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Manuel Rivera
Manuel Rivera
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I was looking at some random problems and questions I liked when I was in high school and I found this one which I still cannot prove.

Does there exist a configuration of a countable number of straight lines in the plane such that:

  1. no two are parallel

  2. no three are concurrent

  3. any bounded subset of the plane is intersected by a finite number of lines

  4. the area of every minimal polygon is equal, where a minimal polygon is a polygon formed by a finite subset of the set of lines such that no lines pass through the inside of the polygon.

The answer is certainly no, but it is not that easy to prove. Any ideas?

I was looking at some random problems and questions I liked when I was in high school and I found this one which I still cannot prove.

Does there exist a configuration of a countable number of straight lines in the plane such that:

  1. no two are parallel

  2. no three are concurrent

  3. any bounded subset of the plane is intersected by a finite number of lines

  4. the area of every minimal polygon is equal, where a minimal polygon is a polygon formed by a finite subset of the set of lines such that no lines pass through the inside of the polygon.

I was looking at some random problems and questions I liked when I was in high school and I found this one which I still cannot prove.

Does there exist a configuration of a countable number of straight lines in the plane such that:

  1. no two are parallel

  2. no three are concurrent

  3. any bounded subset of the plane is intersected by a finite number of lines

  4. the area of every minimal polygon is equal, where a minimal polygon is a polygon formed by a finite subset of the set of lines such that no lines pass through the inside of the polygon.

The answer is certainly no, but it is not that easy to prove. Any ideas?

Source Link
Manuel Rivera
Manuel Rivera
  • 2k
  • 1
  • 14
  • 23

infinite configuration of lines

I was looking at some random problems and questions I liked when I was in high school and I found this one which I still cannot prove.

Does there exist a configuration of a countable number of straight lines in the plane such that:

  1. no two are parallel

  2. no three are concurrent

  3. any bounded subset of the plane is intersected by a finite number of lines

  4. the area of every minimal polygon is equal, where a minimal polygon is a polygon formed by a finite subset of the set of lines such that no lines pass through the inside of the polygon.