Severity: 8192
Message: Creation of dynamic property CI_Cache::$apc is deprecated
Filename: libraries/Driver.php
Line Number: 188
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
Line: 22
Function: driver
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
Line: 17
Function: initiateCache
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 12
Function: __construct
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: 8192
Message: Creation of dynamic property CI_Cache::$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/Article.php
Line: 12
Function: __construct
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: 8192
Message: Creation of dynamic property Contents_model::$best_cnt is deprecated
Filename: ver3/Contents_model.php
Line Number: 17
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
Line: 17
Function: _error_handler
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 440
Function: model
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 29
Function: initMenu
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 12
Function: __construct
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: 8192
Message: Creation of dynamic property Contents_model::$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/Article.php
Line: 12
Function: __construct
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: 8192
Message: Creation of dynamic property Article_model::$best_cnt is deprecated
Filename: ver3/Article_model.php
Line Number: 18
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Article_model.php
Line: 18
Function: _error_handler
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 13
Function: model
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: 8192
Message: Creation of dynamic property Article_model::$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/controllers/ver3/Article.php
Line: 13
Function: model
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: 8192
Message: urldecode(): Passing null to parameter #1 ($string) of type string is deprecated
Filename: ver3/Member_model.php
Line Number: 279
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Member_model.php
Line: 279
Function: urldecode
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 123
Function: getMemberView
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: Warning
Message: Trying to access array offset on null
Filename: ver3/Article.php
Line Number: 124
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 124
Function: _error_handler
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: Warning
Message: Trying to access array offset on null
Filename: ver3/Article.php
Line Number: 125
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 125
Function: _error_handler
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: 8192
Message: Creation of dynamic property CI_Cache::$dummy is deprecated
Filename: libraries/Driver.php
Line Number: 188
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Article_model.php
Line: 674
Function: get
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 266
Function: getComment
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 131
Function: initBoardView
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

시끌벅적한 설날이 돌아왔어~. 즐겁기는 하지만, 차례상 차리는 게 정말 큰 일이라 걱정이지.
그런데 그거 알아? 차례상을 차리는 데도 수학이 필요하다는 사실!
명절 음식 하면 가장 먼저 생각나는 게 뭐야? 나는 사과를 제일 좋아해. 그래서 차례상에 사과는 꼭 올리려고 하는데 어떻게 하면 굴러 떨어지지 않게 쌓을 수 있을까?
케플러는 알고 있었던 사과 쌓기의 전략!
시장에 쌓여있는 사과들을 떠올려봐. 보통 아래 놓인 사과 사이의 빈 공간에 사과를 또 놓고, 위로 갈수록 적게 쌓잖아.
이런 방식을 수학적으로는 ‘면심입방’ 구조라고 해.
재미있는 사실은 이 전략을 1600년대에 이미 알아챈 사람이 있었다는 거야.
바로 독일의 천문학자 요하네스 케플러야. 케플러는 1611년 구 형태의 대포알을 가장 효율적이고 안정적으로 쌓는 방법은 면심입방 구조라고 주장했어.

면심입방으로 사과로 쌓은 모습.(출처 : S. Heitkam)
‘규칙적으로 쌓는 게 아니라 무작위로 쌓으면 더 효율적으로 쌓을 수도 있지 않을까?’라고 생각한 많은 수학자가 케플러의 추측에 도전했지만, 번번히 실패로 돌아갔지.
드디어 1998년 미국의 수학자 토마스 헤일스 피츠버그대학교 수학과 교수가 250쪽에 달하는 엄청난 양의 컴퓨터 계산 결과로 케플러의 추측이 옳다는 걸 증명했어. 무려 387년 만에 증명된 거야.
사과 하나를 쌓는 데에도 이런 깊이 있는 수학적 논의가 가능하다니! 이번 설날에는 먹지만 말고 사과를 면심입방 구조로 쌓아보자고~!
※오늘의 퀴즈
사과를 효율적으로 쌓는 법을 알아낸 독일의 천문학자는?
1. 요하네스 키플링
2. 요하네스 케플러
3. 요하네스 커플링
Severity: Warning
Message: Undefined variable $tag_news_list
Filename: inc/article_view.php
Line Number: 90
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/article_view.php
Line: 90
Function: _error_handler
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 221
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
Severity: Warning
Message: Cannot modify header information - headers already sent by (output started at /volume1/web/PhpstormProjects/www_polymath_co_kr/system/core/Exceptions.php:271)
Filename: core/Common.php
Line Number: 570
Backtrace:
Type: TypeError
Message: count(): Argument #1 ($value) must be of type Countable|array, null given
Filename: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/article_view.php
Line Number: 90
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 221
Function: view
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once