1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Radius of the largest ball inside a complex set.

  1. Jul 30, 2016 #1
    I've been thinking about notions like the following:
    "How far can one be from the nearest road while in a particular country."
    "What's the 'maximum thickness' of a subset of [itex]\mathbb{R}^n[/itex]?"
    "What mountain range has the biggest circular region entirely within it?"

    These sorts of questions lead to defining a quantity which is the "radius of the largest empty (hyper)sphere in the complement of a set" and solving it as a largest empty sphere problem.

    Is there a more convenient name for this quantity?
  2. jcsd
  3. Jul 30, 2016 #2
  4. Jul 30, 2016 #3

    sup { d(x, y) | x, yA } isn't necessarily going to be the same as twice the radius of the largest empty ball in the complement of A.

    For example, consider A as a filled in decagram (10 pointed star.) The diameter will be the same as the diameter of its circumcircle, but the quantity that is twice the radius of the largest empty disc in the complement of A will be a fair bit smaller. Exactly how much smaller depends on which type of decagram it is, but you see the point. The inward pointing wedges of empty space between the points of the star limit the size of disk which can fit fully within the decagram.
  5. Jul 31, 2016 #4


    User Avatar
    2017 Award

    Staff: Mentor

    Incircle or inscribed circle in the special case of a triangle. I don't know if there is a name for the general problem.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Radius of the largest ball inside a complex set.