds.net/vendor/topthink/think-container/src/Facade.php ( 2.71 KB )
  13. /www/wwwroot/a.sjds.net/vendor/symfony/deprecation-contracts/function.php ( 0.99 KB )
  14. /www/wwwroot/a.sjds.net/vendor/symfony/polyfill-mbstring/bootstrap.php ( 8.26 KB )
  15. /www/wwwroot/a.sjds.net/vendor/symfony/polyfill-mbstring/bootstrap80.php ( 9.78 KB )
  16. /www/wwwroot/a.sjds.net/vendor/symfony/var-dumper/Resources/functions/dump.php ( 1.49 KB )
  17. /www/wwwroot/a.sjds.net/vendor/topthink/think-dumper/src/helper.php ( 0.18 KB )
  18. /www/wwwroot/a.sjds.net/vendor/symfony/var-dumper/VarDumper.php ( 4.30 KB )
  19. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/App.php ( 15.30 KB )
  20. /www/wwwroot/a.sjds.net/vendor/topthink/think-container/src/Container.php ( 15.76 KB )
  21. /www/wwwroot/a.sjds.net/vendor/psr/container/src/ContainerInterface.php ( 1.02 KB )
  22. /www/wwwroot/a.sjds.net/app/provider.php ( 0.19 KB )
  23. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/Http.php ( 6.04 KB )
  24. /www/wwwroot/a.sjds.net/vendor/topthink/think-helper/src/helper/Str.php ( 7.29 KB )
  25. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/Env.php ( 4.68 KB )
  26. /www/wwwroot/a.sjds.net/app/common.php ( 0.03 KB )
  27. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/helper.php ( 18.78 KB )
  28. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/Config.php ( 5.54 KB )
  29. /www/wwwroot/a.sjds.net/config/app.php ( 0.95 KB )
  30. /www/wwwroot/a.sjds.net/config/cache.php ( 0.78 KB )
  31. /www/wwwroot/a.sjds.net/config/console.php ( 0.23 KB )
  32. /www/wwwroot/a.sjds.net/config/cookie.php ( 0.56 KB )
  33. /www/wwwroot/a.sjds.net/config/database.php ( 2.48 KB )
  34. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/facade/Env.php ( 1.67 KB )
  35. /www/wwwroot/a.sjds.net/config/filesystem.php ( 0.61 KB )
  36. /www/wwwroot/a.sjds.net/config/lang.php ( 0.91 KB )
  37. /www/wwwroot/a.sjds.net/config/log.php ( 1.35 KB )
  38. /www/wwwroot/a.sjds.net/config/middleware.php ( 0.19 KB )
  39. /www/wwwroot/a.sjds.net/config/route.php ( 1.89 KB )
  40. /www/wwwroot/a.sjds.net/config/session.php ( 0.57 KB )
  41. /www/wwwroot/a.sjds.net/config/trace.php ( 0.34 KB )
  42. /www/wwwroot/a.sjds.net/config/view.php ( 0.82 KB )
  43. /www/wwwroot/a.sjds.net/app/event.php ( 0.25 KB )
  44. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/Event.php ( 7.67 KB )
  45. /www/wwwroot/a.sjds.net/app/service.php ( 0.13 KB )
  46. /www/wwwroot/a.sjds.net/app/AppService.php ( 0.26 KB )
  47. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/Service.php ( 1.64 KB )
  48. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/Lang.php ( 7.35 KB )
  49. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/lang/zh-cn.php ( 13.70 KB )
  50. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/initializer/Error.php ( 3.31 KB )
  51. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/initializer/RegisterService.php ( 1.33 KB )
  52. /www/wwwroot/a.sjds.net/vendor/services.php ( 0.14 KB )
  53. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/service/PaginatorService.php ( 1.52 KB )
  54. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/service/ValidateService.php ( 0.99 KB )
  55. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/service/ModelService.php ( 2.04 KB )
  56. /www/wwwroot/a.sjds.net/vendor/topthink/think-trace/src/Service.php ( 0.77 KB )
  57. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/Middleware.php ( 6.72 KB )
  58. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/initializer/BootService.php ( 0.77 KB )
  59. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/Paginator.php ( 11.86 KB )
  60. /www/wwwroot/a.sjds.net/vendor/topthink/think-validate/src/Validate.php ( 63.20 KB )
  61. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/Model.php ( 23.55 KB )
  62. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/model/concern/Attribute.php ( 21.05 KB )
  63. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/model/concern/AutoWriteData.php ( 4.21 KB )
  64. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/model/concern/Conversion.php ( 6.44 KB )
  65. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/model/concern/DbConnect.php ( 5.16 KB )
  66. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/model/concern/ModelEvent.php ( 2.33 KB )
  67. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/model/concern/RelationShip.php ( 28.29 KB )
  68. /www/wwwroot/a.sjds.net/vendor/topthink/think-helper/src/contract/Arrayable.php ( 0.09 KB )
  69. /www/wwwroot/a.sjds.net/vendor/topthink/think-helper/src/contract/Jsonable.php ( 0.13 KB )
  70. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/model/contract/Modelable.php ( 0.09 KB )
  71. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/Db.php ( 2.88 KB )
  72. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/DbManager.php ( 8.52 KB )
  73. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/Log.php ( 6.28 KB )
  74. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/Manager.php ( 3.92 KB )
  75. /www/wwwroot/a.sjds.net/vendor/psr/log/src/LoggerTrait.php ( 2.69 KB )
  76. /www/wwwroot/a.sjds.net/vendor/psr/log/src/LoggerInterface.php ( 2.71 KB )
  77. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/Cache.php ( 4.92 KB )
  78. /www/wwwroot/a.sjds.net/vendor/psr/simple-cache/src/CacheInterface.php ( 4.71 KB )
  79. /www/wwwroot/a.sjds.net/vendor/topthink/think-helper/src/helper/Arr.php ( 16.63 KB )
  80. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/cache/driver/File.php ( 7.84 KB )
  81. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/cache/Driver.php ( 9.03 KB )
  82. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/contract/CacheHandlerInterface.php ( 1.99 KB )
  83. /www/wwwroot/a.sjds.net/app/Request.php ( 0.09 KB )
  84. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/Request.php ( 55.78 KB )
  85. /www/wwwroot/a.sjds.net/app/middleware.php ( 0.25 KB )
  86. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/Pipeline.php ( 2.61 KB )
  87. /www/wwwroot/a.sjds.net/vendor/topthink/think-trace/src/TraceDebug.php ( 3.40 KB )
  88. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/middleware/SessionInit.php ( 1.94 KB )
  89. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/Session.php ( 1.80 KB )
  90. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/session/driver/File.php ( 6.27 KB )
  91. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/contract/SessionHandlerInterface.php ( 0.87 KB )
  92. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/session/Store.php ( 7.12 KB )
  93. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/Route.php ( 23.73 KB )
  94. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/route/RuleName.php ( 5.75 KB )
  95. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/route/Domain.php ( 2.53 KB )
  96. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/route/RuleGroup.php ( 22.43 KB )
  97. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/route/Rule.php ( 26.95 KB )
  98. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/route/RuleItem.php ( 9.78 KB )
  99. /www/wwwroot/a.sjds.net/route/app.php ( 1.72 KB )
  100. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/facade/Route.php ( 4.70 KB )
  101. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/route/dispatch/Controller.php ( 4.74 KB )
  102. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/route/Dispatch.php ( 10.44 KB )
  103. /www/wwwroot/a.sjds.net/app/controller/Index.php ( 4.81 KB )
  104. /www/wwwroot/a.sjds.net/app/BaseController.php ( 2.05 KB )
  105. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/facade/Db.php ( 0.93 KB )
  106. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/db/connector/Mysql.php ( 5.44 KB )
  107. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/db/PDOConnection.php ( 52.47 KB )
  108. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/db/Connection.php ( 8.39 KB )
  109. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/db/ConnectionInterface.php ( 4.57 KB )
  110. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/db/builder/Mysql.php ( 16.58 KB )
  111. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/db/Builder.php ( 24.06 KB )
  112. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/db/BaseBuilder.php ( 27.50 KB )
  113. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/db/Query.php ( 15.71 KB )
  114. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/db/BaseQuery.php ( 45.13 KB )
  115. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/db/concern/TimeFieldQuery.php ( 7.43 KB )
  116. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/db/concern/AggregateQuery.php ( 3.26 KB )
  117. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/db/concern/ModelRelationQuery.php ( 20.07 KB )
  118. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/db/concern/ParamsBind.php ( 3.66 KB )
  119. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/db/concern/ResultOperation.php ( 7.01 KB )
  120. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/db/concern/WhereQuery.php ( 19.37 KB )
  121. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/db/concern/JoinAndViewQuery.php ( 7.11 KB )
  122. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/db/concern/TableFieldInfo.php ( 2.63 KB )
  123. /www/wwwroot/a.sjds.net/vendor/topthink/think-orm/src/db/concern/Transaction.php ( 2.77 KB )
  124. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/log/driver/File.php ( 5.96 KB )
  125. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/contract/LogHandlerInterface.php ( 0.86 KB )
  126. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/log/Channel.php ( 3.89 KB )
  127. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/event/LogRecord.php ( 1.02 KB )
  128. /www/wwwroot/a.sjds.net/vendor/topthink/think-helper/src/Collection.php ( 16.47 KB )
  129. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/facade/View.php ( 1.70 KB )
  130. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/View.php ( 4.39 KB )
  131. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/Response.php ( 8.81 KB )
  132. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/response/View.php ( 3.29 KB )
  133. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/Cookie.php ( 6.06 KB )
  134. /www/wwwroot/a.sjds.net/vendor/topthink/think-view/src/Think.php ( 8.38 KB )
  135. /www/wwwroot/a.sjds.net/vendor/topthink/framework/src/think/contract/TemplateHandlerInterface.php ( 1.60 KB )
  136. /www/wwwroot/a.sjds.net/vendor/topthink/think-template/src/Template.php ( 46.61 KB )
  137. /www/wwwroot/a.sjds.net/vendor/topthink/think-template/src/template/driver/File.php ( 2.41 KB )
  138. /www/wwwroot/a.sjds.net/vendor/topthink/think-template/src/template/contract/DriverInterface.php ( 0.86 KB )
  139. /www/wwwroot/a.sjds.net/runtime/temp/64ad42204038485b18ca907186edb47b.php ( 8.05 KB )
  140. /www/wwwroot/a.sjds.net/vendor/topthink/think-trace/src/Html.php ( 4.42 KB )
  1. CONNECT:[ UseTime:0.000566s ] mysql:host=172.18.0.4;port=3306;dbname=a_sjds;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000688s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000333s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000322s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000526s ]
  6. SELECT * FROM `set` [ RunTime:0.000286s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000634s ]
  8. SELECT * FROM `article` WHERE `id` = 519005 LIMIT 1 [ RunTime:0.000327s ]
  9. UPDATE `article` SET `lasttime` = 1789916473 WHERE `id` = 519005 [ RunTime:0.001364s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 66 LIMIT 1 [ RunTime:0.000344s ]
  11. SELECT * FROM `article` WHERE `id` < 519005 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000426s ]
  12. SELECT * FROM `article` WHERE `id` > 519005 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.000434s ]
  13. SELECT * FROM `article` WHERE `id` < 519005 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.000694s ]
  14. SELECT * FROM `article` WHERE `id` < 519005 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.000669s ]
  15. SELECT * FROM `article` WHERE `id` < 519005 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.000543s ]
0.086627s