Dividing a Circle Into Segments

I’m insanely busy on a gig right now, plus devoting time to taking care of parents, so once again I apologize for the lack of posts.  Hopefully, things will die down going into the latter part of August and I can get back to regular posting.

In the mean time, I often have to wait a considerable amount of time for a large application to build.  Someone posted an interesting problem (that’s probably pretty old and I’m too lazy to search) regarding the maximum number of segments a circle can be divided into with four lines.

For a minute or so, I was stuck on 10, then came up with 11.  Here’s one solution.

Now, I’m stuck at 11 and no time to think about this problem any more.  Anyone see a way to do 12?  It might be fun to consider how to prove the maximum number.  Ah, once again … too many interesting problems for which that whole making a living thing gets in the way.

Hopefully, I’ll have some new code samples for you around Labor Day.  Thx!

2 thoughts on “Dividing a Circle Into Segments

  1. I think that for a number of lines, the largest number of segments is obtained when each line intersects all the other lines *within* the circle. For four lines, the maximum number of segments is, indeed, 11.

    1. Christian – that’s what my intuition says (with the provision that no intersections are at a common point). Would be interesting one day to flesh it out into a more formal proof. Thanks!

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