The post is titled “60-degree angles on a lattice”, and links to “how to draw a good approximation to an equilateral triangle on a piece of graph paper” — that

The post is titled “60-degree angles on a lattice”, and links to “how to draw a good approximation to an equilateral triangle on a piece of graph paper” — that is, the problem being considered is one where all coordinates have to be integers. If you're willing to use compasses and get arbitrary coordinates, you don't need any of this, not even the first part — it's an entirely different (and much simpler) problem.