有没有好办法？

来源: cma 于 2012-01-01 09:00:01 [] [旧帖] [给我悄悄话] 阅读数 : (6865 bytes)

A beam of light strikes \overline{BC}\, at point C\, with angle of incidence \alpha=19.94^\circ\, and reflects with an equal angle of reflection as shown. The light beam continues its path, reflecting off line segments \overline{AB}\, and \overline{BC}\, according to the rule: angle of incidence equals angle of reflection. Given that \beta=\alpha/10=1.994^\circ\, and AB=AC,\, determine the number of times the light beam will bounce off the two line segments. Include the first reflection at C\, in your count.

AIME 1994 Problem 14.png

所有跟帖： 

• 38次？ -exe- ♂ 给 exe 发送悄悄话 (17 bytes) () 01/01/2012 postreply 13:05:10

• 1 time deal... or... 70 times? -花心鬼- ♂ 给 花心鬼 发送悄悄话 (481 bytes) () 01/01/2012 postreply 14:40:53

• your method only in special case can be OK. -jinjing- ♀ 给 jinjing 发送悄悄话 (192 bytes) () 01/01/2012 postreply 17:39:52

• If it is from Ps Q, We can do like that -jinjing- ♀ 给 jinjing 发送悄悄话 (309 bytes) () 01/02/2012 postreply 11:12:38

• 回复：If it is from Ps Q, We can do like that -cma- ♂ 给 cma 发送悄悄话 (7782 bytes) () 01/02/2012 postreply 13:48:33

• dear cma,81is not good. -jinjing- ♀ 给 jinjing 发送悄悄话 (266 bytes) () 01/02/2012 postreply 16:54:15

• I try by strict Math, the anwser should be between 78 and 81 -jinjing- ♀ 给 jinjing 发送悄悄话 (155 bytes) () 01/03/2012 postreply 12:09:54

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