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Just imagine that your kids need some help, to prepare fishes for April 1st, like

Me: “Sure, Daddy is a champion, actually, I do that everyday at work: drawing fishes – and more generally nice stuff – is exactly Daddy’s job“.

OK, no need to talk neither about Talbot’s curves, ellipse negative pedal curve nor Burleigh’s ovals, unless you don’t want to scare them, e.g.

t=seq(0,2*pi,length=100)
b=.8
c=sqrt(1-b^2)
x=cos(t)-c*sin(t)^2
y=(1-2*c^2+c*cos(t))*sin(t)/b
plot(x,y)

From now on, it is rather simple to draw fishes,

t=seq(0,2*pi,length=100)
y=cos(t)-sin(t)^2/sqrt(2)
x=cos(t)*sin(t)
plot(x,y,type="l",axes=FALSE,xlab="",ylab="")
polygon(c(-2,-2,2,2),
c(-2,2,2,-2),col="light blue",border=NA)
polygon(x,y,col="red",border=NA)
axis(1)
axis(2)
lines(x,y,type="l")

so we can easily get nice fishes,