交叉小径的花园：趣说数学探索史-宝阳悦读网

交叉小径的花园：趣说数学探索史

作者：王亚晖

格式：

mobi/epub/pdf/awz3

浏览量：

105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:1401211620@qq.com)

所属分类:

科学技术 >> 科普读物

点击下载

收藏该图书

内容简介:

一本几乎没有公式和方程的数学书，带你穿越回千百年前，与世界上最聪明的大脑们一起探索数学的世界。

相关推荐

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/mq59.com/public/index.php ( 0.79 KB )
/www/wwwroot/mq59.com/vendor/autoload.php ( 0.75 KB )
/www/wwwroot/mq59.com/vendor/composer/autoload_real.php ( 1.70 KB )
/www/wwwroot/mq59.com/vendor/composer/platform_check.php ( 0.90 KB )
/www/wwwroot/mq59.com/vendor/composer/ClassLoader.php ( 15.69 KB )
/www/wwwroot/mq59.com/vendor/composer/autoload_static.php ( 5.87 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-helper/src/helper.php ( 7.35 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/stubs/load_stubs.php ( 0.16 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/Exception.php ( 1.69 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/Facade.php ( 2.71 KB )
/www/wwwroot/mq59.com/vendor/symfony/polyfill-mbstring/bootstrap.php ( 7.33 KB )
/www/wwwroot/mq59.com/vendor/symfony/polyfill-php72/bootstrap.php ( 1.89 KB )
/www/wwwroot/mq59.com/vendor/symfony/polyfill-php80/bootstrap.php ( 1.50 KB )
/www/wwwroot/mq59.com/vendor/symfony/var-dumper/Resources/functions/dump.php ( 0.79 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-captcha/src/helper.php ( 1.37 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/App.php ( 14.17 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/Container.php ( 15.38 KB )
/www/wwwroot/mq59.com/vendor/psr/container/src/ContainerInterface.php ( 1.02 KB )
/www/wwwroot/mq59.com/app/provider.php ( 0.19 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/Http.php ( 6.12 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-helper/src/helper/Str.php ( 7.28 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/Env.php ( 4.64 KB )
/www/wwwroot/mq59.com/app/common.php ( 14.84 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/helper.php ( 18.44 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/Config.php ( 5.03 KB )
/www/wwwroot/mq59.com/config/app.php ( 1.05 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/facade/Env.php ( 1.67 KB )
/www/wwwroot/mq59.com/config/cache.php ( 0.80 KB )
/www/wwwroot/mq59.com/config/captcha.php ( 1.02 KB )
/www/wwwroot/mq59.com/config/console.php ( 0.23 KB )
/www/wwwroot/mq59.com/config/cookie.php ( 0.56 KB )
/www/wwwroot/mq59.com/config/database.php ( 2.25 KB )
/www/wwwroot/mq59.com/config/default.php ( 2.39 KB )
/www/wwwroot/mq59.com/config/filesystem.php ( 0.63 KB )
/www/wwwroot/mq59.com/config/jump.php ( 0.63 KB )
/www/wwwroot/mq59.com/config/lang.php ( 0.81 KB )
/www/wwwroot/mq59.com/config/log.php ( 1.37 KB )
/www/wwwroot/mq59.com/config/middleware.php ( 0.19 KB )
/www/wwwroot/mq59.com/config/project.php ( 0.61 KB )
/www/wwwroot/mq59.com/config/route.php ( 1.54 KB )
/www/wwwroot/mq59.com/config/session.php ( 0.57 KB )
/www/wwwroot/mq59.com/config/trace.php ( 0.34 KB )
/www/wwwroot/mq59.com/config/view.php ( 1.12 KB )
/www/wwwroot/mq59.com/app/Request.php ( 0.09 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/Request.php ( 54.04 KB )
/www/wwwroot/mq59.com/app/event.php ( 0.25 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/Event.php ( 6.96 KB )
/www/wwwroot/mq59.com/app/service.php ( 0.13 KB )
/www/wwwroot/mq59.com/app/AppService.php ( 0.26 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/Service.php ( 1.67 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/Lang.php ( 7.60 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/lang/zh-cn.php ( 12.88 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/initializer/Error.php ( 3.27 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/initializer/RegisterService.php ( 1.33 KB )
/www/wwwroot/mq59.com/vendor/services.php ( 0.22 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/service/PaginatorService.php ( 1.52 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/service/ValidateService.php ( 0.99 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/service/ModelService.php ( 1.76 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-captcha/src/CaptchaService.php ( 0.52 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-multi-app/src/Service.php ( 1.08 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-trace/src/Service.php ( 0.77 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/Middleware.php ( 6.78 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/initializer/BootService.php ( 0.77 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/Paginator.php ( 11.80 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/Validate.php ( 46.10 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/Model.php ( 25.28 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/model/concern/Attribute.php ( 17.61 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/model/concern/RelationShip.php ( 26.12 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/model/concern/ModelEvent.php ( 2.27 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/model/concern/TimeStamp.php ( 5.70 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/model/concern/Conversion.php ( 10.41 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-helper/src/contract/Arrayable.php ( 0.09 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-helper/src/contract/Jsonable.php ( 0.13 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/Db.php ( 2.87 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/DbManager.php ( 8.49 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/Log.php ( 8.50 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/Manager.php ( 3.98 KB )
/www/wwwroot/mq59.com/vendor/psr/log/Psr/Log/LoggerInterface.php ( 3.04 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/Cache.php ( 4.79 KB )
/www/wwwroot/mq59.com/vendor/psr/simple-cache/src/CacheInterface.php ( 4.50 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-helper/src/helper/Arr.php ( 15.54 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/cache/driver/File.php ( 7.42 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/cache/Driver.php ( 8.06 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/contract/CacheHandlerInterface.php ( 2.25 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/Console.php ( 22.65 KB )
/www/wwwroot/mq59.com/app/middleware.php ( 0.25 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/Pipeline.php ( 2.61 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-trace/src/TraceDebug.php ( 2.94 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/middleware/SessionInit.php ( 2.06 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/Session.php ( 1.80 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/session/driver/File.php ( 6.28 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/contract/SessionHandlerInterface.php ( 0.87 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/session/Store.php ( 7.26 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-multi-app/src/MultiApp.php ( 7.07 KB )
/www/wwwroot/mq59.com/app/index/common.php ( 1.26 KB )
/www/wwwroot/mq59.com/app/index/config/app.php ( 1.42 KB )
/www/wwwroot/mq59.com/app/index/config/route.php ( 1.26 KB )
/www/wwwroot/mq59.com/app/index/event.php ( 0.28 KB )
/www/wwwroot/mq59.com/app/index/middleware.php ( 0.17 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/Route.php ( 23.96 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/route/RuleName.php ( 5.33 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/route/Domain.php ( 5.55 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/route/RuleGroup.php ( 13.61 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/route/Rule.php ( 22.85 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/route/RuleItem.php ( 8.81 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/route/dispatch/Url.php ( 3.42 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/route/dispatch/Controller.php ( 6.61 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/route/Dispatch.php ( 6.49 KB )
/www/wwwroot/mq59.com/app/index/http/middleware/Login.php ( 2.50 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/facade/Cookie.php ( 1.49 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/Cookie.php ( 6.28 KB )
/www/wwwroot/mq59.com/app/index/cache/TokenCache.php ( 1.99 KB )
/www/wwwroot/mq59.com/app/common/cache/CacheBase.php ( 3.18 KB )
/www/wwwroot/mq59.com/app/index/validate/Token.php ( 2.79 KB )
/www/wwwroot/mq59.com/app/index/controller/Goods.php ( 4.04 KB )
/www/wwwroot/mq59.com/app/index/controller/FrontBase.php ( 7.50 KB )
/www/wwwroot/mq59.com/app/BaseController.php ( 2.03 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/facade/View.php ( 1.71 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/View.php ( 4.41 KB )
/www/wwwroot/mq59.com/app/index/logic/GoodsLogic.php ( 18.57 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/facade/Cache.php ( 2.02 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/facade/Db.php ( 0.94 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/db/connector/Mysql.php ( 4.39 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/db/PDOConnection.php ( 52.45 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/db/Connection.php ( 7.67 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/db/ConnectionInterface.php ( 4.56 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/db/builder/Mysql.php ( 15.93 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/db/Builder.php ( 41.58 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/db/Query.php ( 10.64 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/db/BaseQuery.php ( 36.47 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/db/concern/TimeFieldQuery.php ( 7.50 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/db/concern/AggregateQuery.php ( 3.26 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/db/concern/ModelRelationQuery.php ( 16.06 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/db/concern/ResultOperation.php ( 6.29 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/db/concern/Transaction.php ( 2.85 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/db/concern/WhereQuery.php ( 16.22 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/db/concern/JoinAndViewQuery.php ( 6.86 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/db/concern/ParamsBind.php ( 3.36 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/db/concern/TableFieldInfo.php ( 2.51 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/log/driver/File.php ( 6.17 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/contract/LogHandlerInterface.php ( 0.86 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/log/Channel.php ( 6.54 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/event/LogRecord.php ( 0.86 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-helper/src/Collection.php ( 16.10 KB )
/www/wwwroot/mq59.com/app/common/server/UrlServer.php ( 3.45 KB )
/www/wwwroot/mq59.com/app/common/server/ConfigServer.php ( 4.53 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/facade/Config.php ( 1.37 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-view/src/Think.php ( 8.42 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-template/src/Template.php ( 46.85 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-template/src/template/driver/File.php ( 2.33 KB )
/www/wwwroot/mq59.com/app/index/model/Goods.php ( 2.88 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/db/CacheItem.php ( 4.57 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/cache/TagSet.php ( 3.23 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/Response.php ( 8.60 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/response/View.php ( 3.27 KB )
/www/wwwroot/mq59.com/runtime/index/temp/c48fdc783bc8d7aadba91c1d1c242429.php ( 29.37 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/facade/Route.php ( 4.88 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-multi-app/src/Url.php ( 7.70 KB )
/www/wwwroot/mq59.com/vendor/topthink/framework/src/think/route/Url.php ( 14.66 KB )
/www/wwwroot/mq59.com/app/index/controller/Advert.php ( 1.39 KB )
/www/wwwroot/mq59.com/app/index/logic/AdLogic.php ( 3.34 KB )
/www/wwwroot/mq59.com/runtime/index/temp/85b8fe3a6ccd5a4990110b023a2487c7.php ( 0.44 KB )
/www/wwwroot/mq59.com/app/common/taglib/ht/tagLists.php ( 3.93 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-orm/src/model/Collection.php ( 6.78 KB )
/www/wwwroot/mq59.com/vendor/topthink/think-trace/src/Html.php ( 4.49 KB )

CONNECT:[ UseTime:0.000691s ] mysql:host=39.109.117.202;port=3306;dbname=mq59_com;charset=utf8
SHOW FULL COLUMNS FROM `ls_goods_category` [ RunTime:0.000738s ]
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:0.000455s ]
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:0.000794s ]
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:0.000495s ]
SHOW FULL COLUMNS FROM `ls_nav` [ RunTime:0.001037s ]
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:0.000440s ]
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:0.000293s ]
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:0.000256s ]
SHOW FULL COLUMNS FROM `ls_friendly_link` [ RunTime:0.000651s ]
SELECT * FROM `ls_friendly_link` WHERE `is_show` = 1 AND `del` = 0 ORDER BY `id` DESC,`sort` DESC [ RunTime:0.000343s ]
SHOW FULL COLUMNS FROM `ls_goods` [ RunTime:0.001062s ]
SELECT * FROM `ls_goods` WHERE `id` = 155713 AND `status` = 1 LIMIT 1 [ RunTime:0.000532s ]
UPDATE `ls_goods` SET `click_count` = 105 , `update_time` = 1735228782 WHERE `id` = 155713 [ RunTime:0.000664s ]
SELECT `name`,`first_category_id`,`second_category_id` FROM `ls_goods` WHERE `id` = 155713 LIMIT 1 [ RunTime:0.000525s ]
SELECT `id`,`name` FROM `ls_goods_category` WHERE `id` = 46 LIMIT 1 [ RunTime:0.000241s ]
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:0.000460s ]
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:0.000509s ]
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:0.000394s ]
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:0.000652s ]
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:0.000317s ]
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:0.000301s ]
SELECT * FROM `ls_friendly_link` WHERE `is_show` = 1 AND `del` = 0 ORDER BY `id` DESC,`sort` DESC [ RunTime:0.000702s ]
SELECT `id`,`name` FROM `ls_goods_category` WHERE `id` = 5 LIMIT 1 [ RunTime:0.000409s ]
SELECT `id`,`name` FROM `ls_goods_category` WHERE `id` = 46 LIMIT 1 [ RunTime:0.000438s ]
SELECT * FROM `ls_goods` WHERE `del` = 0 AND `status` = 1 AND `create_time` <= 1735228722 ORDER BY `create_time` DESC LIMIT 5 [ RunTime:0.222090s ]

0.283901s