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It seems evident from infinitely many primitive pythagorean triples (a,b,c) that there are infinitely many rational points (a/c, b/c) on the unit circle.

But how would one go about, and show that they are dense, in the sense that for two rational points x and y of angles α and β on the unit circle, if α<β there is

  a third rational point z of angle γ on the unit circle, such that α<γ and γ<β. Is it to expect that this conjecture holds and that it isn't an unsolved number theory problem?

It seems evident from infinitely many primitive pythagorean triples $(a,b,c)$ that there are infinitely many rational points $\left(\frac{a}{c}, \frac{b}{c}\right)$ on the unit circle.

But how would one go about, and show that they are dense, in the sense that for two rational points $x$ and $y$ of angles $α$ and $β$ on the unit circle, if $α<β$ there is a third rational point $z$ of angle $γ$ on the unit circle, such that $α<γ$ and $γ<β$. 

Is it to expect that this conjecture holds and that it isn't an unsolved number theory problem?

It seems evident from infinitely many primitive pythagorean triples (a,b,c) that there are infinitely many rational points (a/c, b/c) on the unit circle.

But how would one go about, and show that they are dense, in the sense that for two rational points x and y of angles α and β on the unit circle, if α<β there is a third rational point z of angle γ on the unit circle, such that α<γ and γ<β.

It seems evident from infinitely many primitive pythagorean triples (a,b,c) that there are infinitely many rational points (a/c, b/c) on the unit circle.

But how would one go about, and show that they are dense, in the sense that for two rational points x and y of angles α and β on the unit circle, if α<β there is 

a third rational point z of angle γ on the unit circle, such that α<γ and γ<β. Is it to expect that this conjecture holds and that it isn't an unsolved number theory problem?

It seems evident from infinitely many primitive pythagorean triples (a,b,c) that there are infinitely many rational points (a/c, b/c) on the unit circle.

But how would one go about, and show that they are dense, in the sense that for two rational points x and y of angles α and β on the unit circle, if α<β there is

  a third rational point z of angle γ on the unit circle, such that α<γ and γ<β. I hope its not some unsolved number theory problem and that this conjecture holds.

It seems evident from infinitely many primitive pythagorean triples (a,b,c) that there are infinitely many rational points (a/c, b/c) on the unit circle.

But how would one go about, and show that they are dense, in the sense that for two rational points x and y of angles α and β on the unit circle, if α<β there is a third rational point z of angle γ on the unit circle, such that α<γ and γ<β.