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Function: require_once

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Function: getComment

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Function: initBoardView

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Line: 315
Function: require_once

자유게시판
수학을 주제로 떠들어 보세요!
[잡담] 질문
아인수타인 2021.07.16 02:54 조회 449
공유하기
페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

이런 그래프에서 면의 개수를 어떻게 정의하나요? 인터넷에 쳐 봐도 안 나오네요...

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  •  
    PMPI Lv.7 2021.07.16 03:34

    마법진같이 생긴...ㅍㅍ

    댓글 작성하기 좋아요0 댓글수0
  •  
    Abiria♡ Lv.8 2021.07.16 07:43

    면이요?

    삼각형 아니고 그냥 면은...문제가 이해가 잘 안되네요

    댓글 작성하기 좋아요0 댓글수2
    •  
      아인수타인 Lv.12 2021.07.16 07:56

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      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
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      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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      Function: getLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
      Line: 200
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      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
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      Function: view

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      Function: require_once

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      Backtrace:

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

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

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      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
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      Function: require_once

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      Filename: libraries/Common.php

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      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/views/ver3/inc/view_comment_list.php
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      Filename: libraries/Common.php

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      Backtrace:

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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      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/views/ver3/inc/view_comment_list.php
      Line: 200
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      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
      Line: 343
      Function: view

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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      Function: require_once

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      Filename: libraries/Common.php

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      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/views/ver3/inc/view_comment_list.php
      Line: 200
      Function: parseLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
      Line: 343
      Function: view

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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      Filename: libraries/Common.php

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

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      Function: getLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
      Line: 200
      Function: parseLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
      Line: 343
      Function: view

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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      Function: view

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      Line: 315
      Function: require_once

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      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/views/ver3/inc/view_comment_list.php
      Line: 200
      Function: parseLatexImg

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
      Line: 343
      Function: view

      File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
      Line: 558
      Function: view

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

      그래프에서 평면그래프(평면에 그려도 선이 교차하지 않게 그릴 수 있음)이면 v-e+f=2(v:점의 개수, e:선의 개수, f:면의 개수)이고, 이게 아니라면 평면그래프가 아니라는데, 위 그래프는 결론부터 말하면 평면그래프가 아닌데 이럴 경우 f의 값을 얼마로 해야 하나 해서요

      좋아요0
    •  
      아인수타인 Lv.12 2021.07.16 07:57

      예를 들어 아래 그래프는 외부 면까지 면이 4개고요

      좋아요0
  •  
    원파 Lv.9 2021.07.16 08:59

    음... 저도 잘 모르겠네요...

    다만 제 예상이라면 면이라는게 정의되지 않을 거 같습니다

    댓글 작성하기 좋아요0 댓글수0
  •  
    집돌이 페렐만 Lv.9 2021.07.17 05:39

    평면그래프인 동형그래프가 있다면 면을 셀 수가 있을텐데 이 경우는 모르겠네용

    댓글 작성하기 좋아요0 댓글수0
  •  
    Abiria♡ Lv.8 2021.07.17 14:59

    이 경우는 애초에 평면그래프가 아니라 오일러 법칙이 통하지 않지 않을까요?

     

    아니면 오히려 오일러 공식을 역으로 적용하면 f = 7 이 되긴 하는데.. 오일러 공식이 평면도형이라는 가정 하에 성립하는 게 원칙이라 의미없는지도 모르겠네요

    댓글 작성하기 좋아요0 댓글수1
    •  
      아인수타인 Lv.12 2021.07.17 20:54

      네, 아는데, 제 말은 '평면그래프이면 오일러 공식이 성립한다'의 대우명제인 '오일러 공식이 성립하지 않으면 평면그래프가 아니다'를 확인하면 평면그래프인지 아닌지 단번에 판별할 수 있을 거 같은데... 면의 개수가 상당히 애매해서요...

      좋아요0

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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
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Function: model

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

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Function: get_footer

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