Skip to main content
replaced http://mathoverflow.net/ with https://mathoverflow.net/
Source Link

Richard Guy has shown that there are six points in the plane—no three collinear, no four cocircular—such that all interpoint distances are rational.

Guy, Richard. Unsolved Problems in Number Theory. Vol. 1. Springer, 2004. D20. Six general points at rational distances. p.185ff:


          ![GuyFig14b][1]

My question is:

Q. Is it known that six is the maximum possible? Or have examples been found in the intervening decade that supersede Guy's result?

Update. This question is essentially a duplicate of "Integer-distance setsInteger-distance sets." Apologies.

Richard Guy has shown that there are six points in the plane—no three collinear, no four cocircular—such that all interpoint distances are rational.

Guy, Richard. Unsolved Problems in Number Theory. Vol. 1. Springer, 2004. D20. Six general points at rational distances. p.185ff:


          ![GuyFig14b][1]

My question is:

Q. Is it known that six is the maximum possible? Or have examples been found in the intervening decade that supersede Guy's result?

Update. This question is essentially a duplicate of "Integer-distance sets." Apologies.

Richard Guy has shown that there are six points in the plane—no three collinear, no four cocircular—such that all interpoint distances are rational.

Guy, Richard. Unsolved Problems in Number Theory. Vol. 1. Springer, 2004. D20. Six general points at rational distances. p.185ff:


          ![GuyFig14b][1]

My question is:

Q. Is it known that six is the maximum possible? Or have examples been found in the intervening decade that supersede Guy's result?

Update. This question is essentially a duplicate of "Integer-distance sets." Apologies.

added 134 characters in body
Source Link
Joseph O'Rourke
  • 150.9k
  • 36
  • 358
  • 958

Richard Guy has shown that there are six points in the plane—no three collinear, no four cocircular—such that all interpoint distances are rational.

Guy, Richard. Unsolved Problems in Number Theory. Vol. 1. Springer, 2004. D20. Six general points at rational distances. p.185ff:


          ![GuyFig14b][1]

My question is:

Q. Is it known that six is the maximum possible? Or have examples been found in the intervening decade that supersede Guy's result?

Update. This question is essentially a duplicate of "Integer-distance sets." Apologies.

Richard Guy has shown that there are six points in the plane—no three collinear, no four cocircular—such that all interpoint distances are rational.

Guy, Richard. Unsolved Problems in Number Theory. Vol. 1. Springer, 2004. D20. Six general points at rational distances. p.185ff:


          ![GuyFig14b][1]

My question is:

Q. Is it known that six is the maximum possible? Or have examples been found in the intervening decade that supersede Guy's result?

Richard Guy has shown that there are six points in the plane—no three collinear, no four cocircular—such that all interpoint distances are rational.

Guy, Richard. Unsolved Problems in Number Theory. Vol. 1. Springer, 2004. D20. Six general points at rational distances. p.185ff:


          ![GuyFig14b][1]

My question is:

Q. Is it known that six is the maximum possible? Or have examples been found in the intervening decade that supersede Guy's result?

Update. This question is essentially a duplicate of "Integer-distance sets." Apologies.

edited body
Source Link
Anthony Quas
  • 23.2k
  • 5
  • 63
  • 98

Richard Guy has shown that there are six points in the plane—no three collinear, no four cocircular—such that all interpoint distances are rational.

Guy, Richard. Unsolved Problems in Number Theory. Vol. 1. Springer, 2004. D20. Six general points at rational distances. p.185ff:


          ![GuyFig14b][1]

My question is:

Q. Is it known that six is the maximum possible? Or have examples been found in the intervening decade that supercedesupersede Guy's result?

Richard Guy has shown that there are six points in the plane—no three collinear, no four cocircular—such that all interpoint distances are rational.

Guy, Richard. Unsolved Problems in Number Theory. Vol. 1. Springer, 2004. D20. Six general points at rational distances. p.185ff:


          ![GuyFig14b][1]

My question is:

Q. Is it known that six is the maximum possible? Or have examples been found in the intervening decade that supercede Guy's result?

Richard Guy has shown that there are six points in the plane—no three collinear, no four cocircular—such that all interpoint distances are rational.

Guy, Richard. Unsolved Problems in Number Theory. Vol. 1. Springer, 2004. D20. Six general points at rational distances. p.185ff:


          ![GuyFig14b][1]

My question is:

Q. Is it known that six is the maximum possible? Or have examples been found in the intervening decade that supersede Guy's result?

Source Link
Joseph O'Rourke
  • 150.9k
  • 36
  • 358
  • 958
Loading