Dear Math Central:
Please help me explain to my fourth graders as to why a cone has a vertex even though it does not have any straight edges.
Richard
Our word VERTEX comes from a Latin word meaning crown of the head, highest point, summit.
According to the Oxford English Dictionary, the word was originally used in geometry to mean
The point opposite to the base of a (plane or solid) figure.
So, one thinks of the triangle ABC sitting on its base BC with its vertex A placed above. With a cone, the base is a curve (typically a circle) sitting in a horizontal plane, and its vertex is the point placed (vertically) above that base that is joined by a straight line to each of its points.
The various other meanings of the word vertex in mathematics apparently were derived from this.
Chris