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[수학 정보] 직육면체 상자의 꼭짓점들의 거리들이 모두 유리수가 되는 상자가 있는가?(모서리, 대각선, 안쪽 대각선)
pure math 2022.03.27 00:14 조회 326
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페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

길이를 1, a, b라 하면, (대각선) a=(m^2+n^2)/2mn, b=(p^2+q^2)/2pq라 할 수 있다.

이걸 토대로 정리하면, n^2/m^2+m^2/n^2+q^2/p^2+p^2/q^2=k2^2/k1^2(단, k2, 2k1은 피타고라스 수)를 만족하는 m,n,p,q가 존재하나? 가 됩니다.

더 정리한것도있는데 원하시면 물어봐주세요! 같이 풀어요!

(최종정리: c가 빗변이고 나머지 변의 길이가 a, b인 직각삼각형에서 a, b, c가 (m2+n2)/2mn꼴인 a, b, c(유리수)가 존재할까?

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