Applicability of Mathematics

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? 

It has to be 900 words or more.