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"?
As Feynman said it is "a piece of plastic for drawing smooth curves--a curly, funny-looking thing". It is used in art classes occasionally. Take ANY smooth curve that has a lowest point, draw a tangent line to the curve at that point. The line will be horizontal because the derivative there will be zero.