■フルヴィッツ曲線(その116)

x=(n-2)acos(nθ)+nacos(n-2)θ+2Rsinθ

y=-(n-2)asin(nθ)+nasin(n-2)θ+2Rcosθ

  xsinθ−ycosθ=p(θ)

に代入すると

(n-2)asin(n+1)θ-nasin(n-3)θ-2Rcos2θ=p(θ)

na(sin(n+1)θ-sin(n-3)θ)-2asin(n+1)-2Rcos2θ=p(θ)

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しかし(x,-y)を

  xsinθ−ycosθ=p(θ)

に代入すると

x=(n-2)acos(nθ)+nacos(n-2)θ+2Rsinθ

y=(n-2)asin(nθ)-nasin(n-2)θ-2Rcosθ

2(n-1)asin(n-1)θ+2R=p(θ)

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