/sci/ - Science & Math

Is there any classification of which numbers can be defined geometrically? I *don't* mean constructible numbers, but numbers that can be defined as dimensionless ratios in some natural geometric way, whether constructible or not (more often not). The main examples I have in mind are the metallic means and pi (both defined as length ratios).

Obviously you can get all (positive) integers by subdividing a segment into n equal parts. And if you repeat the subdivision m times you get m/n. And you can get some transcendental numbers too like pi. But it's not clear which numbers (or algebraic numbers, for simplicity) are representable in a geometric way in general. If you admit a length scale then probably all constructible numbers will also be included.