让鸽子开公交车？看不见的数学如何影响我们的日常-畅读网

　　　　

让鸽子开公交车？看不见的数学如何影响我们的日常

作者：伊恩·斯图尔特

格式：

mobi/epub/pdf/awz3

浏览量：

108次

扫码关注公众号

温馨提示：书籍来自网络收集，版权归原作者所有，仅做学习试读,下载后请24小时内删除,侵权删(联系:214440596@qq.com)

所属分类:

科学技术 >> 自然科学

点击下载

收藏该图书

内容简介:

许多人认为数学离我们很远，除了买菜根本用不着。但他们错了。在英国，280万数学科学从业者一年就为经济贡献了2080亿英镑——也就是说，10%的劳动力贡献了16%的经济产值。为什么公众对数学的认识与现实之间存在如此巨大的鸿沟？作者在书中探讨了这个问题，并从政治、医疗、气候、出行、娱乐、信息安全、智能生活等多个角度切入，展示了在日常生活的背后，数学如何以令人惊讶的方式发挥着至关重要的作用。

相关推荐

企业员工的知识分享

走进云南茶树王国

离离原上花

新时代高校巡察实践、理论与制度创新：西南财经大学党风廉政建设与巡视巡察研究成果集

客服

基本文件流程错误 SQL 调试

/www/wwwroot/a.letssm.cn/public/index.php ( 0.79 KB )
/www/wwwroot/a.letssm.cn/vendor/autoload.php ( 0.75 KB )
/www/wwwroot/a.letssm.cn/vendor/composer/autoload_real.php ( 1.70 KB )
/www/wwwroot/a.letssm.cn/vendor/composer/platform_check.php ( 0.90 KB )
/www/wwwroot/a.letssm.cn/vendor/composer/ClassLoader.php ( 15.69 KB )
/www/wwwroot/a.letssm.cn/vendor/composer/autoload_static.php ( 5.87 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-helper/src/helper.php ( 7.35 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/stubs/load_stubs.php ( 0.16 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/Exception.php ( 1.69 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/Facade.php ( 2.71 KB )
/www/wwwroot/a.letssm.cn/vendor/symfony/polyfill-mbstring/bootstrap.php ( 7.33 KB )
/www/wwwroot/a.letssm.cn/vendor/symfony/polyfill-php72/bootstrap.php ( 1.89 KB )
/www/wwwroot/a.letssm.cn/vendor/symfony/polyfill-php80/bootstrap.php ( 1.50 KB )
/www/wwwroot/a.letssm.cn/vendor/symfony/var-dumper/Resources/functions/dump.php ( 0.79 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-captcha/src/helper.php ( 1.37 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/App.php ( 14.17 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/Container.php ( 15.38 KB )
/www/wwwroot/a.letssm.cn/vendor/psr/container/src/ContainerInterface.php ( 1.02 KB )
/www/wwwroot/a.letssm.cn/app/provider.php ( 0.19 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/Http.php ( 6.12 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-helper/src/helper/Str.php ( 7.28 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/Env.php ( 4.64 KB )
/www/wwwroot/a.letssm.cn/app/common.php ( 14.84 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/helper.php ( 18.44 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/Config.php ( 5.03 KB )
/www/wwwroot/a.letssm.cn/config/app.php ( 1.05 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/facade/Env.php ( 1.67 KB )
/www/wwwroot/a.letssm.cn/config/cache.php ( 0.80 KB )
/www/wwwroot/a.letssm.cn/config/captcha.php ( 1.02 KB )
/www/wwwroot/a.letssm.cn/config/console.php ( 0.23 KB )
/www/wwwroot/a.letssm.cn/config/cookie.php ( 0.56 KB )
/www/wwwroot/a.letssm.cn/config/database.php ( 2.26 KB )
/www/wwwroot/a.letssm.cn/config/default.php ( 2.37 KB )
/www/wwwroot/a.letssm.cn/config/filesystem.php ( 0.63 KB )
/www/wwwroot/a.letssm.cn/config/jump.php ( 0.63 KB )
/www/wwwroot/a.letssm.cn/config/lang.php ( 0.81 KB )
/www/wwwroot/a.letssm.cn/config/log.php ( 1.37 KB )
/www/wwwroot/a.letssm.cn/config/middleware.php ( 0.19 KB )
/www/wwwroot/a.letssm.cn/config/project.php ( 0.92 KB )
/www/wwwroot/a.letssm.cn/config/route.php ( 1.54 KB )
/www/wwwroot/a.letssm.cn/config/session.php ( 0.57 KB )
/www/wwwroot/a.letssm.cn/config/trace.php ( 0.34 KB )
/www/wwwroot/a.letssm.cn/config/view.php ( 1.12 KB )
/www/wwwroot/a.letssm.cn/app/Request.php ( 0.09 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/Request.php ( 54.04 KB )
/www/wwwroot/a.letssm.cn/app/event.php ( 0.25 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/Event.php ( 6.96 KB )
/www/wwwroot/a.letssm.cn/app/service.php ( 0.13 KB )
/www/wwwroot/a.letssm.cn/app/AppService.php ( 0.26 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/Service.php ( 1.67 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/Lang.php ( 7.60 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/lang/zh-cn.php ( 12.88 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/initializer/Error.php ( 3.27 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/initializer/RegisterService.php ( 1.33 KB )
/www/wwwroot/a.letssm.cn/vendor/services.php ( 0.22 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/service/PaginatorService.php ( 1.52 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/service/ValidateService.php ( 0.99 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/service/ModelService.php ( 1.76 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-captcha/src/CaptchaService.php ( 0.52 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-multi-app/src/Service.php ( 1.08 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-trace/src/Service.php ( 0.77 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/Middleware.php ( 6.78 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/initializer/BootService.php ( 0.77 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/Paginator.php ( 11.80 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/Validate.php ( 46.10 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/Model.php ( 25.28 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-helper/src/contract/Arrayable.php ( 0.09 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-helper/src/contract/Jsonable.php ( 0.13 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/model/concern/Attribute.php ( 17.61 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/model/concern/RelationShip.php ( 26.12 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/model/concern/ModelEvent.php ( 2.27 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/model/concern/TimeStamp.php ( 5.70 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/model/concern/Conversion.php ( 10.41 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/Db.php ( 2.87 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/DbManager.php ( 8.49 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/Log.php ( 8.50 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/Manager.php ( 3.98 KB )
/www/wwwroot/a.letssm.cn/vendor/psr/log/Psr/Log/LoggerInterface.php ( 3.04 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/Cache.php ( 4.79 KB )
/www/wwwroot/a.letssm.cn/vendor/psr/simple-cache/src/CacheInterface.php ( 4.50 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-helper/src/helper/Arr.php ( 15.54 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/cache/driver/File.php ( 7.42 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/cache/Driver.php ( 8.06 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/contract/CacheHandlerInterface.php ( 2.25 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/Console.php ( 22.65 KB )
/www/wwwroot/a.letssm.cn/app/middleware.php ( 0.25 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/Pipeline.php ( 2.61 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-trace/src/TraceDebug.php ( 2.94 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/middleware/SessionInit.php ( 2.06 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/Session.php ( 1.80 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/session/driver/File.php ( 6.28 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/contract/SessionHandlerInterface.php ( 0.87 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/session/Store.php ( 7.26 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-multi-app/src/MultiApp.php ( 7.07 KB )
/www/wwwroot/a.letssm.cn/app/index/common.php ( 0.99 KB )
/www/wwwroot/a.letssm.cn/app/index/config/app.php ( 0.30 KB )
/www/wwwroot/a.letssm.cn/app/index/config/route.php ( 0.27 KB )
/www/wwwroot/a.letssm.cn/app/index/event.php ( 0.28 KB )
/www/wwwroot/a.letssm.cn/app/index/middleware.php ( 0.17 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/Route.php ( 23.96 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/route/RuleName.php ( 5.33 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/route/Domain.php ( 5.55 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/route/RuleGroup.php ( 13.61 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/route/Rule.php ( 22.85 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/route/RuleItem.php ( 8.81 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/route/dispatch/Url.php ( 3.42 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/route/dispatch/Controller.php ( 6.61 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/route/Dispatch.php ( 6.49 KB )
/www/wwwroot/a.letssm.cn/app/index/http/middleware/Login.php ( 1.40 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/facade/Cookie.php ( 1.49 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/Cookie.php ( 6.28 KB )
/www/wwwroot/a.letssm.cn/app/index/cache/TokenCache.php ( 0.89 KB )
/www/wwwroot/a.letssm.cn/app/common/cache/CacheBase.php ( 2.06 KB )
/www/wwwroot/a.letssm.cn/app/index/validate/Token.php ( 1.69 KB )
/www/wwwroot/a.letssm.cn/app/index/controller/Goods.php ( 2.81 KB )
/www/wwwroot/a.letssm.cn/app/index/controller/FrontBase.php ( 6.39 KB )
/www/wwwroot/a.letssm.cn/app/BaseController.php ( 2.03 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/facade/View.php ( 1.71 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/View.php ( 4.41 KB )
/www/wwwroot/a.letssm.cn/app/index/logic/GoodsLogic.php ( 18.68 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/facade/Cache.php ( 2.02 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/facade/Db.php ( 0.94 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/db/connector/Mysql.php ( 4.39 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/db/PDOConnection.php ( 52.45 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/db/Connection.php ( 7.67 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/db/ConnectionInterface.php ( 4.56 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/db/builder/Mysql.php ( 15.93 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/db/Builder.php ( 41.58 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/db/Query.php ( 10.64 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/db/BaseQuery.php ( 36.47 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/db/concern/TimeFieldQuery.php ( 7.50 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/db/concern/AggregateQuery.php ( 3.26 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/db/concern/ModelRelationQuery.php ( 16.06 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/db/concern/ResultOperation.php ( 6.29 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/db/concern/Transaction.php ( 2.85 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/db/concern/WhereQuery.php ( 16.22 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/db/concern/JoinAndViewQuery.php ( 6.86 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/db/concern/ParamsBind.php ( 3.36 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/db/concern/TableFieldInfo.php ( 2.51 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/log/driver/File.php ( 6.17 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/contract/LogHandlerInterface.php ( 0.86 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/log/Channel.php ( 6.54 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/event/LogRecord.php ( 0.86 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-helper/src/Collection.php ( 16.10 KB )
/www/wwwroot/a.letssm.cn/app/common/server/UrlServer.php ( 2.33 KB )
/www/wwwroot/a.letssm.cn/app/common/server/ConfigServer.php ( 3.31 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/facade/Config.php ( 1.37 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-view/src/Think.php ( 8.42 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-template/src/Template.php ( 46.85 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-template/src/template/driver/File.php ( 2.33 KB )
/www/wwwroot/a.letssm.cn/app/index/model/Goods.php ( 1.79 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/db/CacheItem.php ( 4.57 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/cache/TagSet.php ( 3.23 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/Response.php ( 8.60 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/response/View.php ( 3.27 KB )
/www/wwwroot/a.letssm.cn/runtime/index/temp/a94256b099ba0fd30aa48881361cb441.php ( 29.34 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/facade/Route.php ( 4.88 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-multi-app/src/Url.php ( 7.70 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/framework/src/think/route/Url.php ( 14.66 KB )
/www/wwwroot/a.letssm.cn/app/index/controller/Advert.php ( 1.38 KB )
/www/wwwroot/a.letssm.cn/app/index/logic/AdLogic.php ( 2.47 KB )
/www/wwwroot/a.letssm.cn/runtime/index/temp/795e5d0af82994c3e0ee7f408c73f8d4.php ( 0.45 KB )
/www/wwwroot/a.letssm.cn/app/common/taglib/ht/tagLists.php ( 3.93 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-orm/src/model/Collection.php ( 6.78 KB )
/www/wwwroot/a.letssm.cn/vendor/topthink/think-trace/src/Html.php ( 4.49 KB )

CONNECT:[ UseTime:0.006524s ] mysql:host=127.0.0.1;port=3306;dbname=mq;charset=utf8mb4
SHOW FULL COLUMNS FROM `ls_goods_category` [ RunTime:0.004943s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`is_show`,`is_recommend` FROM `ls_goods_category` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 1 ORDER BY `id` ASC,`sort` DESC [ RunTime:0.002436s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`is_show`,`is_recommend` FROM `ls_goods_category` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 2 ORDER BY `id` ASC,`sort` DESC [ RunTime:0.003261s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`is_show`,`is_recommend` FROM `ls_goods_category` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 3 ORDER BY `sort` DESC [ RunTime:0.001898s ]
SHOW FULL COLUMNS FROM `ls_nav` [ RunTime:0.008946s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`link`,`module`,`is_show`,`is_recommend` FROM `ls_nav` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 1 ORDER BY `id` ASC,`sort` DESC [ RunTime:0.008580s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`link`,`module`,`is_show`,`is_recommend` FROM `ls_nav` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 2 ORDER BY `id` ASC,`sort` DESC [ RunTime:0.005190s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`link`,`module`,`is_show`,`is_recommend` FROM `ls_nav` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 3 ORDER BY `sort` DESC [ RunTime:0.002888s ]
SHOW FULL COLUMNS FROM `ls_friendly_link` [ RunTime:0.009614s ]
SELECT * FROM `ls_friendly_link` WHERE `is_show` = 1 AND `del` = 0 ORDER BY `id` DESC,`sort` DESC [ RunTime:0.006159s ]
SHOW FULL COLUMNS FROM `ls_goods` [ RunTime:0.003927s ]
SELECT * FROM `ls_goods` WHERE `id` = 157361 AND `status` = 1 LIMIT 1 [ RunTime:0.002205s ]
UPDATE `ls_goods` SET `click_count` = 108 , `update_time` = 1771425235 WHERE `id` = 157361 [ RunTime:0.002267s ]
SELECT `name`,`first_category_id`,`second_category_id` FROM `ls_goods` WHERE `id` = 157361 LIMIT 1 [ RunTime:0.010015s ]
SELECT `id`,`name` FROM `ls_goods_category` WHERE `id` = 48 LIMIT 1 [ RunTime:0.002086s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`is_show`,`is_recommend` FROM `ls_goods_category` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 1 ORDER BY `id` ASC,`sort` DESC [ RunTime:0.001828s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`is_show`,`is_recommend` FROM `ls_goods_category` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 2 ORDER BY `id` ASC,`sort` DESC [ RunTime:0.002732s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`is_show`,`is_recommend` FROM `ls_goods_category` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 3 ORDER BY `sort` DESC [ RunTime:0.003888s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`link`,`module`,`is_show`,`is_recommend` FROM `ls_nav` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 1 ORDER BY `id` ASC,`sort` DESC [ RunTime:0.005966s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`link`,`module`,`is_show`,`is_recommend` FROM `ls_nav` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 2 ORDER BY `id` ASC,`sort` DESC [ RunTime:0.003828s ]
SELECT `id`,`name`,`pid`,`image`,`level`,`link`,`module`,`is_show`,`is_recommend` FROM `ls_nav` WHERE `is_show` = 1 AND `del` = 0 AND `level` = 3 ORDER BY `sort` DESC [ RunTime:0.003363s ]
SELECT * FROM `ls_friendly_link` WHERE `is_show` = 1 AND `del` = 0 ORDER BY `id` DESC,`sort` DESC [ RunTime:0.004347s ]
SHOW FULL COLUMNS FROM `ls_ad` [ RunTime:0.009305s ]
SELECT `a`.*,`ap`.`width`,`ap`.`height` FROM `ls_ad` `a` INNER JOIN `ls_ad_position` `ap` ON `a`.`pid`=`ap`.`id` WHERE `pid` = 10 AND `ap`.`client` = '2' AND `a`.`status` = '1' AND `a`.`del` = '0' AND `ap`.`status` = '1' AND `ap`.`del` = '0' ORDER BY `sort` DESC,`id` DESC [ RunTime:0.022723s ]
SELECT `id`,`name` FROM `ls_goods_category` WHERE `id` = 5 LIMIT 1 [ RunTime:0.002002s ]
SELECT `id`,`name` FROM `ls_goods_category` WHERE `id` = 48 LIMIT 1 [ RunTime:0.007646s ]
SELECT `a`.*,`ap`.`width`,`ap`.`height` FROM `ls_ad` `a` INNER JOIN `ls_ad_position` `ap` ON `a`.`pid`=`ap`.`id` WHERE `pid` = 11 AND `ap`.`client` = '2' AND `a`.`status` = '1' AND `a`.`del` = '0' AND `ap`.`status` = '1' AND `ap`.`del` = '0' ORDER BY `sort` DESC,`id` DESC [ RunTime:0.009494s ]
SELECT `a`.*,`ap`.`width`,`ap`.`height` FROM `ls_ad` `a` INNER JOIN `ls_ad_position` `ap` ON `a`.`pid`=`ap`.`id` WHERE `pid` = 14 AND `ap`.`client` = '2' AND `a`.`status` = '1' AND `a`.`del` = '0' AND `ap`.`status` = '1' AND `ap`.`del` = '0' ORDER BY `sort` DESC,`id` DESC [ RunTime:0.003043s ]
SELECT * FROM `ls_goods` WHERE `del` = 0 AND `status` = 1 AND `create_time` <= 1771425175 ORDER BY `create_time` DESC LIMIT 5 [ RunTime:1.659217s ]

2.538785s

ShowPageTrace