■ハムサンドよりピザが好き(その11)

a=arcsin(sin(π/8−α)/R)−arcsin(−sinα/R)

b=arcsin(sin(π/4−α)−arcsin(sin(π/8−α)/R)

c=arcsin(sin(3π/8−α)/R)−arcsin(sin(π/4−α)/R)

d=arcsin(cosα/R)−arcsin(3π/8−α)/R)

e=arcsin(cos(π/8−α)/R)−arcsin(cosα/R)

f=arcsin(sin(π/4−α)/R)−arcsin(cos(π/8−α)/R)

g=arcsin(cos(3π/8−α)/R)−arcsin(cos(π/4−α)/R)

h=arcsin(sinα/R)−arcsin(cos(3π/8−α)/R)

i=arcsin(−sin(π/8−α)/R)−arcsin(sinα/R)

j=arcsin(−sin(π/4−α)/R)−arcsin(−sin(π/8−α)/R)

k=arcsin(−sin(3π/8−α)/R)−arcsin(−sin(π/4−α)/R)

l=arcsin(−cosα/R)−arcsin(−sin(3π/8−α)/R)

m=arcsin(−cos(π/8−α)/R)−arcsin(−cosα/R)

n=arcsin(−sin(π/4−α)/R)−arcsin(−cos(π/8−α)/R)

o=arcsin(−cos(3π/8−α)/R)−arcsin(−cos(π/4−α)/R)

p=arcsin(−sinα/R)−arcsin(−cos(3π/8−α)/R)

 a+i=0,b+j=0,c+k=0,d+l=0

 m+e=0,n+f=0,o+g=0,p+h=0

a+c+e+g+i+k+m+o=b+d+f+h+j+l+n+pは成り立つ.

a+e+i+m=c+g+k+o=b+f+j+n=d+h+l+pも成り立つ.したがって,4人でも均等に分けることができる可能性がある.

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