[cong-or]

Is there a computational advantage to constructing φ geometrically versus algebraically? In rendering or CAD, would you actually trace the circle/triangle intersections, or just compute (1 + sqrt(5)) / 2 directly?

I’m curious if the geometric approach has any edge-case benefits—like better numerical stability—or if it’s purely for elegance.

[meindnoch]

When a computer does "geometry", it just computes numbers under the hood. There are no tiny people in the CPU with compasses and straightedges.

[cong-or]

Fair enough—I wasn’t imagining tiny compass-wielders. I was thinking more about whether the structure of a geometric construction might map to something computationally useful, like exact arithmetic systems (CGAL-style) that preserve geometric relationships and avoid floating-point degeneracies.

But for a constant like φ, you’re right—(1 + sqrt(5)) / 2 is trivial and stable. No clever construction needed.