deFinetti<-function(g=c(0.09,0.42,0.49)){
x<-seq(from=-1/sqrt(3),to=1/sqrt(3),by=0.01)
y<--1.5*x^2+1/6
plot(x,y,xlim=c(-1/sqrt(3),1/sqrt(3)),ylim=c(-1/3,2/3),type="l")
abline(a=2/3,b=sqrt(3))
abline(a=2/3,b=-sqrt(3))
abline(h=-1/3)
AA<-c(-1/sqrt(3),-1/3)
Aa<-c(0,2/3)
aa<-c(1/sqrt(3),-1/3)
O<-c(0,0)
par(new=T)
plot(AA[1],AA[2],xlim=c(-1/sqrt(3),1/sqrt(3)),ylim=c(-1/3,2/3))
par(new=T)
plot(Aa[1],Aa[2],xlim=c(-1/sqrt(3),1/sqrt(3)),ylim=c(-1/3,2/3))
par(new=T)
plot(aa[1],aa[2],xlim=c(-1/sqrt(3),1/sqrt(3)),ylim=c(-1/3,2/3))
af<-(2*g[1]+g[2])/2
f<-1-g[2]/(2*af*(1-af))
print(f)
X<-2/sqrt(3)*af-1/sqrt(3)
Y<-g[2]-1/3
par(new=T)
plot(X,Y,xlim=c(-1/sqrt(3),1/sqrt(3)),ylim=c(-1/3,2/3),pch=16,col="red")
yf<-(1/2-3/2*x^2)*(1-f)-1/3
par(new=T)
plot(x,yf,xlim=c(-1/sqrt(3),1/sqrt(3)),ylim=c(-1/3,2/3),type="l",col="red")
abline(v=X)
abline(a=1/sqrt(3)*X+Y,b=-1/sqrt(3))
abline(a=-1/sqrt(3)*X+Y,b=1/sqrt(3))
}
deFinetti()
