Erd's Anning Theorem
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Erd s Anning theorem states that an infinite number of points in the plane can have mutual integer distances only if all the points lie on a straight line. It is named after Paul Erd s and Norman H. Anning, who proved it in 1945. An alternative way of stating the theorem is that a non-collinear set of points in the plane with integer distances can only be extended by adding finitely many additional points, before no more points can be added. A set of points to whi...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Erd s Anning theorem states that an infinite number of points in the plane can have mutual integer distances only if all the points lie on a straight line. It is named after Paul Erd s and Norman H. Anning, who proved it in 1945. An alternative way of stating the theorem is that a non-collinear set of points in the plane with integer distances can only be extended by adding finitely many additional points, before no more points can be added. A set of points to which no more can be added, with all points on the integer grid, forms an Erd s-Diophantine graph.
