What is Geometry?

3-manifolds algebraic angles axioms Beltrami boundary Cartan Cartan geometry caso ciò circle concept concetto connected sum construction continuo coordinate covering space curvature curve defined definition definizione deformation principle differential geometry dimension elementi embedded equations Euclid Euclidean geometry Euclidean space example exists finite formula fundamental group G.Sica Gauss geodesic geometrical object Geometrization Conjecture homeomorphic homology homotopy hyperbolic infinitesimal insieme intuition isomorfo Kant Kant’s Kantian Klein Klein geometry locally homogeneous logical matematica Math mathematical metric space naturale non-Euclidean geometries numeri ogni one-dimensional open set ordinato orientation particle philosophy physical geometry Poincaré Poincaré conjecture postulate priori projective plane proper Euclidean geometry properties punti punto può quale quotient space retta Riemann Riemannian geometry Riemannian manifold secondo segmenti sembra Sica solid bodies soltanto space-time geometry spazio sphere straight line T-geometry tempo theorem theory topological space torus triangle vectors world function xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx