



 
We have two responses for you Tom, With his insistence on precise definitions it sounds as if your son will make a good mathematician! The bad news is that his teacher is probably correct  your son has the right definition but the wrong context. (However, it could be that the question was ambiguous, in which case your son could be correct; we would have to see the question for a definitive response.) Chris
That isn't a standard definition. There are several definitions that are standard, each valid in its own context. A vertex of a polyhedron (or equivalent shape in other dimensions) is a point where edges meet. In two dimensions this would always be two edges; in higher dimensions three or more (think of a pyramid). For a general convex body, a vertex is often defined to be a point at which the intersection of all the supporting hyperplanes there is the point. A hyperplane is a line in the plane, a plane in 3D space, etc. It is "supporting" if it contains the point but no point interior to the body.
For a cone, the last definition above would be appropriate, and your son's answer would be wrong. However:
Good Hunting!  


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