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홍차넷
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질문
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- 질문 게시판입니다.
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전체기타게임진로연애가정/육아체육/스포츠교육의료/건강철학/종교IT/컴퓨터여행과학문화/예술법률홍차넷경제
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| Date |
Warning: Use of undefined constant reg_date - assumed 'reg_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 53 20/08/25 09:30:49 Warning: Use of undefined constant mod_date - assumed 'mod_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 56 |
| Name | 먹이 |
| Subject | 수학 잘 아시는 분께 질문... |
|
https://www.bostonglobe.com/2020/08/20/magazine/math-problem-stumped-experts-50-years-this-grad-student-maine-solved-it-days/ 오늘 아침에 퇴근하는 길에 이 기사를 봤는데요 대충 메인 주에 살던 대학원생이 위상수학 내에서 다루어지는 Conway Knot이 slice knot인지 아닌지를 밝혀냈는데 그게 50년간 누구도 못했던 일이었다 뭐 이런 식인 것 같읍니다? 1) 이걸 간단하게 해석해주실 수 있는지... 콘웨이 매듭이랑 매듭의 sliceness가 뭘 의미하는지 모르겠읍니다 (이게 도저히 간단하게 설명할 수 없는 거라면 그렇게 말해주셔도 좋읍니다) 2) 이 발견이 수학계에서 어느 정도의 '임팩트'가 있는지요? 유명 저널에 실었다고는 하는데 어느 정도인지는 잘 모르겠읍니다 미리 감사드립니다 Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 133 Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 146 Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 161 0 이 게시판에 등록된 먹이님의 최근 게시물 |
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90328 class="iamcmt" style="display:none;"> Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 66
90328 class='vcm '>
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90328'> 박태
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수정됨
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20/08/25 11:11
90328>삭제 주소복사
Warning: Use of undefined constant level - assumed 'level' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 150
전 수학자가 아니라 공학쪽 대학원생이지만 예전에 위상수학을 호기심에 배워본적이 있어서 짧은 지식으로 답변을 드립니다.
(물론 학점은 썰림. 전공자가 아니기 때문에 단어나, 맥락이 틀릴수도 있습니다)
우선 위상수학이 뭔지부터 간단히 얘기하면,
어떤 도형 집단(3차원 물체, 끈, 등) 의 수학적인 성질을 잘 정리하여 이 집단 내의 도형 A와 B가 '수학적으로' 같은놈인지 다른놈인지 알려주는 수학적 체계라고 보시면 됩니다.
동그란(구) 찰흙 한덩이가 있다고 칩시다. 이 찰흙을 맘대로 변형하되, 구멍은 뚫지 않는다는 조건을 ... 더 보기
(물론 학점은 썰림. 전공자가 아니기 때문에 단어나, 맥락이 틀릴수도 있습니다)
우선 위상수학이 뭔지부터 간단히 얘기하면,
어떤 도형 집단(3차원 물체, 끈, 등) 의 수학적인 성질을 잘 정리하여 이 집단 내의 도형 A와 B가 '수학적으로' 같은놈인지 다른놈인지 알려주는 수학적 체계라고 보시면 됩니다.
동그란(구) 찰흙 한덩이가 있다고 칩시다. 이 찰흙을 맘대로 변형하되, 구멍은 뚫지 않는다는 조건을 ... 더 보기
전 수학자가 아니라 공학쪽 대학원생이지만 예전에 위상수학을 호기심에 배워본적이 있어서 짧은 지식으로 답변을 드립니다.
(물론 학점은 썰림. 전공자가 아니기 때문에 단어나, 맥락이 틀릴수도 있습니다)
우선 위상수학이 뭔지부터 간단히 얘기하면,
어떤 도형 집단(3차원 물체, 끈, 등) 의 수학적인 성질을 잘 정리하여 이 집단 내의 도형 A와 B가 '수학적으로' 같은놈인지 다른놈인지 알려주는 수학적 체계라고 보시면 됩니다.
동그란(구) 찰흙 한덩이가 있다고 칩시다. 이 찰흙을 맘대로 변형하되, 구멍은 뚫지 않는다는 조건을 걸면 이걸로 원통, 사면체, 세숫대야 같은 모양들을 만들 수 있습니다.
여기서 구멍을 뚫지 않는다가 수학적인 성질, 즉, 도형을 구분하는 조건입니다.
그래서 위상수학 관점에서 구와 원통, 사면체, 세숫대야는 같은 애들입니다.
그다음 도넛모양(이미 구멍이 하나 뚫린) 찰흙이 있다고 칩시다. 구멍 숫자를 유지하면서 맘대로 변형하면 컵모양도 만들 수 있고, 파이프 모양도 만들 수 있습니다. 따라서 도넛과 컵, 창문틀은 위상수학 관점에서 같은애들입니다.
이제 위상수학의 한 분야인 매듭이론 (knot theory) 으로 가겠습니다. 저도 매듭이론은 배우질 않아서 잠깐 위키피디아를 봤는데 재밌더군요
동그란 고무줄하나가 손에 있습니다. 이 고무줄을 자르거나, 묶지 않는 조건을 걸면 사각형 삼각형을 만들 수 있고 아니면 살짝 돌려서 고무줄 위에 고무줄을 8자 모양으로 포개 놓더라도 결국 다시 하나의 동그란 고무줄로 원상복귀가 됩니다.
그래서 위상수학적으로 얘네들은 다 같은애들입니다. 이 고무줄과 같은 그룹인 애들을 unknot 이라고 합니다. un이 붙었으니 매듭이 없는 놈들이라고 보면 되겠죠.
찰흙의 예에서 수학적 성질로 말한 '구멍'이 매듭이론에서는 '매듭(knot)'으로 보면 될것 같습니다. 여기서 매듭이란 아까 그 고무줄을 한번 잘라서 꼬은다음에 다시 붙인걸 말합니다. 이 꼬여진 고무줄은 다시 자르지 않는이상 본래 고무줄(unknot)로 돌아갈 수 없죠. 즉, 위상수학적으로 다른놈이 됩니다. 이런 매듭(knot)이 2개, 3개 등등등 수에 따라 같은 도형들의 집단도 구분할 수 있겠죠
slice는 매듭 도형들의 특성이라고 볼 수 있습니다. 이거는 설명하기 힘드네요 saddle point라는걸 쉽게 말할 수가 없습니다.
매듭이 몇개 지어진 고무줄이 주어졌을때, 그냥 자르는게 아니라 '마법의 가위'를 이용해서 고무줄을 잘 자른다음 늘리고 줄이고 했더니 마술처럼 막 여러개의 동그란 고무줄로 풀렸다! 하면 이 고무줄은 slice knot 입니다. 반면에 분리된 고무줄 일부가 쇠사슬처럼 엉켜있다 하면 slice knot이 아닙니다.
(첨부그림을 보면 좀 이해가 갈수도 있을겁니다. Isotopy는 수학적 성질을 건드리지 않고 매듭도형을 변형하는걸 말하고, Saddle이 마법의 가위라고 보면 됩니다)
Conway knot은 매듭이 11개 지어진 도형 같던데 이게 앞서 말한 slice knot 아닌지를 밝혔다는것 같습니다.
바로 종신 MIT 교수가 됐으니 엄청난 업적 아닐까요?
(물론 학점은 썰림. 전공자가 아니기 때문에 단어나, 맥락이 틀릴수도 있습니다)
우선 위상수학이 뭔지부터 간단히 얘기하면,
어떤 도형 집단(3차원 물체, 끈, 등) 의 수학적인 성질을 잘 정리하여 이 집단 내의 도형 A와 B가 '수학적으로' 같은놈인지 다른놈인지 알려주는 수학적 체계라고 보시면 됩니다.
동그란(구) 찰흙 한덩이가 있다고 칩시다. 이 찰흙을 맘대로 변형하되, 구멍은 뚫지 않는다는 조건을 걸면 이걸로 원통, 사면체, 세숫대야 같은 모양들을 만들 수 있습니다.
여기서 구멍을 뚫지 않는다가 수학적인 성질, 즉, 도형을 구분하는 조건입니다.
그래서 위상수학 관점에서 구와 원통, 사면체, 세숫대야는 같은 애들입니다.
그다음 도넛모양(이미 구멍이 하나 뚫린) 찰흙이 있다고 칩시다. 구멍 숫자를 유지하면서 맘대로 변형하면 컵모양도 만들 수 있고, 파이프 모양도 만들 수 있습니다. 따라서 도넛과 컵, 창문틀은 위상수학 관점에서 같은애들입니다.
이제 위상수학의 한 분야인 매듭이론 (knot theory) 으로 가겠습니다. 저도 매듭이론은 배우질 않아서 잠깐 위키피디아를 봤는데 재밌더군요
동그란 고무줄하나가 손에 있습니다. 이 고무줄을 자르거나, 묶지 않는 조건을 걸면 사각형 삼각형을 만들 수 있고 아니면 살짝 돌려서 고무줄 위에 고무줄을 8자 모양으로 포개 놓더라도 결국 다시 하나의 동그란 고무줄로 원상복귀가 됩니다.
그래서 위상수학적으로 얘네들은 다 같은애들입니다. 이 고무줄과 같은 그룹인 애들을 unknot 이라고 합니다. un이 붙었으니 매듭이 없는 놈들이라고 보면 되겠죠.
찰흙의 예에서 수학적 성질로 말한 '구멍'이 매듭이론에서는 '매듭(knot)'으로 보면 될것 같습니다. 여기서 매듭이란 아까 그 고무줄을 한번 잘라서 꼬은다음에 다시 붙인걸 말합니다. 이 꼬여진 고무줄은 다시 자르지 않는이상 본래 고무줄(unknot)로 돌아갈 수 없죠. 즉, 위상수학적으로 다른놈이 됩니다. 이런 매듭(knot)이 2개, 3개 등등등 수에 따라 같은 도형들의 집단도 구분할 수 있겠죠
slice는 매듭 도형들의 특성이라고 볼 수 있습니다. 이거는 설명하기 힘드네요 saddle point라는걸 쉽게 말할 수가 없습니다.
매듭이 몇개 지어진 고무줄이 주어졌을때, 그냥 자르는게 아니라 '마법의 가위'를 이용해서 고무줄을 잘 자른다음 늘리고 줄이고 했더니 마술처럼 막 여러개의 동그란 고무줄로 풀렸다! 하면 이 고무줄은 slice knot 입니다. 반면에 분리된 고무줄 일부가 쇠사슬처럼 엉켜있다 하면 slice knot이 아닙니다.
(첨부그림을 보면 좀 이해가 갈수도 있을겁니다. Isotopy는 수학적 성질을 건드리지 않고 매듭도형을 변형하는걸 말하고, Saddle이 마법의 가위라고 보면 됩니다)
Conway knot은 매듭이 11개 지어진 도형 같던데 이게 앞서 말한 slice knot 아닌지를 밝혔다는것 같습니다.
바로 종신 MIT 교수가 됐으니 엄청난 업적 아닐까요?
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