| [ guest ] in KIDS 글 쓴 이(By): guest (픽터) **uge00 Guest Auth Key: 37ec60cd5c2a15412c89688aaf9639db 날 짜 (Date): 2011년 11월 28일 (월) 오후 07시 16분 14초 제 목(Title): Re: [픽터] 초딩 산수 ㅋㅋㅋㅋ 8888888888888888888888888888888888888888888888888888888888888888888 8_[A]___________________88888____8__[E]_________________________[B]_8__ 8__________________8888_________88_________________________________8__ 8______________888_____________8_8____________7_[n]________________8__ 8___________8_________________8__8___________7_____________________8__ 8________8___________________8___8__________7______________________98__[P] 8______8____________________8____8_________7______________[m]___99_8__ 8_____8____________________8_____8________7___________________99____8__ 8___8_____________________8______8_______7_________________99_______8__ 8__8_____________________8_______8______7_______________99__________8__ 8_8_____________________8________8_____7_____________99_____________8__ 8_8____________________8_________8____7___________99________________8__ 88____________________8__________8___7_________99___________________8__ 8____________________8___________8__7_______99______________________8__ 8___________________8____________8_7_____99_________________________8__ 8__________________8_____________87___99____________________________8__ 8 _[Q]____________8______________8_[O]_____________________________8__ 8888888888888888888888888888888888888888888888888888888888888888888 8_______________8______________998_____________________________66__8__ 88_____________8____________997__8_________________________66______8__ 88____________8__________99__7___8_____________________66__________8__ 88___________8________99____7____8_________________66______________8__ 8_8_________8_______99_____7_____8____________66___________________8__ 8__8_______8_____99_______7______8________66_______________________8__ 8__88_____8____99________7_______8___66____________________________8__ 8____8___8__99__________7______668_________________________________8__ 8_____8_8_____________7_____66___8_________________________________8__ 8____998__[M]________7__66_______8_________________________________8__________ 8_99__8__8________7_66___________8_________________________________8___ 99___8_____888__66_______________8_________________________________8___ 8___8______66__888_[N]___________8_________________________________8___ 8__8___666________888888_________8_____________________________________ 8_866___________________88888____8_D___________________________________ 8888888888888888888888888888888888888888888888888888888888888888888888 M, m의 좌표는 (1/5, 2,5), (9/5, 8,5) 이다. 66선이 만나는 두 점 N, n의 좌표는y=x에 대한 M, m의 대칭이다. 그래서 N, n의 좌표는 (2/5, 1/5), (8/5, 9/5); 그래서 부채꼴(QOD) = pi/4 = 부채꼴(QOM) + 부채꼴(MON) + 부채꼴(NOD) = atan(1/3) + 부채꼴(MON) + 부채꼴(1/3) = 2atan(1/3) + 부채꼴(MON) 그런데 부채꼴(MON) = atan(tan(각(nMO)) 인데, vector(Mn) = (7/5, 7/5) vector(Mm) = (8/5, 6/5) 그래서 tan(각(nMO)) = cross product/dot product = (42-56)/(56+42) =14/98 = 1/7 그래서 전체적으로 pi/4 = 2atan(1/3) + atan(1/7) 이된다. 이것은 뭐 atan(1/2) = atan(1/3) + atan(1/7) 이기 때문이기도 하다. |