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still not sure whether a cone has a vertex!

Discussion in 'Mathematics' started by CarrieV, May 10, 2011.

  1. CarrieV

    CarrieV Lead commenter

    I always thought it did ( but then I teach primary so am happy to be corrected by those who know better!) and several sources seem to back this up, my maths dictionary for one[​IMG] I appreciate there is some discussion about a vertex being the point where two or more straight lines meet but,as I thought a cone had an infinite number of straight lines, it seemed to pass this test too. However my student teacher has been informed by her training provider that cones do NOT have a vertex and now I'm worried! Can anyone reassure me/disabuse me before I inflict my uninformed opinions on another unsuspecting generation of primary teachers!
     
  2. DM

    DM New commenter

  3. DM

    DM New commenter

    "if you say it has"
     
  4. strawbs

    strawbs Occasional commenter

    it certainly has a pointy bit!
     
  5. strawbs

    strawbs Occasional commenter

  6. CarrieV

    CarrieV Lead commenter

    You see, no wonder I'm confused! One wolfram quote says it doesn't, the other says it does!
    Make your mind up!
     
  7. From The Penguin Dictionary of Mathematics:
    "Cone: A solid figure formed by a close plane curve on a plane (the base) and all the lines joining points of the base to a fixed point (the vertex) not in the plane of the base."
     
  8. And here is another inconsistency, also within mathworld: http://mathworld.wolfram.com/Pyramid.html
    extract: "A pyramid is a polyhedron with one face (known as the "base") a polygon and all the other faces triangles meeting at a common polygon vertex"
    So by this definition a cone is not a pyramid (in the same way a cylinder is not a prism).
    But does this matter? I would suggest not.
    Calling a square a triangle matters. Saying a square is not a rectangle matters (because it is!). Calling the apex of a cone a vertex doesn't seem to affect many other definitions or usages and doesn't therefore lead to sloppy thinking, so it doesn't seem to be a big deal.
     
  9. DM

    DM New commenter

  10. DM

    DM New commenter

    Great spelling from the poster I referenced. He should use a dictionary.
     
  11. DM

    DM New commenter

  12. CarrieV

    CarrieV Lead commenter

    OK, as long as you are all happy for your new year 7's to be convinced a cone has a vertex, I will continue to tell them it does!
    ( I don't like to annoy my secondary counterparts[​IMG])
     
  13. DM

    DM New commenter

    Most year 11 students haven't the slightest idea what vertex means so I would be delighted.
     
  14. bombaysapphire

    bombaysapphire Star commenter

    Mymaths says that it has one so it would be consistent with that. I use some of their games to consolidate work on shape so I say that it has one as well to avoid confusion.
    Welcome back DM, looks like you've missed us!
     
  15. DM

    DM New commenter

    There's no place like cone.
     
  16. Delighted to have you back DM. Hope you haven't lost any of your zing.
    Yes a cone has a vertex. On the other hand, if you talk to someone clued up
    about conic sections, they will tell you that they have to deal with double-cones.
    Such a thing doesn't have a vertex in the dictionary sense.
    Yes a cone ...
     
  17. Agreed, as they will complex numbers, integrals, hyperbolic identites. Im not sure though its something they need to dwell upon so early.
    I think the requirements for level 5 (even 6) NC levels may sit further down the chain
     
  18. So in answer to the question "Does a cone have a vertex?" or "How many vertices does a cone have?" The answer is...?

    I teach 7-11 years & this question comes up quite regularly on 11 plus papers & I do not want to give them incorrect information. Children as we know like a clear yes or no & so do I.
     
  19. bombaysapphire

    bombaysapphire Star commenter

    Our conclusion was that it has one.
     

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