수학동아 - 폴리매스

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함께 풀고 싶은 문제

나도 수학쌤 문장제 문제를 변형해 문제를 내는 곳입니다.

[문장제 문제&개념응용] 하이퍼 사이클로이드

잭과콩나물 2020.12.14 06:45 조회 718

문제 푼 사람 0명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

하이퍼사이클로이드란 작은 원이 큰 원의 안쪽을 내접하여 돌 때 작은 원 위의 한 점이 그리는 곡선을 말한다. 링크: (위키백과)

하이퍼사이클로이드를 이용한 문제를 풀어보자.

1) 하이퍼 사이클로이드가 직선인 경우도 있다는 것을 설명하고, 두 원(큰 원과 큰 원에 내접하는 원)의 반지름 길이의 비를 구해라.

2) 반지름 길이의 비가 5:1인 하이퍼 사이클로이드

가 있다. 이 때, a를 원주의 $\frac{1}{5}$ 로 하는 원의 둘레는 이 하이퍼 사이클로이드를 둘러싸는 원의 둘레와 같다는 것 을 하이퍼 사이클로이드의 성질과 관해 서술해라.

3) 반지름 길이의 비가 6:1인 하이퍼 사이클로이드와 5:1인 하이퍼 사이클로이드의 둘레의 차를 구해라.(이 때, 큰 원에 내접한 작은 원의 반지름은 5cm이다)[풀이는 필수]

(반지름 길이의 비가 6:1인 하이퍼 사이크로이드)

4) 다음 그림을 보고, 오각형과 하이퍼사이클로이드(반지름 길이의 비는 5:1)의 넓이의 차를 구해라.[풀이는 필수]

이전글 [조합] 문제모음 #4

다음글 [연산]줄넘기 점수

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잭과콩나물 Lv.6 2020.12.14 06:46

모든 사진 출처는 위키백과입니다.

참고로, 4번 문제는 아직 답을 구하지 못했습니다. 알아내신 분은 비밀댓글로 알려주시면 감사하겠습니다!

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khr519 Lv.8 2021.01.06 17:32 비밀댓글

비밀 댓글이 등록 되었습니다.

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