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수학동아 - 폴리매스
함께 풀고 싶은 문제
깊이 고민해볼 수 있는 수학 문제를 내는 곳입니다
[세상을 바꿀 문제] 슬기로운 수학 생활 첫 번째 문제에서의 확장판
yh36
2022.02.27 06:46
조회 313
슬기로운 수학 생활 첫 번째 문제의 내용은
"한 변의 길이가 1에 아주 가깝지만 1보다 큰 정육각형의 영역을 한 변의 길이가 1인 정삼각형 7개로 완전히 덮을 수 있는가"
였는데요, 대체적으로 댓글 반응은 '불가능하다'였습니다. 그런데 문제를 풀다 보니
"어떤 평면도형 C의 넓이가 S일 때, C 내부에 포함되는 도형 n개를 그 넓이의 합이 S 이하가 되도록 선택한다. 넓이가 S보다 아주 약간 크고 C와 닮은 도형인 D의 영역을, 선택한 도형 n개를 도합 (n+1)번 사용하여 완전히 덮을 수 있는가?"
라는 궁금증이 생겼습니다. 이건 어떨 것 같나요?
(파생된 문제이기 때문에 댓글로 달까하는 생각도 들었지만 그래도 다른 문제인 것 같아서 여기에 올립니다.)
-
S2-S1의 넓이를 가지면서 두 도형 중 하나에 포함되는 넓이를 가진 도형이 n개 안에 포함되야 될 텐데요... n에 제한이 없고 그 조각의 넓이도 아주 작을 수 있다면, 그 조각을 잘 만들면 가능할 수 있을 것 같습니다.
결론 : 조건이 더 필요할 것 같습니다.
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