What is a French curve, as mentioned by Feynman?

I'm reading "Surely You're Joking, Mr. Feynman!", he says:

I often liked to play tricks on people when I was at MIT. One time, in mechanical drawing class, some joker picked up a French curve (a piece of plastic for drawing smooth curves--a curly, funny-looking thing) and said, "I wonder if the curves on this thing have some special formula?"

I thought for a moment and said, "Sure they do. The curves are very special curves. Lemme show ya," and I picked up my French curve and began to turn it slowly. "The French curve is made so that at the lowest point on each curve, no matter how you turn it, the tangent is horizontal."

All the guys in the class were holding their French curve up at different angles, holding their pencil up to it at the lowest point and laying it along, and discovering that, sure enough, the tangent is horizontal. They were all excited by this "discovery"--even though they had already gone through a certain amount of calculus and had already "learned" that the derivative (tangent) of the minimum (lowest point) of any curve is zero (horizontal). They didn't put two and two together. They didn't even know what they "knew."

I'm a bit lost, what kind of curve is it, and what doe he mean by "at the lowest point on each curve, no matter how you turn it, the tangent is horizontal."?

sorry if the tagging is poor -- there's no simple "curve" tag, for example i'm not sure if french curve is "Elliptic-curves", "algebraic-curves", or "plane-curves"?

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The point of the story is that Feynman convinced his listeners that something well-known (from 1st semester calculus) about all smooth curves is a special property of this curve. – hardmath Aug 1 '14 at 3:28
Try reading the Wikipedia entry on the French curve. – Joel Reyes Noche Aug 1 '14 at 3:31
@hardmath ah i got it. the lower point of course has horizontal tangent! – athos Aug 1 '14 at 3:32
It is also called lekalo. Basically, you use ruler to draw lines, compass to draw circles. For more general curves, you use French curve, that is like a collection of pre-cut shapes made of plastic so you can slide your pen along it to draw different curves. – timur Aug 1 '14 at 3:58
The story is funny though. This is MIT for crying out loud. – timur Aug 1 '14 at 4:03