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
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
Severity: Warning
Message: file_exists(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/112bafd17a86b9e3c6ae875d07566d21.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
Severity: Warning
Message: file_put_contents(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/112bafd17a86b9e3c6ae875d07566d21.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
Severity: Warning
Message: file_put_contents(/DATA/upload/polymath/latex/112bafd17a86b9e3c6ae875d07566d21.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
하이퍼사이클로이드란 작은 원이 큰 원의 안쪽을 내접하여 돌 때 작은 원 위의 한 점이 그리는 곡선을 말한다. 링크: (위키백과)
하이퍼사이클로이드를 이용한 문제를 풀어보자.
1) 하이퍼 사이클로이드가 직선인 경우도 있다는 것을 설명하고, 두 원(큰 원과 큰 원에 내접하는 원)의 반지름 길이의 비를 구해라.
2) 반지름 길이의 비가 5:1인 하이퍼 사이클로이드
가 있다. 이 때, a를 원주의
로 하는 원의 둘레는 이 하이퍼 사이클로이드를 둘러싸는 원의 둘레와 같다는 것 을 하이퍼 사이클로이드의 성질과 관해 서술해라.
3) 반지름 길이의 비가 6:1인 하이퍼 사이클로이드와 5:1인 하이퍼 사이클로이드의 둘레의 차를 구해라.(이 때, 큰 원에 내접한 작은 원의 반지름은 5cm이다)[풀이는 필수]
(반지름 길이의 비가 6:1인 하이퍼 사이크로이드)
4) 다음 그림을 보고, 오각형과 하이퍼사이클로이드(반지름 길이의 비는 5:1)의 넓이의 차를 구해라.[풀이는 필수]
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