A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Cache::$apc is deprecated

Filename: libraries/Driver.php

Line Number: 188

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
Line: 22
Function: driver

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
Line: 17
Function: initiateCache

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Cache::$file is deprecated

Filename: libraries/Driver.php

Line Number: 188

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
Line: 22
Function: driver

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
Line: 17
Function: initiateCache

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents_model::$best_cnt is deprecated

Filename: ver3/Contents_model.php

Line Number: 17

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
Line: 17
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 440
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 29
Function: initMenu

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents_model::$popular_cnt is deprecated

Filename: ver3/Contents_model.php

Line Number: 18

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
Line: 18
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 440
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 29
Function: initMenu

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: is_dir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 201

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 201
Function: is_dir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_exists(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/7405536cde5e8f69b38a6d17f3433ff9.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 212

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 212
Function: file_exists

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/7405536cde5e8f69b38a6d17f3433ff9.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/7405536cde5e8f69b38a6d17f3433ff9.gif): Failed to open stream: Operation not permitted

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: is_dir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 201

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 201
Function: is_dir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_exists(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/7fc56270e7a70fa81a5935b72eacbe29.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 212

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 212
Function: file_exists

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/7fc56270e7a70fa81a5935b72eacbe29.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/7fc56270e7a70fa81a5935b72eacbe29.gif): Failed to open stream: Operation not permitted

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: is_dir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 201

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 201
Function: is_dir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_exists(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/9d5ed678fe57bcca610140957afab571.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 212

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 212
Function: file_exists

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/9d5ed678fe57bcca610140957afab571.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/9d5ed678fe57bcca610140957afab571.gif): Failed to open stream: Operation not permitted

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: is_dir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 201

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 201
Function: is_dir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_exists(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/7e5cd4f7bc59a40b48545b8934f04444.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 212

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 212
Function: file_exists

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/7e5cd4f7bc59a40b48545b8934f04444.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/7e5cd4f7bc59a40b48545b8934f04444.gif): Failed to open stream: Operation not permitted

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: is_dir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 201

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 201
Function: is_dir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_exists(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/7cb32ffe78f1c130914e41e5cf25ca6c.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 212

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 212
Function: file_exists

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/7cb32ffe78f1c130914e41e5cf25ca6c.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/7cb32ffe78f1c130914e41e5cf25ca6c.gif): Failed to open stream: Operation not permitted

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: is_dir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 201

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 201
Function: is_dir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_exists(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/7fc56270e7a70fa81a5935b72eacbe29.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 212

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 212
Function: file_exists

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/7fc56270e7a70fa81a5935b72eacbe29.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/7fc56270e7a70fa81a5935b72eacbe29.gif): Failed to open stream: Operation not permitted

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: is_dir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 201

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 201
Function: is_dir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_exists(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/f85b7b377112c272bc87f3e73f10508d.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 212

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 212
Function: file_exists

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/f85b7b377112c272bc87f3e73f10508d.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/f85b7b377112c272bc87f3e73f10508d.gif): Failed to open stream: Operation not permitted

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: is_dir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 201

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 201
Function: is_dir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_exists(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/a44b87932a0b856c1a2c66a6b35a2bd2.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 212

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 212
Function: file_exists

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/a44b87932a0b856c1a2c66a6b35a2bd2.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/a44b87932a0b856c1a2c66a6b35a2bd2.gif): Failed to open stream: Operation not permitted

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: is_dir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 201

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 201
Function: is_dir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_exists(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/e0e2328417b2daa1c3cd93ecb19207ab.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 212

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 212
Function: file_exists

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/e0e2328417b2daa1c3cd93ecb19207ab.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/e0e2328417b2daa1c3cd93ecb19207ab.gif): Failed to open stream: Operation not permitted

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: is_dir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 201

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 201
Function: is_dir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_exists(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/7e5cd4f7bc59a40b48545b8934f04444.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 212

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 212
Function: file_exists

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/7e5cd4f7bc59a40b48545b8934f04444.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/7e5cd4f7bc59a40b48545b8934f04444.gif): Failed to open stream: Operation not permitted

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: is_dir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 201

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 201
Function: is_dir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_exists(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/affd76202b87a9797ee92d78ee354b22.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 212

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 212
Function: file_exists

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/affd76202b87a9797ee92d78ee354b22.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/affd76202b87a9797ee92d78ee354b22.gif): Failed to open stream: Operation not permitted

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Cache::$dummy is deprecated

Filename: libraries/Driver.php

Line Number: 188

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
Line: 799
Function: get

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 605
Function: getComment

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Article_model::$best_cnt is deprecated

Filename: ver3/Article_model.php

Line Number: 18

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Article_model.php
Line: 18
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 322
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 392
Function: getFloatingMyInfo

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 559
Function: get_footer

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Article_model::$popular_cnt is deprecated

Filename: ver3/Article_model.php

Line Number: 19

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Article_model.php
Line: 19
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 322
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 392
Function: getFloatingMyInfo

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 559
Function: get_footer

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

์ˆ˜ํ•™๋™์•„ - ํด๋ฆฌ๋งค์Šค
๋ณธ๋ฌธ๋ฐ”๋กœ๊ฐ€๊ธฐ
์ฃผ๋‹ˆ์–ด ํด๋ฆฌ๋งค์Šค ๋ฌธ์ œ
์ˆ˜ํ•™ ๋ฌธ์ œ๋ฅผ ํ‘ธ๋Š” ๋งค๋ ฅ์— ๋น ์ ธ ๋ณด์„ธ์š”!
[ํด๋ฆฌ๋งค์Šค ์–ด์…ˆ๋ธ”] [์œ ํƒœ์˜ ๋ฉ˜ํ† ] ๋Œ€์นญ์ ๊ณผ ์ค‘์ 
์ˆ˜ํ•™๋™์•„ 2022.02.22 23:18 ์กฐํšŒ 785
๊ณต์œ ํ•˜๊ธฐ
ํŽ˜์ด์Šค๋ถ ํŠธ์œ„ํ„ฐ ์นด์นด์˜คํ†ก ์นด์นด์˜ค์Šคํ† ๋ฆฌ ๋„ค์ด๋ฒ„๋ธ”๋กœ๊ทธ ๋„ค์ด๋ฒ„๋ฐด๋“œ

โ€˜ํด๋ฆฌ๋งค์Šค ํšŒ์›์ด์—ฌ ๋ชจ์—ฌ๋ผ!โ€™ ์ˆ˜ํ•™ ๋ฉ˜ํ†  ๊ตฐ๋‹จ โ€˜ํด๋ฆฌ๋งค์Šค ์–ด์…ˆ๋ธ”โ€™์ด ๊ฒฐ์„ฑ๋˜์—ˆ์Šต๋‹ˆ๋‹ค.

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๊ตญ์ œ์ˆ˜ํ•™์˜ฌ๋ฆผํ”ผ์•„๋“œ(IMO) ์ถœ์‹  ๋Œ€ํ•™์ƒ ๋ฉ˜ํ†  6๋ช…์ด ์žฌ๋ฏธ์žˆ๊ฒŒ ์ƒ๊ฐํ•ด ๋ณผ ๋งŒํ•œ โ€˜์ฐฝ์˜ ์ˆ˜ํ•™โ€™ ๋ฌธ์ œ๋ฅผ ๋‚ด ์ฃผ๊ณ 

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์ˆ˜ํ•™ ๊ณต๋ถ€๋ฒ•๊ณผ ์ง„๋กœ ๋“ฑ์— ๋Œ€ํ•œ ์ƒ๋‹ด๋„ ํ•ด ์ค„ ๊ณ„ํš์ด์—์š”.

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2022๋…„, ๋‘ ๋ฒˆ์งธ ํด๋ฆฌ๋งค์Šค ์–ด์…ˆ๋ธ” ๋ฌธ์ œ๋ฅผ ๋‚ด ์ค€ ๋ฉ˜ํ† ๋Š”ย ์œ ํƒœ์˜ ๋ฉ˜ํ† ์ž…๋‹ˆ๋‹ค.

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์•ˆ๋…•ํ•˜์„ธ์š”! ํด๋ฆฌ๋งค์Šค ์–ด์…ˆ๋ธ” ๋ฉ˜ํ†  ์œ ํƒœ์˜์ž…๋‹ˆ๋‹ค.ย 

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์ง€๋‚œ 1์›” 25์ผ์— ์ง„ํ–‰ํ•œ <์ˆ˜ํ•™๋™์•„> ์˜จ๋ผ์ธ ํด๋ž˜์Šค์—์„œ ๋งŽ์€ ํšŒ์›๋“ค์ด ์ œ๊ฒŒ ๊ฐ€์žฅ ๊ด€์‹ฌ ์žˆ๋Š” ์ˆ˜ํ•™ ๋ถ„์•ผ๋ฅผ ๋ฌผ์–ด๋ณด์…จ๋Š”๋ฐ์š”. ํ•œ๋งˆ๋””๋กœ '์‘์šฉ ์ˆ˜ํ•™'์ด๋ผ๊ณ  ๋งํ•  ์ˆ˜ ์žˆ์–ด์š”.

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์ˆ˜ํ•™์„ ์ข‹์•„ํ•˜๋Š” ์ œ๊ฐ€ ์ปดํ“จํ„ฐ๊ณตํ•™๋ถ€์— ์ง„ํ•™ํ•œ ์ด์œ ๋Š” '๊ธฐ๊ณ„ํ•™์Šต์„ ์ˆ˜ํ•™์ ์œผ๋กœ ๋ถ„์„ํ•˜๋Š” ์—ฐ๊ตฌ'๋ฅผ ํ•˜๊ณ  ์‹ถ์–ด์„œ์˜ˆ์š”. ๊ธฐ๊ณ„ํ•™์Šต ๊ณผ์ •์ด ์ƒ๊ฐ๋ณด๋‹ค ์ˆ˜ํ•™์ ์ด๋ผ ๋งค๋ ฅ์ ์œผ๋กœ ๋Š๊ปด์กŒ๊ฑฐ๋“ ์š”. ๊ณต๋ถ€ํ•ด ๋ณด๋‹ˆ ๊ฐ€์žฅ ์žฌ๋ฏธ์žˆ๋Š” ๊ฒƒ ๊ฐ™์•„์š”. ๊ธฐ๊ณ„ํ•™์Šต์ด๋ž€ ์ปดํ“จํ„ฐ๊ฐ€ ์Šค์Šค๋กœ ํ•™์Šตํ•˜๋„๋ก ํ•˜๋Š” ์•Œ๊ณ ๋ฆฌ๋“ฌ์„ ๊ฐœ๋ฐœํ•˜๋Š” ๋ถ„์•ผ๋ฅผ ๋งํ•ด์š”.

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์—ฌ๋Ÿฌ๋ถ„ ์ค‘์—์„œ ์ˆœ์ˆ˜ ์ˆ˜ํ•™์„ ์ข‹์•„ํ•˜๋Š” ์นœ๊ตฌ๋„, ์ˆ˜ํ•™์„ ์‘์šฉํ•ด์„œ ์‚ฐ์—…์— ์ ์šฉํ•˜๋Š” ์‘์šฉ ์ˆ˜ํ•™ ๋ถ„์•ผ๋ฅผ ์ข‹์•„ํ•˜๋Š” ์นœ๊ตฌ๋„ ์žˆ์„ ํ…๋ฐ์š”. ํด๋ฆฌ๋งค์Šค ์–ด์…ˆ๋ธ” ๋ฉ˜ํ† ๋“ค์˜ ๊ด€์‹ฌ๋ถ„์•ผ๊ฐ€ ๋‹ค์–‘ํ•˜๋‹ˆ, ์–ด๋–ค ์งˆ๋ฌธ์ด๋ผ๋„ ์Šค์Šค๋Ÿผ์—†์ด ํด๋ฆฌ๋งค์Šค ํ™ˆํŽ˜์ด์ง€ [๋งค์ŠคํŽ€]-[์–ด์…ˆ๋ธ”์—๊ฒŒ ๋ฌผ์–ด๋ด]์— ์˜ฌ๋ ค ์ฃผ์„ธ์š”. ๋ฉ˜ํ† ๋“ค์ด ๋ณด๊ณ  ๋‹ต์„ ๊ฐ€์žฅ ์ž˜ํ•ด ์ค„ ๋ฉ˜ํ† ๊ฐ€ ๋‹ต๋ณ€ํ•ด ์ค„ ๊ฑฐ์˜ˆ์š”. AI๋‚˜ ๊ธฐ๊ณ„ํ•™์Šต๊ณผ ๊ด€๋ จํ•ด์„œ ๊ถ๊ธˆํ•œ ์ ์ด ์žˆ์œผ์‹  ๋ถ„์€ ์ œ๊ฒŒ ์งˆ๋ฌธํ•ด ์ฃผ์„ธ์š”!

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์œ ํƒœ์˜ ๋ฉ˜ํ† ์˜ ํด๋ฆฌ๋งค์Šค ์–ด์…ˆ๋ธ” ๋ฌธ์ œ

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๋ฌธ์ œ1 ๋Œ€์นญ์ ๊ณผ ์ค‘์ 

ํ‰๋ฉด ์œ„์— ์„œ๋กœ ๋‹ค๋ฅธ ์ ย A, B๊ฐ€ ์žˆ์„ ๋•Œ ๋‹ค์Œ ๋ฌธ์ œ๋ฅผ ํ’€์–ด ๋ณด์„ธ์š”.

1) ์ปดํผ์Šค๋งŒ์œผ๋กœ ์ ย A๋ฅผย B์— ๋Œ€์นญ์‹œํ‚จ ์ ์„ ์ž‘๋„ํ•  ์ˆ˜ ์žˆ์Œ์„ ๋ณด์ด์„ธ์š”

2) ์ปดํผ์Šค๋งŒ์œผ๋กœย \overline{AB}์˜ ์ค‘์ ์„ ์ž‘๋„ํ•  ์ˆ˜ ์žˆ์Œ์„ ๋ณด์ด์„ธ์š”.

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๋ฌธ์ œ2ย ๊ธธ์ด ์˜ฎ๊ธฐ๊ธฐ

ํ‰๋ฉด ์œ„์— ์ผ์ง์„ ์ด ์•„๋‹Œ ์ ย A, B, C๊ฐ€ ์žˆ์„ ๋•Œ ๋‹ค์Œ ๋ฌธ์ œ๋ฅผ ํ’€์–ด ๋ณด์„ธ์š”.

1) ์ปดํผ์Šค๋งŒ์œผ๋กœ ์ ย A์—์„œ ์„ ๋ถ„ BC์— ๋‚ด๋ฆฐ ์ˆ˜์„ ์˜ ๋ฐœ์„ ์ž‘๋„ํ•  ์ˆ˜ ์žˆ์Œ์„ ๋ณด์ด์„ธ์š”.

2) ์ปดํผ์Šค๋งŒ์œผ๋กœย \overline{AB}^{2}=\overline{AC} imes\overline{AD}์ธ ์ ์„ ์ž‘๋„ํ•  ์ˆ˜ ์žˆ์Œ์„ ๋ณด์ด์„ธ์š”.

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๋ฌธ์ œ3ย ๊ธธ์ด ์˜ฎ๊ธฐ๊ธฐ

ํ‰๋ฉด ์œ„์— ์–ด๋Š ์„ธ ์ ๋„ ์ผ์ง์„ ์ด ์•„๋‹Œ ์„œ๋กœ ๋‹ค๋ฅธ ์ ย A, B, C, D๊ฐ€ ์žˆ์–ด์š”. ์ด๋•Œย \overline{AB}์™€ย \overline{CD}์˜ ๊ต์ ์„ ์ž‘๋„ํ•  ์ˆ˜ ์žˆ์Œ์„ ๋ณด์ด์„ธ์š”.

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ํ•œ ๊ฑธ์Œ ๋”

์ปดํผ์Šค๋งŒ ์ด์šฉํ•ด์„œ ์ž„์˜์˜ ์›์˜ ์ค‘์‹ฌ์„ ์žก์„ ์ˆ˜ ์žˆ์–ด์š”. ์›๊ณผ ์ง์„ ์˜ ๊ต์ ๋„ ๊ทธ๋ฆด ์ˆ˜ ์žˆ๊ณ ์š”. ๋”ฐ๋ผ์„œ ๋ˆˆ๊ธˆ ์—†๋Š” ์ž์™€ ์ปดํผ์Šค๋กœ ์ž‘๋„ ๊ฐ€๋Šฅํ•œ ๋ชจ๋“  ๋ชจํ˜•์€ ์ปดํผ์Šค๋งŒ์œผ๋กœ๋„ ์ž‘๋„๊ฐ€ ๊ฐ€๋Šฅํ•ฉ๋‹ˆ๋‹ค. ์ด๋ฅผ '๋ชจ๋ฅด-๋งˆ์Šค์ผ€๋กœ๋‹ˆ ์ •๋ฆฌ'๋ผ๊ณ  ํ•ด์š”.

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ํƒœ๊ทธ
#์œ ํƒœ์˜ #์„œ์šธ๋Œ€ #์ˆ˜๋ฆฌ๊ณผํ•™๋ถ€ #KMO #IMO #์ž‘๋„ #๋Œ€์นญ
๋ฌธ์ œ ์ฐœํ•˜๊ธฐ ๋ชฉ๋ก๋ณด๊ธฐ
๋Œ“๊ธ€ 7
๋Œ“๊ธ€ ์ž‘์„ฑํ•˜๊ธฐ
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    ํ•ด๊ฒฐ
    pure math Lv.7 2022.02.24 00:34

    1.

    1) A๋ฅผ ์ค‘์ ์œผ๋กœ ํ•˜๋Š” ์› a์™€ ์› B๋ฅผ ์ค‘์ ์œผ๋กœ ํ•˜๋Š” ์› b๋ฅผ ๊ทธ๋ฆฝ๋‹ˆ๋‹ค. ์ด ๋‘ ์›์˜ ๊ต์ ์„ C, D๋ผ ํ•ฉ์‹œ๋‹ค. C๋ฅผ ์ค‘์ ์œผ๋กœ ํ•˜๊ณ  D๋ฅผ ์ง€๋‚˜๋Š” ์›์ด ์› b์™€ ๋งŒ๋‚˜๋Š” ์ ์ด ์  A๋ฅผ B์— ๋Œ€์นญ์‹œํ‚จ ์ , ์ฆ‰ E ์ž…๋‹ˆ๋‹ค.

    ์ด์œ  : ์„ ๋ถ„ CD์™€ AB๋Š” ์ง๊ต ํ•˜๋Š”๋ฐ, ์  CDE๋Š” ์ •์‚ผ๊ฐํ˜•์„ ์ด๋ฃจ๊ณ , ์„ ๋ถ„ CD์˜ ์ˆ˜์ง์ด๋“ฑ๋ถ„์„  ์œ„์— E๊ฐ€ ์žˆ์œผ๋ฉฐ, B๋กœ๋ถ€ํ„ฐ A์™€ E์˜ ๊ฑฐ๋ฆฌ๋Š” ๊ฐ™์œผ๋‹ˆ ์  E๊ฐ€ ์  A๋ฅผ B์— ๋Œ€์นญ์‹œํ‚จ ์ ์ด๋ฉฐ, ์ž‘๋„ ๊ฐ€๋Šฅํ•ฉ๋‹ˆ๋‹ค.

    2) E๋ฅผ ์ค‘์‹ฌ์œผ๋กœ ํ•˜๊ณ  A๋ฅผ ์ง€๋‚˜๋Š” ์›์ด ์› a์™€ ๋งŒ๋‚˜๋Š” ๋‘ ์ ์„ F, G๋ผ๊ณ  ํ•˜๋ฉด, F, G๋ฅผ ์ค‘์‹ฌ์œผ๋กœ ํ•˜๊ณ , A๋ฅผ ์ง€๋‚˜๋Š” ๋‘ ์›์ด ๋งŒ๋‚˜๋Š” ์ง€์ ์ด A์™€ B์˜ ์ค‘์ , ์ฆ‰ M์ž…๋‹ˆ๋‹ค.

    ์ด์œ  : ์‚ผ๊ฐํ˜• AMF์™€ AFE๋Š” ๋‹ฎ์Œ์ž…๋‹ˆ๋‹ค.(1:2) ์ด๋•Œ, 2AM = AF = AB๊ฐ€ ๋˜๋‹ˆ M์ด A์™€ B์˜ ์ค‘์ ์ด ๋˜๋Š” ๊ฒƒ์ด์ฃ !

    2.

    1) B, C๊ฐ€ ์ค‘์‹ฌ์ด๋ฉด์„œ A๋ฅผ ์ง€๋‚˜๋Š” ๋‘ ์›์„ b, c๋ผ ํ•˜๋ฉด ๋‘ ์›์˜ ๊ต์ ์ด ๋‘ ๊ฐœ๊ฐ€ ์ƒ๊ธฐ๋ฉฐ, A๊ฐ€ ์•„๋‹Œ ๋‹ค๋ฅธ ์ ์„ A1์ด๋ผ ํ•ฉ์‹œ๋‹ค. 1๋ฒˆ ๋ฌธ์ œ๋กœ, A์™€ A1์˜ ์ค‘์ ์„ ์ž‘๋„ ํ•  ์ˆ˜ ์žˆ์œผ๋‹ˆ ๊ทธ๊ฒƒ์ด ์  A์—์„œ ์„ ๋ถ„ BC์— ๋‚ด๋ฆฐ ์ˆ˜์„ ์˜ ๋ฐœ์ž…๋‹ˆ๋‹ค.

    ์ด์œ  : A1์€ A๋ฅผ ์„ ๋ถ„ BC์— ๋Œ€ํ•˜์—ฌ ๋Œ€์นญ์ด๋™ ํ•œ ๊ฒƒ๊ณผ ๊ฐ™์œผ๋ฉฐ, ์„ ๋ถ„ AA1์˜ ์ˆ˜์ง์ด๋“ฑ๋ถ„์„ ์ด ์„ ๋ถ„ BC์™€๋„ ๊ฐ™์Šต๋‹ˆ๋‹ค. ๊ทธ๋ ‡๊ธฐ ๋•Œ๋ฌธ์— AA1์˜ ์ค‘์ ์ด ์  A์—์„œ ์„ ๋ถ„ BC์— ๋‚ด๋ฆฐ ์ˆ˜์„ ์˜ ๋ฐœ์ธ ๊ฒƒ์ด์ฃ .

    2) 1๋ฒˆ ๋ฌธ์ œ์™€ ๊ฐ™์ด ์  B๋ฅผ A์— ๋Œ€์นญ์‹œํ‚จ ์ ์„ ์žก์•„ K๋ผ ํ•ฉ์‹œ๋‹ค. ๊ทธ๋ฆฌ๊ณ , B๋ฅผ ์ค‘์‹ฌ์œผ๋กœ ํ•˜๊ณ  C๋ฅผ ์ง€๋‚˜๋Š” ์›์„ b๋ผ ํ•ฉ์‹œ๋‹ค. ๋˜ํ•œ, ์ด ์ปดํผ์Šค๋ฅผ ๊ทธ๋Œ€๋กœ ์˜ฎ๊ฒจ K์—๋„ ๊ฐ™์€ ๋ฐฉ์‹์œผ๋กœ ํ•ด์ค๋‹ˆ๋‹ค. ๊ทผ๋ฐ, ์ƒํ™ฉ์— ๋”ฐ๋ผ B๋ฅผ K๋กœ ๋ฐ”๊ฟ”์•ผ ํ•  ๋•Œ๊ฐ€ ์žˆ์Šต๋‹ˆ๋‹ค. ์ฆ‰, C์™€ ๋” ๋จผ ๊ฑฐ๋ฆฌ์— ์žˆ๋Š” ์ ๋ถ€ํ„ฐ ์ปดํผ์Šค๋กœ ์‹œํ–‰ํ•ด์•ผ ํ•ฉ๋‹ˆ๋‹ค. ์ž, ์ด์ œ ์ด ๋‘ ์›์ด ๋งŒ๋‚˜๋Š” ์ง€์  ๋‘ ๊ฐœ๊ฐ€ ์ƒ๊ธธ ๊ฒƒ์ž…๋‹ˆ๋‹ค. ๊ทผ๋ฐ, ์—ฌ๊ธฐ์„œ C์™€ ์„ ๋ถ„ BK์— ๋Œ€ํ•˜์—ฌ ๋ฐ˜๋Œ€์ชฝ์— ์žˆ๋Š”, ์ฆ‰ ๋” ๋จผ ์ ์„ ์žก์•„์ค๋‹ˆ๋‹ค. ๊ทธ๋ฆฌ๊ณ , ์ด ์ ์„ O๋ผ ํ•ฉ์‹œ๋‹ค. O๋ฅผ ์ค‘์‹ฌ์œผ๋กœ ํ•˜๊ณ , B, K๋ฅผ ์ง€๋‚˜๋Š” ์› o์„ ๊ทธ๋ ค์ฃผ๋ฉด, ๋™์‹œ์— C๋„ ์ง€๋‚˜๊ฒŒ ๋ฉ๋‹ˆ๋‹ค. C๋ฅผ ์ง€๋‚˜๊ฒŒ ํ•˜๊ธฐ ์œ„ํ•ด์„œ ์ด๋ ‡๊ฒŒ ํ•œ ๊ฒƒ์ž…๋‹ˆ๋‹ค. 

    ์ด์ œ, ์›๊ณผ ์„ ๋ถ„์˜ ๊ต์ ์„ ์ฐพ๋Š” ๋ฐฉ๋ฒ•์œผ๋กœ ์ž‘๋„ํ•ด๋ด…์‹œ๋‹ค.

    A์™€ C๋ฅผ ์ค‘์‹ฌ์œผ๋กœ ํ•˜๊ณ , O๋ฅผ ์ง€๋‚˜๋Š” ๋‘ ์›์„ a, c๋ผ ํ•ด๋ด…์‹œ๋‹ค. ๊ทธ๋Ÿผ, O๊ฐ€ ์•„๋‹Œ ์› a, c๊ฐ€ ๋งŒ๋‚˜๋Š” ์  O1์ด ์ƒ๊ธธ ๊ฒƒ์ž…๋‹ˆ๋‹ค. ๋˜ํ•œ, ์› o์˜ ๋ฐ˜์ง€๋ฆ„์„ ์•„๋‹ˆ, ์ด๊ฑธ ๊ทธ๋Œ€๋กœ ์˜ฎ๊ฒจ ์  O1์„ ์ค‘์‹ฌ์œผ๋กœ ํ•˜๊ณ , ๋ฐ˜์ง€๋ฆ„์ด ๊ฐ™์€ ์› o1์„ ์žก์์‹œ๋‹ค. ๊ทธ๋Ÿผ, ์› o์™€ o1์˜ ๊ต์ ์ด D๊ฐ€ ๋˜๋Š” ๊ฒƒ์ž…๋‹ˆ๋‹ค!

    ์ด์œ  : D๋Š” ์ง์„  AC์™€ ์› o์˜ ๊ต์ ์ž…๋‹ˆ๋‹ค. ๊ทธ ์ด์œ ๋Š” O1์€ O๋ฅผ ์ง์„  AC๋ฅผ ๊ธฐ์ค€์œผ๋กœ ๋Œ€์นญ์ด๋™ํ•œ ๊ฒƒ์ด๊ธฐ ๋•Œ๋ฌธ์ด์ง€์š”. ๋˜ํ•œ, ๋ฐฉ๋ฉฑ์ •๋ฆฌ๋กœ ์ธํ•ด \overline{AB}^{2}=\overline{AC} imes\overline{AD}์ด ๋˜๊ฒŒ ๋˜์„œ, ์  D๋ฅผ ์ž‘๋„ ํ•œ ๊ฒƒ์ž…๋‹ˆ๋‹ค!

    3. 

    ์šฐ์„ , C์—์„œ AB์— ๋‚ด๋ฆฐ ์ˆ˜์„ ์˜ ๋ฐœ์„ K๋ผ ํ•ฉ์‹œ๋‹ค. ๋˜ํ•œ, K์—์„œ CD์— ๋‚ด๋ฆฐ์ˆ˜์„ ์˜ ๋ฐœ์„ L์ด๋ผ ํ•ฉ์‹œ๋‹ค. ๊ทผ๋ฐ, ์ž„์˜๋กœ AB์™€ CD์˜ ๊ต์ ์„ O๋ผ ํ•ฉ์‹œ๋‹ค. ๊ทธ๋Ÿฌ๋ฉด, ์ง๊ฐ์‚ผ๊ฐํ˜•์˜ ์„ฑ์งˆ๋กœ ์ธํ•ด์„œ CK2 = CL * CO ์ž…๋‹ˆ๋‹ค. ์ž, ์ด์ œ 2๋ฒˆ์œผ๋กœ O๊ฐ€ ์•„๋‹Œ, ์•ž์˜ ์ˆ˜์‹์„ ๋งŒ์กฑํ•˜๋Š” ์ž„์˜์˜ ์  O'์„ ์žก์„ ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค. ๊ทธ๋Ÿฌ๋ฉด, C๋ฅผ ์ค‘์‹ฌ์œผ๋กœ ํ•˜๊ณ  O'์„ ์ง€๋‚˜๋Š” ์›์ด ๋‘ ์„ ๋ถ„ AB, CD๊ณผ ๋งŒ๋‚˜๋Š” ์ ์ด ๋ฐ”๋กœ ๋‘ ์„ ๋ถ„์˜ ๊ต์  O์ž…๋‹ˆ๋‹ค.

    ์ด์œ  : CO'์˜ ๊ธธ์ด๋Š” ์•ž์˜ ์‹์„ ๋งŒ์กฑํ•˜๋Š” CO์˜ ๊ธธ์ด์™€ ๊ฐ™์Œ์„ ์•Œ ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค. ๊ณ ๋กœ, C๋ฅผ ์ค‘์‹ฌ์œผ๋กœ ํ•˜๊ณ  O'๋ฅผ ์ง€๋‚˜๋Š” ์›์ด ์„ ๋ถ„ AB, CD์™€ ๋งŒ๋‚˜๋Š” ์ ์ด ๋ฐ”๋กœ ์  O, ์ฆ‰ \overline{AB}์™€ \overline{CD}์˜ ๊ต์ ์„ ์ž‘๋„ํ•œ ๊ฒƒ์ด์ฃ .

    ๋Œ“๊ธ€ ์ž‘์„ฑํ•˜๊ธฐ ์ข‹์•„์š”0 ๋Œ“๊ธ€์ˆ˜6
    •  
      ์œ ํƒœ์˜ ๋ฉ˜ํ†  Lv.3 2022.02.26 18:39

      1-1. ํ’€์ด์˜ ๋Œ€๋žต์ ์ธ ํ๋ฆ„์€ ๋งž์œผ๋‚˜ ์› a,b์— ๋Œ€ํ•œ ์„ค๋ช…์ด ์ž˜๋ชป๋˜์–ด ์žˆ์Šต๋‹ˆ๋‹ค.

      1-2. ๋‹ฎ์Œ์ด๋ผ๋Š” ๊ทผ๊ฑฐ๋ฅผ ์ œ์‹œํ•ด์•ผ ํ•ฉ๋‹ˆ๋‹ค.

      2-1. ์ž˜ ํ‘ธ์…จ์Šต๋‹ˆ๋‹ค.

      2-2. ์› O๋Š” C๋ฅผ ์ง€๋‚˜์ง€ ์•Š์Šต๋‹ˆ๋‹ค. "C์™€ ์„ ๋ถ„ BK์— ๋Œ€ํ•ด ๋ฐ˜๋Œ€์ชฝ"๋ณด๋‹ค "์„ ๋ถ„ BK์— ๋Œ€ํ•ด C์™€ ๋ฐ˜๋Œ€์ธ"์ด ๋” ๋งž๋Š” ํ‘œํ˜„์ž…๋‹ˆ๋‹ค. ์›๊ณผ ์„ ๋ถ„์˜ ๊ต์ ์„ ์ฐพ์„ ๋•Œ A,C,O๊ฐ€ ์ผ์ง์„ ์ด๋ฉด O=O1์ด๋ฏ€๋กœ ๋ฐฉ๋ฒ• ์ ์šฉ์ด ๋ถˆ๊ฐ€๋Šฅํ•ฉ๋‹ˆ๋‹ค.

      3. ์ž˜ ํ‘ธ์…จ์Šต๋‹ˆ๋‹ค.

      ์ข‹์•„์š”0
    •  
      pure math Lv.7 2022.02.26 20:16

      1-1์› a,b์–ด๋””๊ฐ€ ์ž˜๋ชป๋œ ๊ฒƒ์ธ๊ฐ€์š”?? ๋ฐ”๋กœ ์ˆ˜์ •ํ•˜๊ฒ ์Šต๋‹ˆ๋‹คใ…œ

      1-2๊ฐ์‚ฌํ•ฉ๋‹ˆ๋‹ค!

      2-1 ๊ฐ FAM์„ ๊ณต์œ  ํ•˜๋ฉฐ, ๋‘˜ ๋‹ค ์ด๋“ฑ๋ณ€์‚ผ๊ฐํ˜•์ด๋‹ˆ AA๋‹ฎ์Œ์ด ๋˜๋Š” ๊ฒƒ์ž…๋‹ˆ๋‹ค. 

       

      ์ข‹์•„์š”0
    •  
      pure math Lv.7 2022.02.26 20:37

      2-2

      AB์˜ ๊ธธ์ด๋ฅผ a, AC์˜ ๊ธธ์ด๋ฅผ c๋ผ ํ•˜๋ฉด, 

      2a์˜ ๊ธธ์ด๋ฅผ ๊ฐ–๋Š” ๋‹ค๋ฅธ ์„ ๋ถ„(ABํฌํ•จ X)๊ณผ ๊ทธ ์–‘ ๋์ ์„ ํฌํ•จํ•˜๋Š” ์ ๋‹นํžˆ ํฐ ์›, ๋˜ํ•œ ๊ทธ ์„ ๋ถ„์˜ ์ค‘์ ์œผ๋กœ๋ถ€ํ„ฐ ๊ฑฐ๋ฆฌ๊ฐ€ c๋ฉด์„œ ์› ์œ„์— ์žˆ๋Š” ์ ์„ ์ž‘๋„ํ•  ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค. ๊ทธ๋ฆฌ๊ณ  ์ œ๊ฐ€ ์“ด 2๋ฒˆ์˜ ํ’€์ด๋กœ, ์› ์œ„์— ๊ฑฐ๋ฆฌ๊ฐ€ c์ธ ์ ๊ณผ ์ค‘์ ์„ ์—ฐ๊ฒฐํ•œ ์ง์„ ์ด ์›๊ณผ ๋งŒ๋‚˜๋Š” ์ ์„ ์ž‘๋„ํ•  ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค. ๊ทธ ์ค‘์ ๊ณผ ๋ฐฉ๊ธˆ ์ž‘๋„ํ•œ ์ ์˜ ๊ธธ์ด๋ฅผ ์˜ฎ๊ฒจ, A๋กœ ๊ฐ€์ ธ๊ฐ€ ์›์„ ๋Œ๋ฆฌ๋ฉด ๊ทธ ์›์— ์žˆ๋Š” ๋ชจ๋“  ์ ์ด D๊ฐ€ ๋  ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค!

      ์ข‹์•„์š”0
    •  
      ์œ ํƒœ์˜ ๋ฉ˜ํ†  Lv.3 2022.03.07 23:52

      1-1) ์—์„œ ๊ฐ ์› a,b์˜ ์ค‘์ ๊ณผ ๋ฐ˜์ง€๋ฆ„์ด ๋ช…ํ™•ํ•˜์ง€ ์•Š์Šต๋‹ˆ๋‹ค.

      1-2) ๋„ค ๋งž์Šต๋‹ˆ๋‹ค

      2-2) ์ž˜ ํ‘ธ์…จ์Šต๋‹ˆ๋‹ค

      ์ข‹์•„์š”0
    •  
      pure math Lv.7 2022.03.08 00:20

      1-1) ์› a์˜ ์ค‘์‹ฌ์€ A์ด๊ณ , ์›b์˜ ์ค‘์ ์€ B์ž…๋‹ˆ๋‹ค. ๋˜ํ•œ, ์› a๋Š” B๋ฅผ ์ง€๋‚˜๊ณ , ์› b๋Š” A๋ฅผ ์ง€๋‚ฉ๋‹ˆ๋‹ค!

      ๊ฐ์‚ฌํ•ฉ๋‹ˆ๋‹ค!

      ์ข‹์•„์š”0
    •  
      ์œ ํƒœ์˜ ๋ฉ˜ํ†  Lv.3 2022.03.09 05:34

      A,B๋ฅผ ๊ฐ๊ฐ ์ค‘์‹ฌ์œผ๋กœ ํ•˜๊ณ  ๋ฐ˜์ง€๋ฆ„์ด AB์ธ ์› a,b๋ฅผ ์žก์ž.

      ํ˜น์€

      A๋ฅผ ์ค‘์‹ฌ์œผ๋กœ ํ•˜๊ณ  B๋ฅผ ์ง€๋‚˜๋Š” ์›์„ a, B๋ฅผ ์ค‘์‹ฌ์œผ๋กœ ํ•˜๊ณ  A๋ฅผ ์ง€๋‚˜๋Š” ์›์„ b๋ฅผ ์žก์ž.

      ๊ฐ€ ๋” ์ข‹์€ ํ‘œํ˜„์ž…๋‹ˆ๋‹ค.

      ์ˆ˜๊ณ ํ•˜์…จ์Šต๋‹ˆ๋‹ค.

      ์ข‹์•„์š”0
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