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發表 skywalker 於 星期四 十一月 02, 2006 7:23 pm

#ed_op#DIV#ed_cl#設此凸多邊形有n邊#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#其最小外角為24度,又外角和恆為360度#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#n/2[48+6(n-1)]=360#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#=>6n^2+42n-720=0#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#=>n^2+7n-120=0#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#n=-15或8(負不合)#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#n=8#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#

發表 革命萬歲! 於 星期五 三月 10, 2006 9:02 pm

#ed_op#DIV#ed_cl#可知其內角和為:#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#156+156-6+156-6x2+.......+156-6y#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#=156y-3y(1+y)=180度(y-2)#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#156-3y-y^2=180y-360#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#516-183y-y^2=0#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#自己解.#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl#

Re: [問題]問一題數列

發表 piny 於 星期三 三月 01, 2006 4:40 pm

neuron 寫到:#ed_op#DIV#ed_cl#設一凸多邊形內角度數成等差數列,公差為6度,且最大內角為156度,則其邊數為?#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#請問這題該怎麼算呢?謝謝~#ed_op#/DIV#ed_cl#
#ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#凸邊形的內角和為(N-2)*180#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#設最小角為A1,最大角為An#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#所以An=A1+(N-1)*6#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#利用等差和公式可知N(A1+An)/2=(N-2)*180#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#N=-15或8(取正值)#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#所以為八邊形#ed_op#/DIV#ed_cl#

[問題]問一題數列

發表 neuron 於 星期三 三月 01, 2006 2:04 pm

#ed_op#DIV#ed_cl#設一凸多邊形內角度數成等差數列,公差為6度,且最大內角為156度,則其邊數為?#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#請問這題該怎麼算呢?謝謝~#ed_op#/DIV#ed_cl#