Shape

127 What Schemas Show
early stuff, although sometimes there are hints of something new—makes this choice.
Nonetheless, understanding how shapes work may be better served with the second
option. What is it about schemas and how they work that makes me say this? Let’s
take a look at schemas and see what they can do.
Here’s a rule
defined in a schema x fi y that produces the shape
and others of the same kind
formed when polygons are nested or inscribed one in another. An assignment g provides
values for the variables x and y that satisfy this predicate:
x is a polygon with n sides, and y ¼ x þ z, where z is a polygon with n sides inscribed in x.
The predicate can be elaborated in much greater detail. For example, I could say something
more about polygons being convex, etc., and then go on to say that the vertices
of z are points on the sides of x, etc. Thus, it’s easy to see that the schema includes as a
special case rules for shapes in the array