円は正n角形である。n = ?

#背景
周りの人に『円は正?角形』と聞いたら、『意味が分からない』と『ゼロ角形』と答える人は、ほぼ全員だ。本日、やっと『infinity』と答えてくれる人が出てきた。

#正n角形

答えは、『円は正$\infty$角形』

#コード

plot.new()
plot.window( xlim = c(-1,1), ylim = c(-1,1) )

# 正三角形
x3 <- seq( -pi * 1.5, pi * 0.5, length = 4 )
# 正四角形
x4 <- seq( -pi * 1.5, pi * 0.5, length = 5 )
# 正五角形
x5 <- seq( -pi * 1.5, pi * 0.5, length = 6 )
# 正六角形
x6 <- seq( -pi * 1.5, pi * 0.5, length = 7 )
# 正八角形
x8 <- seq( -pi * 1.5, pi * 0.5, length = 9 )
# 正十六角形
x16 <- seq( -pi * 1.5, pi * 0.5, length = 17 )
# 正三十二角形
x32 <- seq( -pi * 1.5, pi * 0.5, length = 33 )
# 正六十四角形
x64 <- seq( -pi * 1.5, pi * 0.5, length = 65 )
# 正n角形
n <- 2^10 # 任意な数字
xn <- seq( -pi * 1.5, pi * 0.5, length = n+1 )

fname　<- paste( "正n角形", ".png", sep="" )
png( file = fname, height = 800, width = 800 )
par( mfrow = c(3,3) )
plot( cos(x3), sin(x3), type = "l", xlab = "3", ylab = "" )
plot( cos(x4), sin(x4), type = "l", xlab = "4", ylab = "" )
plot( cos(x5), sin(x5), type = "l", xlab = "5", ylab = "" )
plot( cos(x6), sin(x6), type = "l", xlab = "6", ylab = "" )
plot( cos(x8), sin(x8), type = "l", xlab = "8", ylab = "" )
plot( cos(x16), sin(x16), type = "l", xlab = "16", ylab = "" )
plot( cos(x32), sin(x32), type = "l", xlab = "32", ylab = "" )
plot( cos(x64), sin(x64), type = "l", xlab = "64", ylab = "" )
plot( cos(xn), sin(xn), type = "l", xlab = "n", ylab = "" )
dev.off()