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Is it possible to find an infinite set of point belonging to the circle of radius r such that $\sqrt{r} \notin \mathbb{Q}$ and where the distance between any pair is rational?
For example, can we find such set for $r=\frac{4}{3}$ This is related to the following question: nD SPACE RATIONAL DISTANCEnD SPACE RATIONAL DISTANCE
The difference is the new condition on the radius (in the link, the argument is given for the unit circle).
My idea would be then to construct infinite sets in n-dimensional spaces considering the unions of such circles in 2D subspaces (and adding points on an axis when n is odd)

Is it possible to find an infinite set of point belonging to the circle of radius r such that $\sqrt{r} \notin \mathbb{Q}$ and where the distance between any pair is rational?
For example, can we find such set for $r=\frac{4}{3}$ This is related to the following question: nD SPACE RATIONAL DISTANCE
The difference is the new condition on the radius (in the link, the argument is given for the unit circle).
My idea would be then to construct infinite sets in n-dimensional spaces considering the unions of such circles in 2D subspaces (and adding points on an axis when n is odd)

Is it possible to find an infinite set of point belonging to the circle of radius r such that $\sqrt{r} \notin \mathbb{Q}$ and where the distance between any pair is rational?
For example, can we find such set for $r=\frac{4}{3}$ This is related to the following question: nD SPACE RATIONAL DISTANCE
The difference is the new condition on the radius (in the link, the argument is given for the unit circle).
My idea would be then to construct infinite sets in n-dimensional spaces considering the unions of such circles in 2D subspaces (and adding points on an axis when n is odd)

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Edouard L.
Edouard L.
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Rational distance between any pair of an infinite set on a specific circle

Is it possible to find an infinite set of point belonging to the circle of radius r such that $\sqrt{r} \notin \mathbb{Q}$ and where the distance between any pair is rational?
For example, can we find such set for $r=\frac{4}{3}$ This is related to the following question: nD SPACE RATIONAL DISTANCE
The difference is the new condition on the radius (in the link, the argument is given for the unit circle).
My idea would be then to construct sets infinite sets in n-dimensional spaces considering the unions of such circles in 2D subspaces (and adding points on an axis when n is odd)

Rational distance between any pair of an infinite set on specific circle

Is it possible to find an infinite set of point belonging to the circle of radius r such that $\sqrt{r} \notin \mathbb{Q}$ and where the distance between any pair is rational?
For example, can we find such set for $r=\frac{4}{3}$ This is related to the following question: nD SPACE RATIONAL DISTANCE
The difference is the new condition on the radius (in the link, the argument is given for the unit circle).
My idea would be then to construct sets infinite sets in n-dimensional spaces considering the unions of such circles in 2D subspaces (and adding points on an axis when n is odd)

Rational distance between any pair of an infinite set on a specific circle

Is it possible to find an infinite set of point belonging to the circle of radius r such that $\sqrt{r} \notin \mathbb{Q}$ and where the distance between any pair is rational?
For example, can we find such set for $r=\frac{4}{3}$ This is related to the following question: nD SPACE RATIONAL DISTANCE
The difference is the new condition on the radius (in the link, the argument is given for the unit circle).
My idea would be then to construct infinite sets in n-dimensional spaces considering the unions of such circles in 2D subspaces (and adding points on an axis when n is odd)

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Edouard L.
Edouard L.
  • 581
  • 2
  • 9

Rational distance between any pair of an infinite set on specific circle

Is it possible to find an infinite set of point belonging to the circle of radius r such that $\sqrt{r} \notin \mathbb{Q}$ and where the distance between any pair is rational?
For example, can we find such set for $r=\frac{4}{3}$ This is related to the following question: nD SPACE RATIONAL DISTANCE
The difference is the new condition on the radius (in the link, the argument is given for the unit circle).
My idea would be then to construct sets infinite sets in n-dimensional spaces considering the unions of such circles in 2D subspaces (and adding points on an axis when n is odd)