Visible Points in a Lattice
Standing at the origin, gazing out into Quadrant I, some lattice points are visible ( such as (1,1)), but others are obscured by the visible points (for example, any point behind (1,1), such as (2,2), (3,3), and so on).
Any point (x,y) is visible from the origin if and only if the GCD(x,y) = 1. As the size of the grid of points increases, the proportion of visible points approaches 6/2.
Drag the slider to change the size of the grid (up to 50x50). Drag the red point on the left to see the line of sight or to see which points block it from view.