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수학동아 - 폴리매스
함께 풀고 싶은 문제
깊이 고민해볼 수 있는 수학 문제를 내는 곳입니다
[세상을 바꿀 문제] 버뮤다 삼각지대에 준하는 큐브드 삼각지대
Scubed
2021.07.16 09:32
조회 712
버뮤다 삼각지대는 배나 비행기가 지나가기만 해도 사람이 죽는다고 알려진 악명 높은 곳이다. 궁금하면 구글이나 네이버를 찾아보도록 하세요.
그리고 나는 큐브드 삼각지대를 만들었다. 큐브드 삼각지대는 2차원에서 다음과 같이 정의된다.
임의의 점 A,B,C에 대해 A,B,C를 모두 지나는 직사각형과 삼각형 ABC가 있다. 배는 원모양으로, 배의 절반 이상이 삼각형 ABC에 들어가면 배는 잠긴다.
즉 이런 소리다.
/resources/contentsMember/2021/07/629a719d733a5cc8d05e40441f5b57e4.JPG
여기서 배 G는 살고, 배 I는 죽는다.
배의 중심은 직사각형의 둘레를 포함하여 직사각형 안을 돌아다닐 수 있다.
여기서, 삼각형 ABC의 넓이를 T, 직사각형의 넓이를 R이라고 했을 때, 배가 빠질 확률은 T/R 이하임을 보이시오.
단, 배의 반지름은 충분히 작다고 가정한다(문제를 이해하시면 제가 왜 충분히 작다고 했는지 이해하실 겁니다).
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원파
Lv.9
2021.07.17 08:06
배 전체가 반드시 직사각형 내부에 존재해야 하나요?
혹은, 배의 중심만 직사각형 내부에 존재하여도 되는건가요?
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khr519
Lv.8
2021.07.19 14:35
비밀댓글
비밀 댓글이 등록 되었습니다.
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김미래_기자
Lv.15
2021.07.23 01:54
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뉴＿턴
Lv.8
2021.09.03 00:28
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Scubed
Lv.7
2021.09.03 00:29
비밀댓글
비밀 댓글이 등록 되었습니다!
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High
Lv.2
2022.08.08 03:45
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비밀 댓글이 등록 되었습니다.
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