Results 1 to 3 of 3

Math Help - Ellipses and Equiangular Polygons

  1. #1
    Junior Member Mathhead200's Avatar
    Joined
    Oct 2011
    From
    Washington DC
    Posts
    50
    Thanks
    6

    Ellipses and Equiangular Polygons

    - Is it possible to inscribe a unique ellipse with maximal area into any arbitrary equiangular polygon?
    - Is it possible to circumscribe a unique ellipse with minimal area around any arbitrary equiangular polygon?
    - Are those inscribed and circumscribed ellipses similar (in the geometric sense)?

    E.g. I believe a circle circumscribes, and then maximally inscribes an equiangular triangle;
    and, I believe that a unique ellipse inscribes a rectangle, and then a similar ellipse minimally circumscribes the same rectangle.

    (I don't know if my two examples are correct so, if they are not, please correct and post a counter examples.)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member Mathhead200's Avatar
    Joined
    Oct 2011
    From
    Washington DC
    Posts
    50
    Thanks
    6

    Re: Ellipses and Equiangular Polygons

    No answer? I really don't know how to go about proving if this is true, (or finding a counter-example.) My experience in college has mainly been with algebra. Is there as way to abstract this problem to one in algebra? I've done some very basic work in algebraic geometry, but I wouldn't know how to express the equiangular shapes as subsets of \mathbb{A}_{\mathbb{R}}^2. I don't think they can be expressed as algebraic sets (like the ellipses can be)...? (And how would I even know if my two algebraic sets represent two similar ellipses?)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member Mathhead200's Avatar
    Joined
    Oct 2011
    From
    Washington DC
    Posts
    50
    Thanks
    6

    Re: Ellipses and Equiangular Polygons

    By the way, I know this was posted last year, but I still don't have an answer.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. ellipses
    Posted in the Pre-Calculus Forum
    Replies: 7
    Last Post: December 17th 2010, 06:39 PM
  2. Ellipses
    Posted in the Pre-Calculus Forum
    Replies: 8
    Last Post: November 24th 2007, 03:40 PM
  3. Polygons
    Posted in the Geometry Forum
    Replies: 2
    Last Post: September 26th 2007, 10:27 AM
  4. Polygons
    Posted in the Statistics Forum
    Replies: 3
    Last Post: January 25th 2007, 04:25 PM
  5. Polygons Help!
    Posted in the Geometry Forum
    Replies: 4
    Last Post: January 6th 2007, 07:06 AM

Search Tags


/mathhelpforum @mathhelpforum