수학동아 - 폴리매스

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[잡담] 무한한 직사각형

집돌이 페렐만 2019.11.11 01:57 조회 439

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

(만약 로딩이 있다면 이곳에서 풀어주세요)

모든 양의 정수 $k\geq 1$ 에 대하여, 변의 길이가 각각 $\frac{1}{k}, \frac{1}{k+1}$ 인 직사각형이 한 개씩 있다.

무한히 많은 이 직사각형들을 변의 길이가 1인 정사각형 내부에 겹치지 않고 모두 채울 수 있을까?

(참고로 이 직사각형들의 넓이의 합은 $\frac{1}{1 imes 2}+\frac{1}{2 imes 3}+\frac{1}{3 imes 4}+\cdots=1$ 이다.)

-출처 : Exercise 2.37, Concrete Mathematics (Graham, Knuth, and Patashnik)-

이전글 무한한 직사각형 문제 보조 논의

다음글 안녕하십니까! 2222

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