At last...."Geometry" was the category for Final Jeopardy on 10/23/07. As host Alex Trebek stated, a "very difficult-sounding category."
Assuming you had $10,000 built up, how much would you bet on this category?
The given answer was: "It's an ellipse with an eccentricity of zero."
First, Alex Trebek admitted that it was a long time since he had geometry and had no idea when he saw the clue. Then, all three contestants formed the correct question: "What is a circle?"
My question: Is eccentricity taught as part of most geometry courses? I don't think so....and I think the contestants were lucky with their guesses!
In case you have forgotten, eccentricity e of an ellipse is the constant ratio of the distance of a point on the ellipse from a focus to the point's distance from the corresponding directrix. And, for an ellipse with semimajor axis a and semiminor axis b, eccentricity e = SQRT[1 - (a/b)2]. For a circle, a = b, which implies that e = 0.