Hey there Sign in to join this conversationNew here? Join for free

Torus Equation

Announcements Posted on
Study Help needs new mods! 14-04-2014
We're up for a Webby! Vote TSR to help us win. 10-04-2014
    • Thread Starter
    • 3 followers
    Online

    ReputationRep:
    Let T be a circle with diameter AC=a, and let B be a point on T such that AB=b<a. Let T' be the semicircle with diameter AC in the plane perpendicular to that of T.

    Rotating T' around the perpendicular at A to the plane ABC generates a torus  \mathcal{T} of internal radius 0. Give the equation of  \mathcal{T} .
    __

    I've started by drawing everything out. If the circle is in the x-y plane, with the point A as at the origin, then the perpendicular is the z axis and the semi circle T' is in the x-z plane. Rotating around the z axis I can't see how this produces a torus? At best I get an upper half of a torus?
    • 24 followers
    Offline

    (Original post by miml)
    At best I get an upper half of a torus?
    Yep, that's what I make it.

    Edit: There also seems to be redundant information there. Multipart question?
    • Thread Starter
    • 3 followers
    Online

    ReputationRep:
    (Original post by ghostwalker)
    Yep, that's what I make it.

    Edit: There also seems to be redundant information there. Multipart question?
    Thanks, I think what they want is to extend the semi-circle to a circle in the x-z plane, rotate it, give the equation of the resulting torus and then for the following parts only consider the upper half.

    Archytas' solution to doubling the cube if you're interested.

Reply

Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?

    this is what you'll be called on TSR

  2. this can't be left blank
    this email is already registered. Forgotten your password?

    never shared and never spammed

  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. By completing the slider below you agree to The Student Room's terms & conditions and site rules

  2. Slide the button to the right to create your account

    Slide to join now Processing…

    You don't slide that way? No problem.

Updated: October 23, 2012
Article updates
Reputation gems:
You get these gems as you gain rep from other members for making good contributions and giving helpful advice.