Life on the edge - a maths question!

I was just asked a great maths question from the wonderful boys and girls at Screen National School (5th and 6th class) in Wexford.  These children are on the ball with their technology as the question came through twitter and they also have a fab blog that you should check out!

So here is the question.....

"Does a cone have one edge or is it not an edge at all because it is a curved line?"

The answer is .... it depends on how you define and edge!

photo credit: L. Marie via photopin cc

The basic definition of an edge is the line where two faces meet.  If we look at any geometrical object that has flat surfaces, such as a cube, then it is easy to count the number of edges.

This definition works well for all polyhedra. However it gets a lot more tricky when we talk about solid objects with curved surfaces.  If we go by this definition when talking about a cone shape then we would have to say NO, the cone does not have a line where two faces (flat surfaces) meet.

So the answer is .... a cone has zero edges!

... if we look at the definition of an edge as being the line where two surfaces meet we could count the curved surface of the cone as one surface and the flat circular base as the other surface, so we have an edge where both meet.  This is how my daughter's teacher (3rd class) approaches the issue of how many edges a cone has... she counts the circular line where the base touches the curved face of the cone as one edge!

So the answer is ... a cone has one edge!

BUT... edge can also be defined as a boundary of a geometric figure.  This definition works better when we are considering curved surfaces like the one we find on the cone.  If we look at the cone with this definition then we could say that the cone has one curved edge.  When I posed this question to Helen Bullock of Anseo a Mhuinteoir she said she includes this classification when counting edges of cones within the classroom.

So the answer is.... a cone has two edges!

So there you go, ask a question and sometimes you get more answers than you bargained for!  It would appear that all three answers are correct once you state which definition of an edge you are using!

A bit more fun...

Did you know that......Ireland's Maths Week 2013  takes place from 12th to 20th October with events all around the Country?  Check out the official website for more details!

If you have any questions or ideas to add please leave your comment below, I always love to hear from you!

Furter Resources:
Seomra Ranga - Maths links 
Maths Websites for kids
Manga High
IXL Maths

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