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Holowitz
Holowitz
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What is the least possible cardinality $K$, of a set S of points in the plane, such that there exists a point P in the plane and an open ball B centered at P, such that for all points X in B, not all the euclidean distances from X to points of S are rational?

Can we do better then $3\leq K \leq 2^{\aleph_0}$?

What can be said about K if all the points of S must be at integer distance from eachother, or algebraic distancecan it be proved to be finite?

What is the least possible cardinality $K$, of a set S of points in the plane, such that there exists a point P in the plane and an open ball B centered at P, such that for all points X in B, not all the euclidean distances from X to points of S are rational?

Can we do better then $3\leq K \leq 2^{\aleph_0}$?

What can be said about K if all the points of S must be at integer distance from eachother, or algebraic distance?

What is the least possible cardinality $K$, of a set S of points in the plane, such that there exists a point P in the plane and an open ball B centered at P, such that for all points X in B, not all the euclidean distances from X to points of S are rational?

Can we do better then $3\leq K \leq 2^{\aleph_0}$?

What can be said about K if all the points of S must be at integer distance from eachother, can it be proved to be finite?

added 95 characters in body; added 23 characters in body
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Holowitz
Holowitz
  • 98
  • 5

What is the least possible cardinality $K$, of a set S of points in the plane, such that there exists a point P in the plane and an open ball B centered at P, such that for all points X in B, not all the euclidean distances from X to points of S are rational?

Can we do better then $3\leq K \leq 2^{\aleph_0}$?

What can be said about K if all the points of S must be at integer distance from eachother, or algebraic distance?

What is the least possible cardinality $K$, of a set S of points in the plane, such that there exists a point P in the plane and an open ball B centered at P, such that for all points X in B, not all the euclidean distances from X to points of S are rational?

Can we do better then $3\leq K \leq 2^{\aleph_0}$?

What is the least possible cardinality $K$, of a set S of points in the plane, such that there exists a point P in the plane and an open ball B centered at P, such that for all points X in B, not all the euclidean distances from X to points of S are rational?

Can we do better then $3\leq K \leq 2^{\aleph_0}$?

What can be said about K if all the points of S must be at integer distance from eachother, or algebraic distance?

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Holowitz
Holowitz
  • 98
  • 5

What is the least possible cardinality $K$, of a set S of points in the plane, such that there exists a point P in the plane and an open ball B aroundcentered at P, such that for all points X in B, not all the euclidean distances from X to points of S are rational?

Can we do better then $3\leq K \leq 2^{\aleph_0}$?

What is the least possible cardinality $K$, of a set S of points in the plane, such that there exists a point P in the plane and an open ball B around P, such that for all points X in B, not all the euclidean distances from X to points of S are rational?

Can we do better then $3\leq K \leq 2^{\aleph_0}$?

What is the least possible cardinality $K$, of a set S of points in the plane, such that there exists a point P in the plane and an open ball B centered at P, such that for all points X in B, not all the euclidean distances from X to points of S are rational?

Can we do better then $3\leq K \leq 2^{\aleph_0}$?

Source Link
Holowitz
Holowitz
  • 98
  • 5