How do you explain the applicability of these abstract constructions to the physical world?

Points, lines and circles as used in Euclidean geometry are abstract objects that have no equivalent in the physical world. In your view, do we “bring them into existence” by considering axioms and postulates about them, or do they exist independently of us? 


At any rate, geometry turns out to be useful in understanding the physical world (think of what we have seen regarding measurements of the Earth, the Moon, The Sun and their distances). How do you explain the applicability of these abstract constructions to the physical world? Given what you have seen of the Meno and the Phaedo, what do you think Plato’s position is in this respect? What is yours and why?