I had a PhD supervisor who refused to work with me because he did not like my political opinions. My work was nothing to do with politics. Still wondering whether to do something about this because discrimination based on political views is unlawful.

Countries that are not even on the map.

a=sqrt(3) for y=rx^2 we need a=sqrt(3)/r

The blue outline is an equilateral triangle. The red triangle is approximately equilateral with integer grid point vertices. The black triangle is equilateral triangle shifted by half the distance to the apex of the grid triangle.

Overlaid blue equilateral triangle (0,0), (152,0), (76,76*sqrt(3)) and red outline (0,0),(152,0),(76,132). Then an enlargement at the apex to show the error.

Yes. We can approximate sqrt(3) by a rational expression. It is possible to make this approximation as accurate as we desire. Here is one of my favourite methods.

Generally, we can fit a quadratic with rational coefficients.

Same three points with three of the coefficients not rational.