Geometry

There was a time when “geometry” meant such relationships as could be demonstrated on three-dimensional objects or in two-dimensional diagrams...In those days a form which was suggested by geometry but which could not be demonstrated in ordinary space was suspect or inacceptable. Ordinary space dominated geometry. Today the position is quite different...Today it is geometry that contains the terrestrial forms, and not vice versa, for the terrestrial forms are merely special cases in an all- embracing geometry. The gain achieved by geometry’s development hardly needs to be pointed out. Geometry now acts as a framework on which all terrestrial forms can find their natural place, with the relations between the various forms readily appreciable. With this increased understanding goes a correspondingly increased power of control. 7