mathematics. The two relatively simple problems, the 
     determination of the diagonal of a square and that of the 
     circumference of a circle, revealed the existence of new 
     mathematical beings for which no place could be found 
     within the rational domain. . .
          A further analysis showed that the procedures of 
     algebra were generally just as inadequate. So it became 
     apparent that an extension of the number field was 
     unavoidable. . . . And since the old concept failed on the 
     terrain of geometry, we must seek in geometry a model 
     for the new. The continuous indefinite straight line seems 
     ideally adapted for such a model.

     Number is the dimension of tactility, as Ivins explained in 
Art and Geometry  (p. 7): “In any continuous pattern the hand 
needs simple and static forms and it likes repeated ones. It