1st Step for All

Science: 천문학 Astronomy; 생물학 Biology; 화학 Chemistry; 지질학 Geology; 수학 Mathematics; 물리 Physics

Engineering: 항공우주 Aerospace; 농업 Agriculture; 생물 Biological; 화학 Chemical; 토목공학 Civil; 전기공학 Electrical; 환경 Environmental; 산업 Industrial; 해양 Marine; 재료 Materials; 기계 Mechanical; 원자력 Nuclear

Architecture: 건축 Architecture

Health: 건강보건 Health

ETC: 기타 ETC

현재 위치

Minimum circumference length of a triangle having each of its three vertices on the sides of a isosceles right triangle

작성자 Uploader : 208st 작성일 Upload Date: 2018-10-15변경일 Update Date: 2018-10-17조회수 View : 403

There is an isosceles right triangle (AB=BC) as shown in figure. Assuming a point P at a fixed position on the side AB, and points Q and
R at arbitrary position on the sides AC and BC respectively, the minimum circumference length of the triangle PQR is calculated as below.

By symmetric transpositions of the triangle PQR with respect
to the side AC and to the side BC, we get
three triangles in contact, as shown in figure. Then, the circumference of the triangle PQR will be the minimum when the route PP becomes a straight line.

Letting the side length of the isosceles triangle as L (=AB=BC) and length of side AP as a, the minimum circumference length, Smin, is.

Smin = (a^2 + (L+(L-a))^2)^(1/2) = (a^2 + (2*L-a)^2)^(1/2)

*** 참고문헌[References] ***

Smin = (a^2 + (2*L-a)^2)^(1/2)

작성자의 수식그림이 없습니다. No picture for this formula


변수명 Variable	변수값 Value	변 수 설 명 Description of the variable

※ 이 사이트는 광고수익으로 운영됩니다.

★ 로그인 후 수식작성 및 즐겨찾기에 추가할 수 있습니다.
★ To make new formula or to add this formula in your bookmark, log on please.

1st Step for All

현재 위치

Minimum circumference length of a triangle having each of its three vertices on the sides of a isosceles right triangle

코멘트