A rational diagonal is easier to draw, \(c=\cfrac{a}{b}\) means a line \(b\) on the x axis and \(a\) up on the y axis; a line through cutting the both axes at these point is \(c\). But what else?
The effect of not allowing other numbers for \(c\) is an incomplete set of spaced ellipses.
But what look like a ellipse is an ellipse. Since every ellipse can be drawn on a pixelized computer screen, there are finite number of rational points on every ellipse. Birch and Swinnerton-Dyer conjecture is half proven!
The latter part of the Conjecture, "...and the first non-zero coefficient in the Taylor expansion of L(E, s) at s = 1 is given by more refined arithmetic data attached to E over K", suggests an irrational coefficient, possibly involving \(\sqrt{2}\) and \(\pi\).
Dithering is after the ellipse has been drawn. A kind of fuzz to made the lines smooth.
A made-up question to plot ellipse on cartesian points. Not fun.
Note: \(c\) is used to general the ellipse; rational \(c\), plots rational points on the ellipse. If \(c\) not rational move diagonal to next rational points and start there.
